Effects of Ion Flow Energy on Self-Consistent Double-Layer
K. Takahashi, T. Kaneko, and R. Hatakeyama
Department of Electronic Engineering, Tohoku University, Sendai 980-8579, Japan
Abstract. Formations of plasma potential structure and electron cyclotron wave propagations are investigated in
inhomogeneously magnetized plasmas, in which an ion flow energy can precisely be controlled by a plasma synthesis
method, when microwaves with the azimuthal mode numbers of m = +1 and –1 are selectively launched from a high
magnetic-field side by using a horn antenna with a dielectric polarizer. It is observed that a double layer, whose potential
height is self-consistently determined by the ion flow energy for maintaining the charge neutrality, is formed near the
electron cyclotron resonance point. Moreover, the electron cyclotron waves with m = +1 and −1 modes contribute to the
electron heating and the double-layer formations in the center and the edge regions of the plasma column, respectively. It
is found that the radial profiles of wave polarizations are relevant to the different structures between m = +1 and –1
Keywords: Double Layer, Ion Flow, Electron Cyclotron Resonance, Inhomogeneously Magnetized Plasma
PACS: 52.30.-q, 52.35.Hr, 52.40.Fd, 52.55.Jd
Formations of field-aligned potential structures are important issues relating to laboratory , space/astronomy
, and fusion-oriented plasmas . Nonlinear potential structures were observed near an electron cyclotron
resonance (ECR) point when an electron cyclotron wave was launched into Q-machine plasmas in conversing or
well-shaped magnetic-field configurations . However, it has not been experimentally proved what decides the
potential height of the structure, although an ion flow energy of about 2 eV in the Q-machine plasma has been
expected to affect it. In order to investigate the effects of the ion flow energy on the potential structure, we have
developed a novel plasma source for controlling the ion flow energy . On the other hand, we guess that the wave
propagation near the ECR point also plays an important role in the structure formation. In previous paper, we
reported that a polarization reversal induces an unexpected absorption of a left-hand polarized wave near the ECR
point [6,7]. Thus, it is conjectured that the wave polarization is also important issue in the potential structure
formation near the ECR point.
Based on these backgrounds, the purpose of the present work is to clarify the detailed dynamics of the potentialstructure
formation in injection of the electron cyclotron waves, and to systematize relations between the potentialstructure
formation and the wave propagation.
Experiments are performed in QT-Upgrade machine of Tohoku University as shown in Fig. 1, which has a
cylindrical vacuum chamber of about 450 cm in length and 20.8 cm in diameter. A conversing magnetic-field
configuration as presented at the bottom of Fig. 1 can be formed by two series of solenoid coils. An argon plasma, in
which the ion flow energy can precisely be controlled by a plasma synthesis method , is produced in a low
magnetic-field side. We have already reported that the ion flow energy is proportional to an anode potential Va. The
plasma is terminated by a glass endplate and its radius is limited to about 3 cm by a limiter located at the same position as the anode. Microwaves (frequency: 6 GHz, power: Pμ = 50 W) with m = +1 and –1 modes are selectively
launched from the high magnetic-field side by using a horn antenna with a dielectric polarizer, which is located at
the back of the endplate. Here, m is an azimuthal mode number. The ECR point of 6 GHz microwave is z = 26 cm,
since the ECR magnetic-field strength is 2.14 kG. The wave propagates from the high magnetic-field side toward the
ECR point satisfying the condition of ω /ωce < 1. Spatial profiles of a space potential, an electron density, and an
electron temperature at 30 μsec after the microwave injection are measured by movable Langmuir probes through a
boxcar averager. Here, since an ionization of Ar gas by the microwave does not start at this time, we can observe the
modified structure of the plasma flow from the source located on the right side of Fig. 1. An ion energy distribution
function (IEDF) is obtained by using an electrostatic ion energy analyzer.
Figure 2 shows typical axial profiles of the space potential
, the electron density ne, and the electron temperature Te at the
radial center of the plasma column for Pμ = 0 (open circle) and
50 W (closed circle), which are measured at 30 μsec after the m
= +1 mode microwave injection, where arrows at z = 26 cm
indicate the ECR point of 6 GHz microwave. For Pμ = 0 W, φ
and Te are almost constant, and ne increases in the high
magnetic-field area due to the conversing magnetic-field
configuration. On the other hand, it is shown that the electron
temperature increases around the ECR point by ECR for Pμ =
50 W. A localized potential rise, i.e., an electric double layer, is
clearly observed near the ECR point as shown at the top of Fig.
