J. Plasma Fusion Res. SERIES, Vol.2 (1999) 310_313

Control of Type-l Intermittency Gaused bylon Acoustic Instability
TANIGUCHI Kazunari and KAWAI yoshinobu
Inte rdisciplinary Graduate School of Engineering Sc ience s,

Kyushu University, Kasuga 816-8580, Japan(Received: 9 December l99g / Accepted: 2g June 1999)

Abstract
We have experimentally attempted the control of intermittent chaos caused by the cunent-driven ion
acoustic instability. When a positive pulse is applied to one of two mesh grids which are installed toexcite the current-driven ion acoustic instability in a Double plasma, the instability is suddenlysuppressed. On the other hand, when a negative pulse is applied, the chaotic state is well controlled withmaintaining the instability.

Keywords:
controlling chaos, current-driven ion acoustic instability, drift velocity, OGy method, time-delayed
feedback technique

1. Introduction

paper, we report the first experimental investigation on

Recently, as a concept of chaos is universallyan attempt of the control of chaos caused by the current-understood, there has been an interest in the field ofapplied chaos, particularly, the controlling chaos hascome to take notice in various dynamical systems. With
regard to controlling chaos mainly two methods werefamous, the first proposed by Ott, Grebogi, and yorke

driven IAI without the "external" feedback technique.

2. Experimental Apparatus
The experiments were performed using a Double

Plasma (D.P.) device. The chamber and themeasurement system are the same setting as our(OGY) [], and the second by Pyragas [2]. As acommon characteristic of both methods, the point thatthe feedback technique is used for controlling chaos iscited. In plasma physics, chaos have been no longer rare
phenomena, and frequently observed in instabilities

chamber with pressure of 4.0 x l0-4Torr. Typical plasma
parameters were as follows: the electron density r" -concerning the plasma sheath, the discharge, and so on.

l.5eV and Tt - T. / (10-15), respectively. In order toOn the other hand, the experiments on controlling chaos
have been mainly performed for chaotic phenomena of

excite current-driven IAI, we installed two mesh grids
G1 and G2 at interval L of about 2-5cm, and applied adc potential V. to Gl. Furthermore, the experiments on

previous work [4]. Argon gases were introduced into thel08cm-3, the electron and the ion temperature 7e = 0.5-

ionization waves, so far [3], where the time-delayed
feedback technique was used. Therefore, there havebeen no studies on the control of chaos caused byinstabilities in a wave-plasma system so far. Recently,

positive or a negative pulse to Gr, where the pulse width
and the amplitude lVol were fixed at 2.0ms and 2.0V,

we observed the type-l intermittent chaos caused by therespectively. The electron drift velocit! D6 was

the control of chaos were performed by applying acuffent-driven ion acoustic insrability (IAI) [4]. In this@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author's e-mail: gucci@ toyota-ti.ac.jp
310

Taniguchi K. et al., Control of Type- I Intermittency Caused by Ion Acoustic Instability

IAI signals, and Figs. l(bXc) are for applying the pulse
with different polarities. In the case of applying apositive pulse, the IAI signals including turbulent bursts

measured using a directional rotatable probe, which was
located in the center of the grids. Time series signals forchaotic analysis were obtained from fluctuating

suddenly change to the small amplitude signals as soon
as the pulse is applied, as shown in the upper trace in
Fig. l(b). These small amplitude signals are similar to
one before the IAI is excited. On the other hand, Fig.
l(c) shows the case of applying a negative pulse. The

components of the currents 1 on G1, and were sampledwith a digital oscilloscope.

