Polarization-Reversal-Induced Absorption of an Axisymmetric

K. Takahashi, T. Kaneko, and R. Hatakeyama
Department of Electronic Engineering, Tohoku University, Sendai 980-8579, Japan
Abstract. Propagations and absorptions of electron cyclotron waves with azimuthally axisymmetric mode are
investigated when left-hand polarized waves (LHPW) are selectively launched by a helical antenna in inhomogeneously
magnetized plasmas. It is found that the LHPW with second order radial mode is absorbed near an electron cyclotron
resonance (ECR) point due to a polarization reversal from the LHPW to a right-hand polarized wave, which can be
explained by a dispersion relation including the effects of the radial boundary determining a wavenumber perpendicular
to the magnetic-field lines. On the other hand, the LHPW with fundamental radial mode passes through the ECR point
without the absorption because the polarization reversal does not occur in this mode.
Keywords: Electron Cyclotron Resonance, Polarization Reversal, Left-Hand Polarized Wave, Boundary Condition.
PACS: 52.35.Hr, 52.40.Fd, 52.25.Mq
INTRODUCTION
Electromagnetic waves with electron cyclotron resonance (ECR) frequency in magnetized plasmas have been
one of significant research subjects for electron heating in plasmas, plasma production, and so on. The propagation
characteristics and mechanisms have been investigated for a long time. In recent years, we have discovered that the
greater part of excited electromagnetic waves is absorbed near an ECR point even when left-hand polarized waves
(LHPWs) with an axisymmetric mode are excited by a helical antenna in an inhomogeneously magnetized plasma
[1,2]. It has also been reported that the absorption originates in a polarization reversal from the LHPW to a righthand
polarized wave [3,4], which can quantitatively be explained by the dispersion theory including effects of a
radial boundary [4,5]. On the other hand, it is observed that a part of the LHPWs is not absorbed and passes through
the ECR point in the above-mentioned experiments, whose mechanisms were not described so far.
In this paper, we report the difference in the propagation mechanisms between these axisymmetric LHPWs, one
of which is absorbed near the ECR point and the other of which passes the ECR point without the absorption.
EXPERIMENTAL SETUP
Experiments are performed in the QT-Upgrade Machine of Tohoku University shown at the top of Fig. 1, which
has a cylindrical vacuum chamber of about 450 cm in length and 20.8 cm in inner diameter. An inhomogeneous
magnetic field presented at the bottom of Fig. 1 is applied by two parties of solenoidal coils along the z axis. Since
the ECR magnetic-field strength for 6 GHz microwave is 2.14 kG, the ECR point is located at z = 78 cm. The
plasma is produced by a DC discharge between an oxide cathode and a tungsten mesh anode in low pressure argon
gas of 90 mPa. As the plasma column is terminated by a glass endplate, the electron velocity distribution gets
maxwellian. The electron density and the temperature are measured by small Langmuir probes, and the operating
electron density and temperature at the ECR point are fixed at 9 x 1010 cm-3 (ωpe / ωce < 1) and 2.5 eV, respectively.
The formation of clear boundary between the plasma and the peripheral vacuum layer is realized by using a limiter,
which is located in front of the anode and has an inner diameter of 6 cm.

EXPERIMENTAL RESULTS
Figure 2(a) shows interferometric wave patterns of Ex (dashed line) and Ey (solid line), where a solid arrow at z =
78 cm represents the ECR point of 6 GHz microwave. The observed wave patterns indicate the damping of the
launched wave near the ECR point in spite of the selective
launch of the LHPW, which has been considered not to be
related to ECR. Moreover, it is to be noted in Fig. 2(a) that
the wave patterns include both a long (LW) and a short
(SW) wavelength component. The LW and SW are
decomposed from the wave patterns in Fig. 2(a) by using
Fourier analysis and presented in Fig. 2(b). Figure 2(b)
shows that the LW damps and the SW grows around z =
60 cm, and that the wave patterns of Ex in the LW and the
SW are shifted to the left and to the right of the wave
patterns of Ey, respectively. From these phase differences
between Ex and Ey, the LW and the SW are identified as
the LHPW and the RHPW, respectively. Therefore, the
observed wave patterns evidence that the LHPW damps
and the RHPW grows around z = 60 cm, i.e., polarization
reversal from the LHPW to the RHPW occurs. As a result
of the polarization reversal, the greater part of the launched
LHPW is found to be absorbed near the ECR point. On the
other hand, it is noticed that a slight part of the LHPW
penetrates the ECR point without absorption. In this paper,
we describe the propagation mechanisms of these wave
components, one of which is absorbed near the ECR point
due to the polarization reversal, and the other of which
passes through the ECR point as shown in Fig. 2 (b).
The radial profile of the axial component of the wave
power Pz at z = 40 cm is presented in Fig. 3(a) as a solid

