J. Plasma Fusion Res. SERIES, Vol. 5 (2002) 459462

Behaviors of Unstable Low Frequency Waves byPump hf Waves in an Inhomogeneous Plasma
in the Presence of Beam lon
KOUKETU TaKamasa, UTSUNOMIYA Shoheil, KAGAYAMA Yoshiaki, SUGAWA Masao,
MAEHARA Tsunehiro and SUGAYA Reiji
Department of Physics, Faculty of Science, Ehime Uniyersity, Matsuyama 790-8577, Japan
IMatsuyama Shinonome Junior College, Matsuyama 790-8531,
Japan(Received: 1l December 2001 / Accepted: 17 June 2002)

Abstract
In an ion beam-inhomogeneous plasma system, multiple ion cyclotron harmonic (ICH) waves up tono"i, (t4i is the ion cyclotron frequency, n is the integer) have been unstable [1], where n is determinedby the inhomogeneity of the plasma. Further, it is observed that low frequency waves with frequencies in
the neighborhood of the lower hybrid frequency are unstable

B1'the external application of high frequency (i/) field, the suppressions of unstable waves areobserved. The suppression is due to the ponderomotive force of the pump hffield and fields of bothsideband waves. This suppression occurs, as the frequency of pump hf field is only lower than thefrequency of the Trivelpiece-Gould (T-G) mode. These behaviors and results agree qualitatively withnumerical analyses by the theory.

Keywords:
ion cyclotron harmonic modes, lower hybrid waves, inhomogeneity, high frequency modes,
ponderomotive force

By the external application of ft/ field, thesuppression of unstable ICH waves has been observed[6]. The all or partial suppression of low frequency
unstable waves are observed by the external application

1. Introduction
In the vicinity of polar cusp region of themagnetosphere, the broadband electrostatic emission at
the ICH has been observed [2,3], but the mechanism ongeneration of this emission remains uncertain. When theelectron drift frequency o* exceeds harmonics of theof hf field in the neighborhood of frequency of T-Gmodes. The suppression occurs, only when theion cyclotron frequency nat";, ICH waves may beexcited by coupling between electron drift waves [4]frequency of hf field is lower than the frequency of theT-G mode. This behavior agree qualitatively with thegenerated by the inhomogeneity and the ion Bernsteinnumerical analysis due to the theory.

waves [5]. We have observed the excitation of ICH
waves, when the ion beam is injected parallel to themagnetic field in a cylindrical plasma [1,5]. Further,
unstable low frequency waves near the lower hybrid
frequency are observed. These low frequency waves areidentified as lower hybrid waves.

2. Experimental Procedures
Experiments are performed in the linear vacuum
chamber of l0 cm in diameter and 90 cm long [1]. Theion beam source generated by an argon gas discharge

Corresponding author's e-mail : sugawa@ phys.sci. ehime -u.ac jp459@2002 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchKoutetu. et al., Behaviors of Unstable Low Frequency Waves by Pump hf Waves in an Inhomogeneous Plasma

electron, respectively, ar"" is the electron cyclotron
frequency, mi and me are ion and electron masses.

(via a cold cathode) is set at the end of the chamber inthe uniform magnetic field Bs (Bo = 100-700 G). Ion
beam with diameter = 9 mm is extracted by applying thedc potential (% = 100-500 V) between the anode

Therefore, these unstable waves are identified as lower

hybrid waves.

electrode of the ion beam source and the meshaccelerating electrode (diameter of mesh = l0 mm). An
ion beam is continuously injected into the plasma
produced by a dc argon gas discharge (via a hotcathode) at the opposite side of the ion beam source.
The external hf field is applied to one of accelerating

frequency of the T-G modes (a = (Dpe (k11lk)) isexternally applied. Then frequency spectra of unstablewaves are shown in Fig. l(b) and by the solid curve in
Fig.2 for the pump hf field with the frequency 60.16
MHz. Here the frequency a7 of the T-G mode iselectrodes of the ion beam. The region in a beam-plasma

estimated to 60.5 MHz, if (ktolkd2 = 0.003 is assumed.

