J. Plasma Fusion Res. SERIES, Vol. 8 (2009)

Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma
Kunihiro KAMATAKI 1), Sanae –I. ITOH2), Yoshihiko NAGASHIMA3), Shigeru INAGAKI2),
Shunjiro SHINOHARA1), Masatoshi YAGI2), Takuma YAMADA3), Yoshinobu KAWAI1),
Akihide FUJISAWA4), and Kimitaka ITOH4)
1)

Interdisciplinary Graduate School of Engineering Science, Kyushu University,
Kasuga, Fukuoka 816-8580, Japan
2)
Research Institute for Applied Mechanics, Kyushu University,Kasuga, Fukuoka 816-8580, Japan
3)
Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8561, Japan4)

National Institute for Fusion Science, Toki, Gifu 509-5292, Japan(Received: 17 September 2008 / Accepted: 10 December 2008)

Competitive and coexistence phenomena of a drift mode and a flute mode have been observed experimentally in linear
cylindrical electron cyclotron resonance (ECR) plasmas. The drift mode is dominant in the low neutral gas pressure. The
flute mode is excited and become dominant with the increase in the neutral gas pressure. The coexistence of the drift andflute modes is observed in the intermediate neutral gas pressure regime. The radial profiles of density, its gradient scale
length and floating potential are different in the each regime. In the coexistence regime, the drift mode and the flute mode
appear alternately in a single discharge. This competition is related to the rise and the crash of the density and its gradient,and the crash occurs inside and outside of this plasma at the same time, and density increases simultaneously outside when
the density decrease abruptly in the central plasma region.
Keywords: competition, coexistence, crash, drift mode, flute mode, and linear cylindrical ECR plasma

1. Introduction

comprehensively the multi-scale turbulence. In this article
we report the dynamics of the drift mode and the flutemode, focusing on the competitive and the coexistence
phenomena.

The nonlinear self-regulation mechanism of drift wave
turbulence has been subject to attention in order to show
the structural formation of plasma turbulence [1-2]. The
plasma transport across the magnetic field is strongly
affected by low frequency (much lower than the ion
cyclotron frequency) fluctuations, e.g. the drift wave
instability. In addition, the multi-scale interaction between
dissipative instabilities and reactive instabilities hasattracted attentions in the magnetic confinement devices[3]. The collisional drift mode is dissipative and the flute
mode is reactive. The coupling between dissipative andreactive instabilities has attracted attention in studies ofthe magnetic confinement devices [4]. The drift wave iswell known as a universal low frequency instability driven
by the free energy provided by a pressure gradienttransverse to the magnetic field [5]. In mirror machines,
the averaged magnetic curvature is responsible for aneffective gravity, which allows the flute instability todevelop. Several studies [6-8] on the drift and the flute(interchange) modes have been reported. However, thecoupling of the drift and the flute modes has not beenclarified yet.
We have already observed the coexistence of thecollisional drift mode and the flute mode in linear
cylindrical ECR plasma [9]. Studies of the coexistence
phenomena are expected to clarify the dynamics between
the drift mode and flute mode, and to understand2. Experimental setup

The experiments have been performed on a linear
cylindrical ECR plasma device [9]. The cylindricalvacuum chamber consists of stainless steel with the innerdiameter is 40 cm and the axial length is 120 cm. Argon
gas is fed into the vacuum chamber using a mass flow
controller. The chamber is evacuated to a base pressureless than 10-7 Torr using a rotary pump and a 1000 1/s
turbo molecular pump [working pressure is p(Ar) = (0.2 2.0) mTorr]. Eight magnetic coils (axial width is 6.4 cm inz-direction and outer diameter is 71.5 cm) form a mirror
magnetic field configuration. Microwave with thefrequency of 2.45 GHz and the output power P� = 300W is
launched into a chamber through the coaxial waveguideconverter (inner diameter is 10 cm and axial length is 21cm). The reflected power is reduced by a three-stub tuner
and a movable metal plate in the coaxial waveguide. Theaxial boundary condition is determined from both ends ofthe vacuum chamber (terminated by metal flanges).
The plasma fluctuations (ion saturation current Iis andfloating potential Vf) are measured with the Langmuirprobes (a tungsten tip with 1mm in diameter and 2 mm inlength). Time traces of Iis and Vf signals are recorded by adata logger with a sampling rate of 1 MHz (16 bit). The

author’s e-mail: kamataki@riam.kyushu-u.ac.jp82©2009 by The Japan Society of Plasma
Science and Nuclear Fusion Research