3. Experimental Results and Discussion
When dc potential V. applied to G1 exceeds atime series signals change from the signals including

critical value, the current-driven ion acoustic instability(IAI) is excited between the grids G1 and G2. The
instability was excited for 22.5 < y. < 35V. In thepresent experiments, V, and I which are the control
parameter of the IAI were fixed at 25Y and - 3cm,respectively. Figures 1 show the typical variance of theturbulent bursts to the periodic one which has the sameamplitude as the bursts, as shown in the upper trace inFig. l(c). Then, in order to investigate the variance offrequency components by applying a pulse, we carefullycompared with the power spectra for each property ofpulse. In the case of applying a positive pulse, as shown

time series (upper trace in each figure) and the power
spectrum (lower trace), where Fig. l(a) is only for thein the lower trace in Fig. l(b), there are no discrete andbroad peaks which are characteristic of the IAI [5].

Thus, these results suggest that the IAI is well(a)suppressed by applying a positive pulse. On the otherhand, in the case of applying a negative pulse, as shown

Ic2 to'in the lower trace in Fig. l(c), the largest frequency
peak (- 80kHz) agrees with the fundamental frequencyof the IAI, and the frequency spectrum become more

3a 100coherent at the same time when the pulse is applied.

Furthermore, higher harmonics remarkably appear.
Thus, it is found that the frequency of the periodic

5froq,r-"y(l'fiI"9signals is nearly - 80kHz. Note that the power spectrum

for a negative pulse still keep the characteristic of the(b)IAI.
In order to quantitatively evaluate the influence ofapplying a pulse on the system of the current-driven IAI,
we measured the electron drift velocity u6, which is asignificant parameter to excite the IAI. The solid and

a 106
a39'"

open circles indicated in Fig. 2 show the typicalvariance of t.ra / c" as a function of V. before and after
applying a positive pulse with lVol = 5V, respectively,
where c, is the ion acoustic velocity. With increasing V.
before applying a pulse, u6 / c, suddenly increases forV^=25Y, and then D4/ c"- 20 -30 for V* - 25 -35V.
The value of measured drift velocities agree with thenumerical results obtained from the kinetic theory [6].
Where the excited region of the IAI is u6 / c. 2 l8 forT.l Ti= 13. The solid and open boxes in Fig. 2 show thedrift velocity in the case of applying the pulse withdifferent polarities. In the case of applying a positivepulse (solid box), the drift velocity decrease to od / cs -eL-(c)3tglnilhffiffiffi

B ro'3tooSo00.5

Frcqt&nct(MIz)6, and as a result the current-driven IAI can not beexcited. It is also found that the instability is wellFig. 1 Time series (top trace) and power spectra (downtrace) for l%l = 2.0V. {a) before applying a pulse,(b) applying a positive pulse and (c) applying anegative pulse, where V^ = 25Y, and L - 3cm.

suppressed by applying a positive pulse. On the otherhand, note that in the case of applying a negative pulse3ll

Taniguchi K. et al., control of rype-l Intermittency caused by Ion Acoustic Instability

40

I(t+2r)Fe,**'$fIor,rllo_l| . P*iti*

I o H"o",lt II(t+r)

olo)

ol*
lr---->€toQ
v''aaooo

i20'/
40

ApplicdVoltage(V)Fig. 2 The electron drift velocity ua / c. as a function ofV-. Where solid circle and the other symbols

show before and after applying a pulse,
respectively, and L - 3cm. The dotted lines denotethe lower and upper limit for the excitation of theFig. 3 The reconstructed trajectories on phase space. (a)current-driven lAl

before applying a pulse. (b) applying a positivepulse and (c) applying a negative pulse, where V=25V,L - 3cm, the sampling time At= 1.0 x 10-6s,
and the time delay z= 1oAf.

