J. Plasma Fusion Res. SERIES, Vol.2 (1999) 356_359

Experimental study on Instabirities of Explosive Typein Beam-Plasma Systems
HONZAWA Tadao, HOSHINA Takao and SAITOU yoshifumi
Department of Electric and Electronic Engineering,Uts unomiya University, IJtsunomiya 32 t -8 5 g5, Japan(Received: 8 December 1998 / Accepted: 13 Mav 1999)

Abstract
In this experiment, a slow ion-beam mode externally excited in an ion-beam-plasma system, which
is a negative energy wave, is observed to be self-modulated above a threshold probably because
ofwavewave interaction among three different waves (at, fto), Got, k) and (a4, t2). spectral analysis

of suchevolving waves and identification of each of the three waves make it possible to clarify the feature of thewave interaction, characterizedby (h= Ch- ar1, althoughkn= ftr- ft1 can not be precisely confirmed
because of difficult measurement of the exact value of I t, l. tn spite of this, the results are enoughtoverify the realization of instabilities of explosive type in the system.

Keywords:
ion-beam mode, self-modulation, three-wave interaction, negative energy waves, instability of explosive
type, beam-plasma system

1. Introduction

pump wave and then verify the realization of

According to the theoretical works Il], explosive

instabilities of explosive type in the system.

instabilities are known to be possibly caused by resonant
three-wave interaction in a system including negative

2. Experimental Methods

and positive energy waves. However, only a few

Experiments were carried out with a conventional
double plasma (DP) device [4-5]. In the device twoargon plasmas were produced by dc discharges at aexperimental works have been tried to realize explosive
instabilities in plasmas. Among them Nakamura [2]succeeded in observation of explosive instability in an
ion-beam-plasma system. Thereafter, Kawai et at. l3l
also tried to make a similar experiment, but they couldpressure P = (2-3) x 10-4Torr. Plasma parameters weresuch as densities n" = (4-6) x 108cm-3, electron
temperature T"=2-3 eV and ion temperatureTi=Tel20.
An ion-beam with an average energy of 5-10 eV wasobserve only an instability of decay type because of the

deficiency of pump power.

stationarily injected into the target plasma. Here, thebeam energy was externally controllable by changing

In this paper, we wish to report observation ofinstabilities of explosive type during the nonlinear

the potential difference Vs between the two plasmas.
Thus, an ion-beam-plasma system was formed in themodulation of a large amplitude wave excited in an ionbeam-plasma system. Here, the "slow" ion-beam mode,target plasma region. To excite a wave in the system, an

being a negative energy wave, is found to be self-rf voltage with a maximum amplitude %* = 0.5-6V wasmodulated above a threshold. Further, we identify eachsuperposed to Vs. In most cases the rf frequency/s. wasof the three waves causing the self-modulation of theCorresponding author's e-mail: honzawa@ cc,utsunomiya-u.acjp356@1999 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchHonzawa T. et al., Expeimental Study on Instabilities of Explosive Type in Beam-Plasma Systems

group with increasing x. In addition to this, the pumpin the range of l6G-3fi)kHz. Furthermore, the rf voltage
was externally amplitude-modulated at a low frequency

wave was found to be self-modulated at any fixed
position x, if V"* became above a threshold. Typicalexamples of wave forms, observed at various values ofV.* but at x = 5.0cm, are shown in Fig. 3. Here, thethreshold of V"^ for the self-modulation to occur is about
2.2V. Further, the amplitude and number per group of
the resultant spikes on the envelope increase withof l-lOkHz.

3. Experimental Results
In this experiment we used an ion-beam-plasma
system, containing an ion-beam with a velocity vs 2 3C.

and a density n,, = (0.1-0.2)ns, where C. is the ionacoustic velocity and n6 is the background plasma
density. Dispersion relations of waves excitable in thesystem are shown in Fig. 1. Further, we also studied thedependences of the wave velocities on the beam velocity
v6. These results show that the velocity 4w of the main(pump) wave is always slightly lower than v6 and isincreasing V"*.

From evolving waveforms as shown in Fig. 2, weget
an information on the propagation of the spikes
canor wave packets. Distance-time relations of individual

roughly proportional to v5. This leads us to conclude thatthe pump wave belongs to the "slow" ion-beam mode,
being a negative energy wave. Fig. I also indicates thatapplied rf
vottageercited wane!
(tthe ion-acoustic wave is also possibly excited in thesystem, though its damping is strong.
When the applied rf voltage V"* was raised above alevel, the pump wave was observed to be self-modulated
and to cause a series of spikes on its wave envelope.
The spikes spatially grow in amplitude and they also.tat X= 2.20cmozzI

3.25

lrJo

4.10c

1.40

3.5 5fFJ

change their forms during propagation. Typicaloscilloscope traces of evolving waves are shown in Fig.
2. The traces demonstrate that the self-modulation of thepump wave first starts at x = 2.5cm around the central

4.8 5
5.4 050 Ysec/div

part of an externally given broad packet and proceeds
more and more with increasing.r. At the same time thespikes gradually grow in amplitude and number perFig. 2 Typical oscilloscope traces of evolving waves.

showing the self-modulation.

(1,, ( MHz )fpp,"263.4kHz X= 5.0cm

Vb.4.4rlo5cm/src .i

apptied rt.iot'oJ

2.0!.
Vre.ir' aVql= 2.10 Vo\'ozzra"'larrla!'.

alra-Ja

envelgpe lorm
excited wave at

52.30
Z.r.O

2.15

lr,ao:)

2.53

o.