K. Kamataki et al., Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma

Langumuir probes are set at eight azimuthal positions andfive axial positions. The azimuthal mode number m andthe parallel wave number n can be determined from thesemeasurements. Here, n = 1 indicates that the half
wavelength is the same as the device length. In order tomeasure the spatio-temporal structures of modes, we havedeveloped a multi-channel Langmuir probe array. The
array has stainless-steel rings (outer diameter of 3 mm,
inner diameter of 2.5 mm and length of 1.2 mm)
positioned in the radial direction (with the radialseparation of 10 mm), which are based on an alumina tube
(outer diameter of 2 mm, inner diameter of 1.5 mm andlength of 200 mm). The same type of probe array in a
toroidal plasma device is in Ref. [10]. The time-averaged
and the fluctuated radial density gradient are determinedfrom this probe array. Typical plasma parameters are as
follows: electron density ne ~ 1011 cm-3 and electron
temperature Te ~ 2 eV under the typical discharge
condition (the measurement point of z = 30 cm and r = 3
cm with magnetic field strength B = 685 Gauss). These are
obtained from current-voltage (I-V) characteristics of theLangumuir probe.

Fig. 1 Dependence of square of drift and flute modes
fluctuations amplitude on the neutral gas pressure
including the line to divide operation regions into states
1-3. (quoted from Ref. [11])The Iis at the center increases with the increase in theneutral gas pressure (from the state 1 to the state 3). The
radial profiles of Шn/n in each state are shown in Figs. 2(d), 2 (e), and 2 (f). In the state 1, the Шn/n is peaked at r
= 4 cm, where the drift mode has maximum amplitude(not shown). The Шn/n is peaked at r = 3 cm, where thedrift mode and the flute mode have the largest amplitudes(not shown) in the state 2. Moreover, the peak value ofШn/n increases as the neutral gas pressure increase in thestate 1 and 2. The radial position of peak Шn/n is r = 3 – 5cm where the flute mode is excited most strongly (notshown). The radial profiles of Шn/n are corresponding to
the excitations of both modes. The radial profiles of Vf ineach state are shown in Figs. 2 (g), 2 (h), and 2 (i). The
radial profile of Vf is flat at r > 4 cm and decreases
strongly toward the plasma center at p(Ar) = 0.4 mTorr inthe state 1. The radial profile of Vf are almost same whilethat of Iis changes at p(Ar) = 1.0 – 1.4 mTorr in state 2. TheVf at the center increases from ~ -25 V to ~ -5V as theneutral gas pressure increases from state 1 to state 2. Atp(Ar) = 2.0 mTorr (in the state 3), that of Vf remain
relatively flat at all radial positions. The space potential Vs
is calculated from the equation Vs = Vf + �Te (� is theconstant). The ion saturation current Iis is proportional tone Te1/2. The radial profile of Te remains relatively flat atp(Ar) = 1.0 mTorr [9]. It is assumed that that of Te is flat inthese experiments, which leads ШVf ~ШVs and ШIis/Iis~Шn/n, and the influence of electron temperaturefluctuations is negligible. The qualitative features ofdynamics of two modes discussed in this paper are notaffected by these assumptions. The measurement of thefull radial profile of Te is left for the future work.
Moreover, the results in Figs. 2(a) - 2(c) indicate that theamplitudes of both ne and Te change with the increment of
the neutral gas pressure. Therefore, the profile of Vs maychange drastically with the increment of neutral gas