60 cm) of the wave propagation and of the RHPW (open circle) near the ECR point (55 cm < z < 78 cm), which are
obtained from the decomposed wave patterns in Fig. 2(b). The experimental results of both the LHPW and the
RHPW are in good agreement with the calculated dispersion curve of the slow wave (bold line). The calculated
polarization index S corresponding to the dispersion relation in Fig. 4(a) is presented in Fig. 4(b). The calculated S of
the slow wave (bold line) shows that the wave polarizations are left-handed (S > 1) and right-handed (S < 1) in the
range of ω/ωce < 0.85 and ω/ωce > 0.85, respectively. Thus, the observed polarization reversal to the RHPW is
clarified to occur in obedience to the dispersion relation including the effects of the radial boundary between the
plasma and the peripheral vacuum layer. We mentioned that a part of the LHPW can penetrate the ECR point
without the absorption as seen in Fig. 2. This residual LHPW cannot be explained by the dispersion relation of n = 2
mode in Fig. 4(a). Then, the calculated dispersion relations of n = 1 mode are compared with the experimental
dispersion relation of the residual LHPW, which are plotted in Fig. 4(c) as solid lines and closed squares,
respectively. The experimental dispersion relation is in good agreement with the calculated curve of the fast wave
(bold line). The polarization index of the fast wave, which is shown in Fig. 4(d) as a bold line, always designates the
left-handed polarization (S > 1). Therefore, the LHPW of n = 1 mode is found to pass through the ECR point,
because the polarization reversal to the RHPW never occurs. In our experimental configuration, the value of ω/ωce at
the position of the microwave exciter, i.e., the helical antenna, is about 0.75 as shown at the bottom of Fig. 1. Since
the helical antenna generates the LHPW and the waves with left-handed polarization at ω/ωce ≅ 0.75 are only the fast
wave for n = 1 and the slow wave for n = 2 in the dispersion relations in Fig. 4, the excited n = 1 and n = 2 modes
result in the formation of the fast and slow waves, respectively.
SAMMARY
The propagation and absorption of the left-hand polarized waves (LHPWs) with ECR frequency are investigated
when the axisymmetric LHPW is selectively launched by the helical antenna in the inhomogeneously magnetized
plasma. Our experimental results demonstrate the absorption of the LHPW with second order radial mode (n = 2)
due to the polarization reversal from the LHPW to the right-hand polarized wave (RHPW). On the other hand, the
residual LHPW passing through the ECR point is found to be a fundamental radial mode (n = 1), whose polarization
is kept at the left-handed polarization. The observed phenomena can well be interpreted by the dispersion theory
including the effects of the radial boundary.
ACKNOWLEDGMENTS
The authors are indebted to H. Ishida for his technical assistance. We also express our gratitude to Professor K.
Sawaya for his 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 Scientists.
REFERENCES
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2. K. Takahashi, T. Kaneko, and R. Hatakeyama, Trans. Fusion Sci. Technol. 43 95 − 97 (2003).
3. K. Takahashi, T. Kaneko, and R. Hatakeyama, J. Plasma Fusion Res. 79 447 − 448 (2003).
4. K. Takahashi, T. Kaneko, and R. Hatakeyama, Phys. Rev. Lett. 94 215001-1 − 4 (2005).
5. K. Takahashi, T. Kaneko, and R. Hatakeyama, Phys. Plasmas 12 102107-1 − 7 (2005).
6. J. D. Kraus, Antennas (McGraw-Hill, New York, 1950).

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