J. Plasma Fusion Res. SERIES, Yol.2 (1999\ 165-16g

Interaction of Unstable lon Cyclotron Harmonic Waves andLower Hybrid waves in an lon Beam-plasma system
UTSUNOMIYA Shohei, SUGAWA Masao, SHARMA Suresh C..
MAEHARA Tsumehiro and SUGAYA Reiji
Department of Physics, Faculty of Science, Ehime University,
Matsuyama 790-8577, Japan(Received: 8 December 1998 / Accepted: 24 August 1999)

Abstract
In an ion beam-inhomogeneous plasma system, when the drift frequency al* exceeds the harmonics
of the ion cyclotron frequency n&)"1, ion cyclotron harmonic waves with frequencies up to n6oci areobserved experimentally. By the application of externally launched rf field near the lower hybrid
frequency, the suppression of these unstable waves has been observed. Suppression is based on the
ponderomotive force due to a combination of the pump rf field and fields of both sideband waves. Whenthe frequency of pump rffreld is higher than the lower hybrid frequency, the enhancement ofunstablewaves has been observed. These results agree qualitatively with analyses from the nonlocal theory taken

into account of the ponderomotive force via applied fields.

Keywords:
ion cyclotron modes, inhomogeneity, parametric instability, ponderomotive force

1. lntroduction
The instability at the multiple ion cyclotron

emission mechanism. In the vicinity of polar cusp region

unstable ICH waves has been observed. Also, thesuppression of naturally excited drift waves in thissystem has been previously observed [3]. When thefrequency of applied rf field is higher than the lower
hybrid frequency, the enhancement of unstable ICHof the magnetosphere, the broadband electrostatic

waves has been observed.

emission at the ion cyclotron harmonics has beenobserved [,2] but, the mechanism on generation of

2. Experimental Procedures

harmonics in the magnetized ion beam-plasma system isof interest, in part, in order to obtain its possible

these emission remains uncertain. When the electron

Experiments are performed in the linear vacuum
chamber of l0 cm in diameter and 90 cm long [5]. The
ion beam source generated by an argon gas discharge(via a cold cathode) is set at the end of the chamber inthe uniform magnetic field .86 (Bo = 100-700G). Ion
beam with diameter = 9mm is extracted by applying thedrift frequency al* exceeds harmonics of the ion
cyclotron frequency n@"t, ion cyclotron harmonic (ICH)waves may be excited by coupling between electron
drift waves [3] generated by the inhomogeneity and theion Bernstein waves [4]. We have observed the strong
excitation of ICH waves, when the ion beam is injected
parallel to the magnetic field in a cylindrical plasma [5].
By the application of externally launched y'field near
the lower hybrid frequency, the suppressiou of thesedc potential (% = 100-500V) between the anodeelectrode of the ion beam source and the meshaccelerating electrode (diameter of mesh = lOmm). AnC orre spondin g autho r' s e -mai I : s u gaw a @ phy s. s ci. e hime - u. ac.j p

165@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Utsunomiya S. et aI., lnteraction of Unstable Ion Cyclotron Harmonic Waves and Lower Hybrid Waves in an Ion Beam-Plasma

estimated to 0.046cm-r (for mode 1) and 0.092cm-' (formodes 2, 3), and the velocity of an ion beam v6 is vo =3.8 x l06cm/s (energy 300 eV). Then modes l-3 canion 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 externally rf field is applied to one of accelerating

satisfy approximately the relation a= k1y,, for mode I ora = k(6 - n@"; for mode 2 (n = 2) and mode 3 (n = l)'electrodes of the ion beam. The region in a beam-plasma

Therefore unstable modes of 1-3 are 2rd-4th ICH

system is maintained at pressure p = lmTorr. Thewaves excited by the plasma inhomogeneity and the ion

plasma density and electron temperature are measured
by axially and radially movable Langmuir probes, andbeam injection [5], but the mode 0 may be thefundamental ICH wave excited by only the plasma

the wave intensity received with axially and radially
movable antennas is detected by the spectrum analyzer.

inhomogeneity.