3. Experimental results

In this linear plasma, both of the drift mode and theflute mode are excited in a particular neutral pressure
region [9]. The two modes [the drift mode (m/n = 4/1) andthe flute mode (m/n = 2/0)] were identified from themeasurement of the axial and the azimuthal wave numbers,
phase differences between density and potential
fluctuations, and the comparison between normalized
amplitudes of density and potential fluctuations. Figure 1(quoted from Ref. [11]) shows the amplitude of bothmodes as a function of the neutral gas pressure, which isused as an index of the collisional damping of each mode.
In the lower filling gas pressure regime p(Ar) = (0.2 – 0.6)
mTorr (state 1), the drift mode is excited but the flute
mode is stabilized. In the higher pressure regime p(Ar) =(1.6 – 2.0) mTorr (state 3), the flute mode is excited andonly the drift mode is stabilized. In an intermediate regimep(Ar) = (0.6 – 1.6) mTorr (state 2), the drift mode isgradually suppressed and the flute mode becomes unstableand thus the two modes are coexistent. A linear stability
analysis using the Hasegawa-Wakatani model [12] gives
similar growth rates of two modes in this coexistence
condition [9]. The state 2 is considered to be a
middle-state for a smooth transition from the state 1 to thestate 3. Figure 2 shows the radial profiles of Iis, inverse
scale length of density gradient Шn/n and Vf in the each ofstates [the state 1 (p(Ar) = (0.2 and 0.4) mTorr), the state 2(p(Ar) = (0.8, 1.0, 1.2 and 1.4) mTorr), and the state 3 (p(Ar)= (1.8 and 2.0) mTorr)]. Figures 2 (a), 2 (b), and 2 (c)show that Iis has peaked radial profiles in each of states.

83

K. Kamataki et al., Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasmapressure, similar to that of Vf. It is found that the radial
profiles of typical plasma parameters in each state havedifferent features, which indicates that the drastic changeof the radial profiles is related to the change of thedominant mode.
Figures 1 and 2 showed the features of the time
averaged phenomena. In order to clarify the dynamics
between the drift mode and the flute mode, we focus on
the temporal behavior of both modes. In fact, the state 2 isa non stationary state. Figures 3 (a), 3 (b), and 3 (c) show
the typical time evolutions of Iis and the equilibrium
quantity Iis0 (red lines) (using a low pass filter f < 100 Hz)
in each of states. The fluctuation levels of Iis and Iis0 in thestate 1 and the state 3 are almost constant with time. On
the other hand, Iis and Iis0 repeated the rise and the drop ata certain period in the state 2. Time evolutions of density
gradient Шne0 are similar to Iis0 in each of states (shown inFigs. 3 (d), 3 (c), and 3 (e)). This repetition of Iis0 and Ш
ne0 indicates that a relaxation of global parameter takes
place. The envelope analysis of each mode is useful todiscuss the dynamics of waves. The envelopes of thefluctuation intensity in each of states, which are the drift
mode and/or the flute mode measured using the band-passfilter, are shown in Figs. 3 (g), 3 (h) and 3 (i). Env. D (F)indicates the amplitude of the drift (flute) mode calculated
from the envelope analysis. In the states 1 and 3, the drift
mode and the flute mode stay with high amplitudes withtime. In the state 2, it is found that there are two phases for
one period in the coexistent modes: The state 2 is divided
into the phase A and the phase B, as indicated by thevertical dashed lines. The amplitude of the drift mode islarger than that of flute mode in the phase A. On the other
hand, the amplitude of flute mode is larger than that ofdrift mode in the phase B. It is found that the change ofthe dominant mode is observed between the phase A andphase B. In the phase A, the drift mode stays with higher
amplitude with the smaller amplitude of the flute modeand Iis and Шne0 grow slowly. When the Iis and Шne0
exceed a critical value, the amplitude of the flute mode
begins to increase suddenly (phase B). The amplitude ofthe drift mode decreases as that of the flute modeincreases. Finally, when the Iis and Шne0 reach a limit at
the end of the phase B, the ‘crash’ (the rapid drop) of Iisand Шne0 take place and it leads to the decrease (increase)of the flute (drift) mode and the phase A starts again. The
coexistent state of the drift and the flute modes is realized
by a competitive oscillation between them. The transitionof each mode may be coupled.
The phenomena of the ‘crash’ appear in only the state
2. Finally, the characteristics of the crash are illustrated.
The rise and the crash of Iis and Шne with a certain period
begin abruptly as the flute mode begins to be excitedamong the state 1 and the state 2, and finished as the drift
mode is suppressed among the state 2 and the state 3. This

Fig. 2 Radial profiles of (a)-(c) the density, (d)-(f) its gradient inverse scale length, and (g)-(i) the floating potential in
the each of states. [The state 1 (p(Ar) = (0.2 and 0.4) mTorr), the state 2 (p(Ar) = (0.8, 1.0, 1.2 and 1.4) mTorr), and thestate 3 (p(Ar) = (1.8 and 2.0) mTorr)]84

