J. Plasma Fusion Res. SERIES, Vol.4 (2001)

587_590

Gontrol of Intermittent Chaos Caused bylon Acoustic Instability
FUKUYAMA Takao*, TANIGUCHI Kazunaril
and KAWAI Yoshinobu
Interdisciplinary Graduate school of Engineeringsciences, Kyushu (Jniversity,Kasuga-kouen 6-1, Kasuga, Fukuoka gt6_g5g0,
Japan
tDepartmentof Science, Kyoto (Jniversity of Education

Fujimori_cho l, Fukakusa, Fushimi_ku, Kyoto(Received: 5 December 2000 / Accepted:

612-g522, Japan

14 September 2001)

Abstract
The control of intermittent chaos caused by the current-driven
ion acoustic instability is attempted
and the controlling mechanism is investigated. It
is found that when a negative DC-voltage is applied,thesystem changes from chaotic state to periodic
state with maintaining the instability, showing
thatthechaotic state caused by the instability is well controlled
by applying a iegative DC voltage. Furthermore,
it is found that hysteresis is observed on the v-I curveof the mesh grid where the DC voltage to control
chaos is applied.

Keywords:
nonlinear phenomena' intermittent chaos, controlling

1. Introduction

mechanism of control clearer. Especially, experimental
results of controlling chaos by applying a negative DC

Ott, Grebogi, and yorke (OGy) [l] firstly proposeda general way to control chaos using a feedback system.

voltage are reported. Furthermore, exciting of driven_chaos by applying a negative DC voltage is reported.

Thereafter, the OGY method was experimentally andtheoretically modified to realize the control of chaos inreal systems by many authors, so far. pyragas[2]suggested a time-delayed feedback technique, which ismore appropriate for the experiment than the OGymethod. However the experiments on controlling chaosin plasma have, so far, been only performed for chaotic
phenomena in the DC discharge system[3_6]. Theseexperiments were mainly carried out using the Time_
Delayed Auto Synchronization (TDAS) method[3,7] orthe modified OGY method. We have observed that rhesystem becomes chaos via the type-1 intermittency[g]caused by the current-driven ion acoustic instability(IAI) which is one of typical instabilities in a plasma

2. Experimental Apparatus
The experiments were performed using a DoublePlasma device Ill] whose dimensions were 70 cm indiameter and 120 cm in length. Here, the plasma wasproduced by DC discharges between tungsten filaments
and a chamber wall only in the target region on thiswork. The chamber was evacuated to 4.0 x l0-7 Torr,
and then argon gases were introduced into the chamberx

with pressure of 4.0 10-a Torr. Typical plasma
parameters were as follows; the electron densityn"= 108

cm-3, the electron and the ion temperature T"= 0.5_1.0
eV and Ti= T.l(10-15), respectively. In previous work[9], and succeeded in controlling chaos by applying anegative pulse [10]. Here, we attempted to make the*Cchaos, hysteresis, ion acoustic instability[9], the current driven IAI was excited bv theorre sponding author's e -mail : fukuyama@ aees.lqtushu_u. ac jp587@2001 by The Japan Society of plasma
Science and Nuclear Fusion ResearchFukuyarna T. et al., Controlof Intermittent

Chaos Caused by Ion Acoustic Instability

against ionsis caused by the relative motion of electrons
were the control parameters[12]. Here, V- and whichF-6o@--?

tof the IAI were fixed at 23 Y and 3 cm' respectively'
Fig. 1(a) shows the typical chaotic state before
seriescontrolling, the power spectra and the timephase space using theFrom time series signal' thesignals, reconstruct trajectories on"it"OOlngmethod [13].

characteristic of the IAI signals that include

pig. f Sct ematic O,rnrrrn of the experimental

controllingo.de, to evaluate whether the system before
is chaotic or not; the calculations of the correlation

aPParatus'

performed'
dimension and the Lyapunov exponent wereandGrassberger
ofmethodtheIn the former calculation
onbasedthatlaterin
theProcaccia [14] was used, andweresult'aAs
Wolf's algorithm [15] was used'that the system in absence of controlling isgrids wereand two mesh grids G1 and G2 whose

measurement system that two parallel meshinstalled,

turbulentchaotic
bursts was observed. Then, we performed
incontrollingofanalysis from time series in absence

atdimensions are 6 cm in diameter and 50 mesh/in'interval L of 2 - 5 cm. A DC potential V. was applied
G1 in order to excite IAI' Furthermore' theconfirmed
chaotic state, since the value of correlation dimension

towaswas non-integer and the largest Lyapunov exponent
state'
chaotic
theofcharacteristic
positive, which is theby
experiments on the control of chaos were performed"Vnc"tovoltageapplying a positive or a negative DC