The hf field with the frequenc] o)6 near thesystem is maintained at pressure p - 1 mTorr. The
plasma density and electron temperature are measured
by axially and radially movable Langmuir probes, andthe wave intensity received with axially and radiallyIt is seen in Fig. 1(b) that the lst, 2nd and 3rd ICH
waves are at least suppressed by the pump of hf field,

movable antennas is detected by the spectrum analyzer(a)3. Experimental Results and Comparisonswith Theory
In an ion beam-plasma system, spontaneously
excited waves appear at the frequency a> no)"1 and atpump offo=c
J.ci

0.000(IJc)

the frequency in the neighborhood of the lower hybrid
frequency. The frequency spectra of unstable waves
with frequency near nocr are shown in Fig. 1(a), whereo"il2n = 10.4 kHz. At least, waves with frequencies up
to 6th harmonics of ar.; are unstable. These waves havebeen identified as ICH waves in previous papers [,5].
Then the number of modes of unstable ICH waves is!
f,.=E.
Eoo(t0500determined by the inhomogeneity of plasma, that is, nar"i100

Frequency (kHz)< of (0f is the electron drift frequency). Spectra of theanother unstable waves with frequency near the lower
hybrid frequency are shown by the dotted curve in Fig.
2. This unstable wave was not observed previously[,5]. These unstable waves are confined within the(b)Pump ono.=fa;plasma column, and axial and radial interferometer wave

$o o.ooor

patterns can not be obtained. It is considered that waves!
5are standing waves. The wave number ft;1 parallel to 86,=of this wave is estimated to 0.046 cm-r. The velocity ofan ion beam v5 is also 2.5 x lO6 cm/s (energy 140 eV).
Then observed frequency of unstable wave (frequency- 0.58 MHz) satisfies o)= k1vt. Therefore, this unstablewave is excited by the coupling with the slow spacecharge wave of an ion beam. On the other hand, Thewave number ft1 perpendicular to 86 is estimated fromthe radial profile of waves amplitude which corresponds
to the profile of lst Bessel function. Then ft1 - 1.52
cm-r. These wave numbers and observed frequency
satisfy the dispersion relation of the lower hybrid wave
6z = 1a2o1l0 + a2o"laz)) (l + (mi/m.) (k?tlk2t)), whereabi and ape ate plasma frequencies of the ion and theE.
Noo0050100

FrequencY (kHz)Fig. 1 (a) Frequency spectra of spontaneously excited
ICH waves, where plasma density np = 2.4 x 1O1o
cm-3, 4 - 4 eY, beam density ratio nrlno - 0.01,
beam energy Vr= 140 eV. (b) Frequency spectraof unstable ICH waves for pump hf field with60.16 MHz.
460

Kour.etu. et al., Behaviors of Unstable Low Frequency Waves by Pump hf Waves in an Inhomogeneous Plasma

a0.001

f.=ri

Pump wave

zocri.lojrui,oEd;l"tqtoEl==E.

EGEU.
(u-ooo(U60.1160.2

Frequency (MHz)Frequency (MHz)Fig.3 Lower and upper sideband frequency spectra
around the frequency spectrum of pump rf field

Fig. 2 Frequenoy spectra of unstable lower hybrid waves

for no hf field (dotted curve) and pump hf field(solid curve) with 60.16 MHz.

with 60.16 MHz.