The y' field with the frequency t)0 near the lower
hybrid frequency is externally launched. Then typicalfrequency spectra of unstable waves (frequency o) are

3. Experimental Results and Gomparisonswith Theory
In an ion beam-plasma system, spontaneously

shown in Fig. 2 for the pump of rf field with thefrequency 60.16MH2. Here the lower hybrid frequency
rrll is estimated to 60.5MH2, if (kxslko)2 = 0.003 is
assumed. It is seen that the fundamental, 3rd and 4th
ICH waves (modes 0,2 and 3) are reduced by the pumpof y'field, and the 2nd ICH wave (mode of 1) almost

excited waves appear at the frequency @> no"1 (n is aninteger, ar"1 is the ion cyclotron frequency). The typicalfrequency spectra ofunstable waves are shown in Fig. l,where to"il2n = l2.4kHz. The magnitude a*lo),iindicates the inhomogeneity of the plasma density. This
plasma inhomogeneity is estimated to of la"r= 4.8 fromthe observed density gradient, if the azimuthal mode
number of the drift mode I is taken up to l, = 2. Thenwaves with frequencies up to 4th harmonics of the ion

disappears. Fig. 3 shows frequency spectra of lower andupper sideband waves around the frequency of y'field.

Then amplitudes of lower and upper sideband waves(frequency to1 and rrt2) have nearly equal magnitude,
and the relation @t.2 = ao + ar is satisfied (e.g. for mode
0 with frequency 0.0l3MHz, both sideband waves havecyclotron wave may be unstable [4,5]. In Fig. I, themode denoted by 0 is the fundamental wave, and modes
denoted by 1,2,3 are waves with frequencies = no)"i (n= 2,3,4). Also, the wave number/<11System@t.z= 6O.156

t 0.013MH2). It is seen that amplitudes ofboth sideband waves corresponding to mode I areexcited most strongly. It is considered that theparallel to 86 isa.E1Cf,

dLoo
EJ.=

EEoo(U.>

50

Frequency (kHz)100

Frequency (kHz)Fig. 1 Frequency spectra of unstable waves for no rf
field, where plasma density np=2.4 x 1010cm-3,
I" = seV, beam density ratio nolno = 0.01, beamenergy % = 300eV.

Fig. 2 Frequency spectra of unstable waves for pump rf

field with frequency 60.16MH2.

r66

Utsunomiya S. et al., Interaction of Unstable Ion Cyclotron Harmonic Waves and Lower Hybrid Waves in an Ion Beam-plasma

suppression of unstable ICH waves is occurred by thepump ry'field and fields of borh sideband waves.
On the other hand, when the frequency of appliedrf field is higher than the lower hybrid frequency oL, theSystem1

Pump waveo.=

c:fenhancement ofunstable ICH waves is observed. Radialct

profiles of the wave amplitude of the unstable 2nd ICH(IImode (mode denoted by I in Fig. l) are shown in Fig. 4oEf

for no pump and the pump of rf field, respectively,=E.

where the pump frequency aro is 64MHz.It is seen thatthe wave amplitude increases with the pump of rf field,
and the increment of the wave amplitude is dominant inf;0.
oo

the region of the maximum plasma inhomogeneity.
Radial profiles of another modes are similar to that ofmode l, but the increment of the wave amplitude issomewhat small, although data are not shown. In this"case, the amplitude of lower sideband waves (frequency60.1

60.2

Frequency (MHz)arr) is much larger than that of upper sideband waves(frequency ar2), although data are not shown in here.

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

We attempt the numerical analysis of unstable ICH

waves in the presence of the applied r/ field. Thewith frequency 60. 1 6MHz.

analysis are performed by taking in the boundary
condition perpendicular to the magnetic field in thecylindrical ion beam and plasma column i.e., thenonlocal theory. The treatment is similar to that in ref.
[3], and the ponderomotive force due to the pump r/
field and fields of both sideband waves is taken in
nonlinear terms. The obtained nonlinear dispersion

Solid line : Pump, aro = 64 MHz
Dot line: No pumpoECJ

relation is given by-ct
L('e+FrFz

atkrll ro

ark11l ro,a"-a -An''l'o-0, (1)EJH

1oo+o -An''('oEooo,\r-l r,,'=ffir: r:,.,,!i.,1[, (' - ,e)^ao^ -'ii' L(,',,, (€1 dr) lr,
T "- Eo,'t,of,, (l M,kiu,, ^ (elm")Qu^ .____!
@rr=+--'"Yr )2, @o=#" l+a'zFla'z",
c!
m.kl,' "12 In,.,,t,."=2(2n'r+t2 Orkt.zll ro j,I(6i,z= -#r,r+ 1).