In preuious work [10], we succeeded in controlling
work' wechaos by applying a pulse, however, in thisused a DC voltage instead of a pulse, because thefrequency of the pulse is sufficiently smaller than thefundamental one of IAI'

G2, as shown in Fig. 1 and time series signals foranalysis were obtained from the fluctuating componentsof the currents on the V. biased mesh grids' and weresampled with a digital oscilloscope'

It was found that when a positive voltage was

3. Experimental Results and Discussion

inapplied to one of two mesh grids which were installedabove
a plasma, the instability was suddenly suppressed

The current-driven ion acoustic instability (IAI)
was excited by inverse electron Landau damping which(a)gW-lry.

1l)6>\oq0200 {00 600

Time (! sec)

Frequency (kIIz)(b)0200 400 600

W W
0t00

200Fig.2Thechangeofthesystembyapp|ying.a-negativevo|tage.Powerspectra,timeseriesandreconstructedorbitare
illustrated,respectively.(a)beforeapplying,(b)aboveathreshold'588

Fukuyama T. et al., contror of Intermittent chaos caused by Ion Acoustic

a threshold (+3 V). On the other hand, as shown in Fig.

Instability

Furthermore, under these experiments, we observed

2, when a negative voltage was applied, the systemthat the system becomes the state where periodic

changed from chaotic state to periodic state above thethreshold (-3 V). For the periodic state, Fig. 2(b) showsthat the instability is maintained. These results indicatethat the chaotic state caused by the instability was wellcomponent was dominant in some parameter's region. InFig. 3, the change ofthe system is illustrated against thep,uameter y,. IAI is excited in B and D region, and thesystem becomes periodic in C region. Then, when weapply a negative voltage to C region in the same way, asshown in Fig. 4, the system becomes the chaotic state

controlled by applying a negative voltage, without
directly using well-known OGY method [1] and TDAS
method [3,7].

(c) via the bifurcation, where the applied negative
voltage is a control parameter. For chaotic state (c),"driven-chaos" [16] was excited, because the system

30 36 46 (V)became chaotic via the bifurcation and the fundamental

frequency was about 140 KHz, which was completely

different from IAI's one (about 70 KHz). Sampling thevmABCD

unstable states with period-3 are our future works.

E4. Conclusion
The control of intermittent chaos caused by the IAI

was attempted by applying DC voltages. When apositive voltage was applied to one of two mesh grids
installed in a plasma, the instability was suddenly

Fig. 3 The change of the system against the parameter
V.; A: before exciting lAl, B: lAl, C: periodic state,
D: lAl, E: vanishing of lAl.

(u)

gM-ru
EM0200 400 600

Frequency (kHz)(b)

suppressed. On the other hand, when a negative voltage

F L-----;r-* ,}--4""
Time (g sec)

'W Lry050100(c)Fig. 4 The change of the system by applying a negative voltage Vo", Power spectra, time series and reconstructed orbit
are illustrated respectively, (a) before applying, (b) period-doubling, (c) chaotic state.
589

Fukuyama T. et aL, Control of Intermittent Chaos Caused by Ion Acoustic Instability

t6l W.X. Ding, H.Q. She, W. Huang and C'X' Yu'

was applied, the system changed from chaotic state toperiodic one with maintaining the instability, showingthat the chaotic state caused by the instability was wellPhys. Rev. Lett.72,96 (1994).
D.J. Gauthier, et al.,Phys. Rev. E 50'2343 (1994)'

t7l
t8l Y. Pomeau and P. Manneville, Commun' Math'controlled by applying a negative voltage. Furthermore,Phys.74, 189 (1980).

when we applied a negative voltage to the system whereperiodic components were dominant, the system becamechaos via the bifurcation.

t9l K. Taniguchi, H. Kuwae, N. Hayashi and Y'Kawai, Phys. Plasmas 5, 401 (1998).
t10l K. Taniguchi and Y. Kawai, Phys. Rev. Lett' 83,
s48 (r999).
tlll R.J. Taylor, K.R. Mackenzie and H. Ikezi, Rev'Thus, interesting phenomena that the applying
negative DC voltage leads to controlling chaos while
exciting driven-chaos was found.

Sci. Instrum. 43,1675 (1972).

ll2lIF'. Tanaca, A. Hirose and M. Koganei, Phys' Rev'
16l,94 (1967).
Packard, J.P. Crutchfield, J.D. Farmer andN.H.
t13l

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