2.60

FJ:"a"tt=o |2 3*:xr?'-161 7 I

2.70
100 psec/divFig. 3 Oscilloscope traces of waveforms as a function ofFig. 1 Dispersion relations of waves excited in an ionbeam-plasma system.

the rf voltage %,.
357

Honzawa T. et al., Experimental Study on Instabilities of Explosive Type in Beam-Plasma Systems

spikes in traces of Fig. 2 (not shown here) indicate thatmost of spikes propagate in the negative -r-direction withthe waves. As a result, it is known that the low
frequency wave (with Arf) belongs to the ion- acoustic

velocities as low as (4-8) x l0acm/sec. This factsuggests that a low frequency wave with an averagemode and the upper sideband wave (with /u5) to the"fast" ion-beam mode. Both the waves are known to be

frequency A/ = 30-60kHz, consisting of a series of
spikes described above, probably belongs to an ionsound or acoustic wave propagating in the negative xdirection. This means that the wave number k becomes
negative (ft < 0). Another different way for measuring
the wave patterns, as will be described below, enables
us to identify this low frequency wave with an ionacoustic wave from its velocity.

positive energy waves.
Furthermore, we observed the frequency spectra of
the waves at various values of V"*(at x - 4.5cm) to study
the correlation among the changing three wave powers.

Relations of the wave powers with V"* thus obtained areshown in Fig. 5. The data indicate that the pump wave

power increases roughly in proportion to V.* at smallvalues of V"^, but it clearly deviates from the linear

Spatial changes of the frequency spectra ofevolving waves were studied by use of a spectral

increase above a threshold (%" = l.8V). We also findthat the upper sideband (with/rr5) and the low frequency(with A,f) waves newly appear above the threshold andtheir powers rapidly increase up to some levels withanalyzer. Typical examples of such spectra at various .r
are shown in Fig. 4. It is found from these that the self-

modulation of the pump wave (with/*.) is caused by thenonlinear excitation of an upper sideband wave (withincreasing V"". The fact, indicating that all the three
wave powers simultaneously increase with increasing/g5) and a low frequency one (with Arf). From this wecan find that the three-wave interaction satisfies aresonant condition such as

V"* above the threshold, lets us conclude that therealization of instabilities of explosive type is confirmed
at Vex > 1 .8V in the ion-beam-plasma system.

-f*" =-fus - A,f(1)4. Discussions and Conclusion

among these wave frequencies. In addition to these, we

In this experiment we observed the self-modulation

could observe the wave pattern of each of the threeof the "slow" ion-beam mode (pump wave) externallywaves, using a technique for selecting only one of themwith a band-pass filter. Wavelengths of the waves

excited in an ion-beam-plasma system. As a result of theself-modulation, the pump wave was observed to split

estimated from these patterns, obtained at frequencies

into a series of wave packets. On the other hand,

known from the spectra, enable us to identify each ofspectral analyses of the evolving waves indicate that thetE ?fRr di3tance?

IIx(cm)ll ^ "0rlt-mdut Uon

2.7 0c

3.4 5ixoaoao;tI-3tr.1

t3.90.gF["U..=t04.3 0

1.7 0

r40?80420560+f(kHz)MAXTMUM RF YOLTAGE

Fig. 4 Frequency spectra of evolving waves, observed atVq(Y)Fig.5 Relations of the three wave powers with thevarious positions x.

applied rf voltage V",.
358

Honzawa T. et al., Experimental Study on Instabilities of Explosive Type in Beam-Plasma Systems

self-modulation is caused by the nonlinear excitation ofupper sideband (with/us) and low frequency (with A,f)waves. It is also found from these that a resonant

range of %^ (1.8V S %* < 2.2Y),we conclude that suchwave-wave interaction possibly causes instabilities of
explosive type in an ion-beam-plasma system.

In the above discussions we interpret thecondition such as _fnr = .fus - A,f is always satisfied
among the three wave frequencies. The resonantcondition as /pp = "fus - A/ makes us expect theoccurrence of fesonant interaction among the threeexperimental results on the basis of the three wave
interaction. Another treatment of the phenomenon,
based on the wave-particle interaction [6], may be also
possible. Discussions on the latter subject will be madein future reports.

coherent waves, including a negative and two positiveenergy waves. On the other hand, observations of thewave pattems of the three waves enable us to know thatthe low frequency (with Afl and the upper side band(with /us) waves belong to the ion-acoustic mode andReferences[]

R.E. Aamodt and M.L. Sloam, Phys. Rev. Lett. 19,
1227 (1967],.

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t3l Y. Kawai, M. Kono and Ch. Hollenstein, Phys.
Fluids 24, 1056 (1981).

wavenumber such as ftnn= ftus- Aft, where ftpp, ku5 andAft correspond to the waves with ,fnr, ,fus and A/,[4] R.J. Taylor, K.R. MacKenzie and H. Ikezi, Rev.

respectively. This is because the wavelength h(= Lkl2n),being comparable to the size of the wave-existingregion, could be roughly but not precisely measured. In
spite of these, considering the fact that all the powers ofthe interacting three waves (negative and positivewaves) simultaneously increase with increasing V"* in aSci. Instrum. 43,1675 (1972).

t5l R. Limpaecher and K.R. MacKenzie, Rev. Sci.
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Theory (W.A. Benjamin, New York, 1967).

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