although higher ICH modes do not disappear. Further,as shown in trig. 2, the amplitude of unstable lower
hybrid waves is also reduced. Figure 3 shows frequency
spectra of low:r and upper sideband waves around the+:;L=0, )o)rkrrro torkrrro
a"- a -'unr'|, -d;Td - "nr'(,(1)!,,=& nr1"^11,t['o l, - {] :" "r''2 '''' Jo\ ,"I'"

frequency ar6 of pump hf field. Then amplitudes ofO?tO2olower and uppor sideband waves (frequency a1 and a2)
have nearly equal magnitude, and the relation ar2= ao+ ar satisfies. These sideband fields interact with thepump ft/field and a ponderomotive force acting on the
low frequency unstable waves is generated. It isconsidered that this ponderomotive force suppresses
unstable waves [7]. Figure 4 shows the amplitude ofunstable lowerr hybrid waves as a function of thefrequency of the pump hf field. In the frequency regionof applied hf field whose frequency is lower than theaO"x J t (kLnr ,"{ro , -')' 6(,,r, t'^t,:.1r?i.rldr l2 ,E"raoo=941b,,4=114.
'cik;

at k\znto 12E2
5ir=ffA,

1n,,r.,,.r=2(2n,.r+ lr.r+l) 'where € is the local linear dielectric function of an inhomogeneous ion beam-plasma system tl,51, (ar, k), (ao,ki, (ar, ft1) and (az, kr) are the unstable, pump hf,
lower and upper sideband modes, pe is the wave poten-frequency (rorl2x = 60.5 MHz) of the T-G mode,unstable waves are suppressed. On the other hand, when

the frequency of applied hf field is higher than 44,

tial of hf field, c" is ion acoustic velocity, I and [,.,

unstable waves; enhance.

are the normalized factor. With respect to the wave po-

We attenrpt the numerical analysis of unstablewaves in the presence of the applied ft/ field. Theanalysis is per,-ormed by taking the boundary condition
perpendicular to the magnetic field as the cylindrical ion
beam and plasma column i.e., the nonlocal theory. Thetential for the finite mode of each v,taye, n 1,2 ard L y2 areradial and azimuthal mode numbers of each mode, 16 is
the plasma radius, I s is (.th Bessel function, Lf is nthand l-order generalized Laguerre polynomials, and othernotations are standard. We have calculated the growth
rates of unstable lower hybrid waves for the pump ft/
field from eq.(1). The growth rates of unstable waves astreatment is similar to that in ref. [7], and theponderomotive force due to the pump ft/field and fields

a function of the frequency of the pump hf field arc
shown in Fig. 5 for various applied normalized potentialof both sideband waves is taken in nonlinear terms. The
obtained nonlinear dispersion relation is given by461

Koutetu. et al., Behaviors of Unstable Low Frequency Waves by Pump hf Waves in an Inhomogeneous Plasmamode, the growth rate of waves is decreases with increasing of the pump wave intensity, and then waves
damps for @o = 5.0. Also, when ars is higher than a7.,
growth rates of unstable waves increase. Therefore although there is somewhat a discrepancy (at least = 83of of the hf field. It is seen in Fig. 5 that growth rates of
unstable waves are reduced, when the frequency ars ofpump waves is less than the frequency a4 of the T-GVo)betvteen the calculation and the experiment, the nu-merical behaviors agree qualitatively with the experimental ones for the dependence of the growth rate ofunstable waves on the pump hf fteld.
levelAmplitude
for 1>umtr> off

A4. Conclusions
In an ion beam-inhomogeneous plasma system,
when the drift frequency rrl exceeds the harmonics ofonal.;, multiple ICH waves are excited by the plasma
inhomogeneity and by an ion beam injection. Further,
the lower hybrid wave is unstable. The excitation of
unstable lower hybrid wave occurs by the coupling withthe slow space charge wave of an ion beam. By theextemal application of hf field near the frequency of theT-G mode, the suppression of these unstable waves areobserved. When the frequency of pump hf tield is lower(higher) than the frequency of the T-G mode, unstablewaves suppress (enhance). These behaviors of unstablewaves agree qualitatively with that of the nonlocal
theory taken into account of the ponderomotive force
due to a combination of the applied hf field and fields ofFaoF

40

50

60

70

Pump frequency (MHz)Fig. 4 Wave amplitude of unstable lower hybrid waves(frequency = 0.58 MHz) versus frequencies ofpump hffield.

both sideband waves.
0.1

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