(open box), the drift velocity D6 / c" - 20, suggestingthat the current-driven IAI is theoretically still excited,though turbulent signals of the IAI change to theperiodic one by applying a negative pulse, as shown inFig. l(b).
In the present experiments, it is confirmed that for
22.5Y < y- < 35V, the instability is excited and rhe

0.0001. These results suggest that the system become aperiodic state, as expected from the periodic time series
signals shown in Fig. l(c). Consequently, the currentdriven IAI is well suppressed at the same time when thedrift velocity decreases by applying a positive pulse, andthen chaotic state caused by the IAI also vanishes. On

system becomes a chaotic state. For example, as shownin Fig. 3(a) before applying a pulse, the reconstructedtrajectory on phase space shows a strange attractor. Inaddition, its the correlation dimension D and the largest
Lyapunov exponent )4 arc D = 2.51 and 11 = 0.16,
respectively, thus, the system is at a chaotic state. In
order to investigate the influence of applying a pulse on
the chaotic system from the chaotic point of view, weperformed chaotic analysis from the time series whichcorrespond to the duration time of the pulse. Figure 3(b)shows the reconstructed trajectory in the case ofapplying a positive pulse. As shown in this figure, thetrajectory is converged and behaved randomly. Then,since D does not saturate and continues to increase in

the other hand, note that the system is changed fromchaotic state periodic state by applying a negative pulse,with maintenance of the IAI in the system.
Here, we discuss about the mechanism of above
phenomena observed by applying a negative pulse. The
control of chaos means that unstable periodic orbits

embedded in the chaotic attractor are stabilized toperiodic orbits. Therefore, it is concluded that thecontrol of chaos is well achieved by applying a negative
pulse. In the current-driven IAI, the existence of a
feedback mechanism for unstable wave between thegrids is well known [5]. Thus, the reason why chaoscaused by the IAI is controlled by applying a negative
pulse may be explained by means of the follow scenario.
When a negative pulse is applied to G2, at least the dc
electric field between the grids does not decrease incomparison with that before the pulse is applied. Thus,
since the electron drift velocity does not decrease, thecurrent-driven IAI is maintained. Consequently,

spite of increasing the embedding dimensions, and thelargest Lyapunov exponent takes a negative value, /,1 -0.013. Thus, the system is changed from a chaotic state
to so-called "white noise" state by applying a positivepulse. On the other hand, as shown in Fig. 3(c) in thecase of the negative pulse, the trajectory shows a limit

cycle. Furthermore, the system takes D = l, ht 312

Taniguchi K. et al., control of Type-1 Intermittency caused by Ion Acoustic Instability

applying a negative pulse influences on the feedback
mechanism of the unstable wave with information ofpulse was applied, u6 / c, hardly changed and thus thechaos, and as a result chaos is controlled. These results
are consistent with the fact that the frequency of thechanged from chaotic orbits to periodic orbits, whose
frequency agrees with the fundamental frequency ofthe
IAI. Consequently, these results suggest that the control
ofchaos is achieved by applying a negative pulse.

IAI was maintained. However, the state of the system

periodic orbits splected when the chaos is controlledagrees with the fundamental frequency - 80kHz of theIAI, which is determined by the interval Z between thegrids. This controlling method suggests a possibility ofcontrolling chaos in the plasma instabilities with aReferences

inh e re nt feedback mechanism.

lll E. Ott, C. Grebogi and J.A. Yorke, Phys. Rev. Lett.
64, 1169 (1990).
I2l K.Pyragas, Phys. Lett. A l7O, 421 (1992).

4. Gonclusions

t3l Th. Pierre, G. Bonhomme and A. Atipo, Phys. Rev.
Lett.76,2290 (1996).

We examined the control of chaos caused by thecurrent-driven ion acoustic instability by applying apulse to one of two mesh grids which are installed in a
Double Plasma. When a positive pulse was applied, theelectron drift velocity u6 / c. rapidly decreased and thecurrent-driven IAI was well suppressed. Therefore thet4l K. Taniguchi, H. Kuwae, N. Hayashi and Y.
Kawai, Phys. Plasmas 5, 401 (1998).
A. Hirose and M. Koganei, Phys. Rev.
H.Tanaca,
t5l

16r,94 (1967).

16l D.B. Fenneman, M. Raether and M. Yamada, Phys.
Fluids 16. 871(197r.

chaotic system also vanished and became the so-called"white noise" state. On the other hand, when a negative

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