K. Kamataki et al., Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma

Fig. 3 Time evolutions of Iis in (a) the state 1, (b) the state 2, and (c) the state 3, an equilibrium quantity Шne0 in (d)the state 1, (e) the state 2, and (f) the state 3, envelopes (Env.) of (g) the drift (D) mode in the state 1, (h) the drift andflute (F) modes in the state 2 and (i) the flute mode in the state 3 at r = 4 cm (state 1), 3 cm (state 2), and 6 cm (state3), where the amplitudes of the drift mode and/or flute mode at each of states peak.
result suggests the repetitions of Iis and Шne are related tothe competition of both modes. Figure 4 (a) and 4(b) show
time evolutions of Iis0 at r = 5cm (inside) and r =12 cm(outside) at p(Ar) = 0.8 mTorr (the state 2), respectively.
Here, �T and �A indicate the interval time from thecrash to the next one and the change of the amplitude ofIis0 before and after the crash, respectively. The
comparison of the radial profiles of Iis before and after thecrash is shown in Fig. 4 (c). The simultaneous
measurement of the crash at different radial positions
shows the sudden break of density occurs at the same time
inside and outside of this plasma, and when the density
decrease abruptly in the central region (r < 9 cm), it
increases simultaneously outside (r >10 cm). The �T at
the central plasma (r = 0 cm) is the largest in the all radialpositions. Figures 4 (d) and 4 (e) show the dependence onthe �T and the relative amplitude �A /<Iis> on theneutral gas pressure at r = 0 cm in the state 2, respectively.
Here, <> is the temporal average. The �T increases

slowly from as the neutral gas pressure increase (p(Ar) =(0.8 – 1.4) mTorr). After that gas pressure region, the�T increases strongly and can’t be measured aroundp(Ar) ~ 1.6 mTorr. The discharge period is 1s. The
�A /<Iis> increases from ~ 20 % to ~ 30 % as the pressure
increases. At p(Ar) > 1.1mTorr, the flute mode is larger thanthe drift mode (as shown in Fig. 1) These results indicate
the relative strength of the drift and flute modes may berelated to the characteristics of the crash in the coexistencestate, which is left for the future work.

4. Conclusion

In conclusion, we have investigated the dynamics ofthe drift mode and the flute mode through the state 1 to thestate 3 observed in the linear cylindrical ECR plasma. The
radial profiles in each profile are different respectively,
which indicates that the changes of the radial profiles arerelated to the changes of the dominant modes. The state 2
is considered to be a middle-state for a smooth transition

Fig.4 Time evolutions of Iis0 at (a) r = 5cm (inside) and (b) r =12 cm (outside) at p(Ar) = 0.8 mTorr. (state 2). (c)Comparison of typical radial profiles of Iis before and after crash in Fig.4 (a). Crash starts at (A) t = 0.601s and ends at(B) t = 0.614.Vertical dash lines show start of crash. Here, ǍT and ǍA are illustrated in text. Dependence on (d) ǍT and (e) relative amplitudeǍA on the neutral gas pressure at r = 0 cm in state 2.

85

K. Kamataki et al., Dynamics of Drift and Flute Modes in Linear Cylindrical ECR Plasma(NIFS) (NIFS07KOAP017).

from the state 1 to the state 3. The coexistent state of thedrift and the flute modes is realized by a competitiveoscillation between them. The rise and the drop (the crash)of Iis and Ш ne with a certain period appear in only
coexistence state. It is found that the sudden break ofdensity occurs at the same time inside and outside of thisplasma, and density increases simultaneously outsidewhen the density decrease abruptly in the central plasma
region.

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Acknowledgements

We would like to acknowledge useful discussions
with Dr. A. Fukuyama, Dr. N. Kasuya, and Dr. S.
Nishimura. This work is partly supported by aGrant-in-Aid for Specially-Promoted Research of MEXT
of Japan (16002005), by Research Fellowships of theJapan Society for the Promotion of Science for Young
Scientists, and by a collaborative program between theResearch Institute for Applied Mechanics of Kyushu
University and The National Institute for Fusion Science86