2, which plays a role in the reflection of the ions flowing
toward the high magnetic-field side. The electron density ne
drops in the high magnetic-field side due to the electron
reflection by magnetic mirror effects, which is dramatically
enhanced by the ECR acceleration perpendicular to the
magnetic-field lines and yields the increase in ne in the low
magnetic-field side as presented at the center of Fig. 2. We can
roughly estimate the degree of the electron reflection from the
difference in ne between Pμ = 0 W and Pμ = 50 W, e.g., the
reflection ratio for Fig. 2 is about 0.47.
In order to investigate the effects of the ion flow energy on the electric double layer, the axial profile of the space
s for m = +1 mode microwave injection
with Va as a parameter is presented in Fig. 3, where
Va is the parameter controlling the ion flow energy.
The IEDF for each Va is described later. The potential
profiles for Pμ = 0 W are also denoted in Fig. 3 as
open circles and are independent of Va. It is found
that the potential height of the electric double layer
increases with an increase in Va, i.e., an increase in
the ion flow energy, under the spatially constant
potential in the low magnetic-field side. The position
of the double layers for each Va is found to be
unchanged. Therefore, it is experimentally
demonstrated that the ion flow energy affects only
the potential height of the double layer.
Now, our attention is focused on the problem why
the potential height of the double layer is determined
by the ion flow energy. Figure 4(a) gives the IEDF
measured by the electrostatic ion energy analyzer for
Pμ = 0 W with Va as a parameter, where Vc is the
collector voltage applied with respect to the ground and a solid arrow indicates the space potential. The ion flow
energy linearly increases with an increase in Va. In our experiments, although the electron reflection near the ECR
point is driven by the electron acceleration perpendicular to the magnetic-field lines, the ions are not affected by the
microwave. Thus, ions are expected to be reflected by some effects for maintaining the charge neutrality. We
estimate the potential in the high magnetic-field area, which reflects a part of the ions and keeps the charge
neutrality there, using the electron-reflection ratio and the IEDF [gray part of Fig. 4(a)]. The estimated potentials for
each Va are plotted in Fig. 4(b) as open squares, together with the experimental potentials observed by the Langmuir
probe for Pμ = 0 W (open circle) and 50 W (closed square). The potential for Pμ = 0 W is invariable for Va, while the
potential for Pμ = 50 W rises with an increase in Va and is in good agreement with the estimated value from the IEDF.
Thus, it is considered that the potential height of the double layer is self-consistently determined for reflecting the
ions flowing from the low magnetic-field side and satisfying the charge neutrality in the high magnetic-field side.
Figure 5 presents r-z profiles of the space potential φ
s for (a)Pμ = 0 W, (b)Pμ = 50 W and m = +1 mode, and (c)Pμ
= 50 W and m = −1 mode, where the m = +1 and –1 modes microwaves are selectively excited by only changing the
magnetic-field direction, namely, the direction of the electron cyclotron motion. Figure 5(a) denotes that the
potential profile before the
microwave injection is almost
uniform. It is found in Fig.
5(b) that the double layer is
formed in the center region of
the plasma column when the m
= +1 mode microwave is
excited. On the other hand, the
microwave with m = −1 mode
is observed to contribute to the
double-layer formation in the
edge region of the plasma
column as given in Fig. 5(c). It
is conjectured that the different
structures between the m = +1
and −1 modes are related to
the wave propagations near the
ECR point. Radial profiles of
wave polarizations are
examined by measuring the
phase difference between two.
components of the microwave electric field perpendicular to the magnetic-field lines. As a result, it is clarified that
the wave polarizations become right-handed in the center region of the plasma column for m = +1 mode excitation,
and in the edge region of the plasma column for m = −1 mode excitation. Therefore, the wave polarization is also an
important parameter for the double layer formation as well as the ion flow energy.
Formations of the electric double layer and the electron cyclotron wave propagations are investigated in
inhomogeneously magnetized plasmas, in which the ion flow energy is precisely controlled by the plasma synthesis
method, when the microwaves with m = +1 and –1 modes are selectively launched from the high magnetic-field side
by using a horn antenna with a dielectric polarizer. It is experimentally demonstrated that the double layer is formed
near the electron cyclotron resonance point and its potential height in the high magnetic-field area is selfconsistently
adjusted for keeping the charge neutrality by reflecting the ion flow from the low magnetic-field side.
Moreover, the electron cyclotron waves with m = +1 and −1 modes contribute to the double-layer formations in the
center and the edge regions of the plasma column, respectively. It is found that the radial profiles of wave
polarizations are relevant to the different structures between the m = +1 and –1 modes.
The authors are indebted to H. Ishida for his technical assistance. We also express our gratitude to Professor K.
Sawaya and Associate Professor Q. Chen for their useful comments in the design of the microwave antenna. The
work was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young
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