4\.......:'x J p (ker)20

10r (mm),30

Fig. 4 Radial profile of fundamental ICH wave for pumprf field with frequency 64MHz.

I6

where eis the local linear dielectric function ofan inhomogeneous ion beam-plasma system I4), (a, k), (aro,kd, (ar kr) and (az, k) are the unstable, pump rf,lower

and azimuthal mode numbers of each mode, re is theplasma radius, Ja is (, th Bessel function, Zj is nthand l,-order generalized Laguerre polynomials, andother notations are standard. We have calculated the fre-and upper sideband modes, @s is the wave potential of y'field, c, is ion acoustic sound velocity, ln and 1,1,2 arequency and growth rate of unstable ICH waves for thepump y'field from eq.(l). The growth rates of three ICH
waves as a function of the normalized frequency of thethe nomalized factor with respect to the wave potential

for the finite mode of each waye, tr1.2 and t y.2 are radial167

Utsunomiya S. et al., Interaction of Unstable Ion Cyclotron Harmonic Waves and Lower Hybrid Waves in an Ion Beam-Plasma

System

4. Conclusions

pump dfield are shown in Fig. 5, where curves denoted
by 0, 1,2 are growth rates of the fundamental,2nd and3rd ICH modes, respectively. It is seen in Fig. 5 thatgrowth rates of three unstable ICH waves are strongly
reduced, when the frequency of pump waves arg is less

In an ion beam-inhomogeneous plasma system, thedrift frequency cr* exceeds the harmonics of the ion
cyclotron frequency no"i, ICH waves are excited by theplasma inhomogeneity, and ICH waves are enhanced byan ion beam injection. By the application of externallylaunched r/field near the lower hybrid frequency, thethan the frequency of lower hybrid waves to1. And
when at6 is higher than ro1, growth rates of three ICH
waves increase. But, the plasma density no used in calculation is somewhat smaller (= 83Vo) than that in ex-

suppression of these unstable waves has been observed.

This suppression is based on the ponderomotive force
due to a combination of the applied rf freld and fields ofthe lower and upper sideband wave. When the frequency

periment, and the azimuthal mode number of each modeis calculated only for ( or {'r,z= l' Then numericallower hybrid frequency is lower (at least = 83Vo) thanthat of the experiment. Therefore although there is sucha discrepancy between the calculation and the experiment, numerical results agree qualitatively with the experimental results for the dependence of the growth rateof pump rf field is higher than the lower hybrid
frequency, the enhancement of unstable waves has beenobserved. This behavior of unstable ICH waves agree
qualitatively with that of the nonlocal theory taken into

account of the ponderomotive force due to a
combination of the applied rf field and fields of bothof ICH waves on the pump f field.

sideband waves.

References

0.1

tll M. Ashour-Abdalla and R.M. Thorne, Geophys.
Res. Lett. 4.45 (1977\.

t2l R.F. Benson, J. Geophys. Res.90, 2753 (1985).
l3l G. Praburam, H. Honda and M. Sugawa, J. Phys.

go. 08
FoSoc. Jpn. 62,4262 (1993).

(Ilt4l A.B. Mikhailovskii, Theory of Plasma Instabilities

Eo.
EVol. 2 Instabilities of an Inhomogeneous Plasma(Consultants Bureau, New York-London, 1974)

CIPart 1.

I

t5l M.Sugawa, S. Iwamoto, T. Kondo, S. Utsunomiya,T. Maehara and R. Sugaya, Proceedings of the1996 International Conference on Plasma Physics,
Nagoya (The Japan Society of Plasma Science and4500

Nuclear Fusion Research, 1996) Vol. l, p. 82.

Pump frequency oJol@"tFig. 5 Numerical growth rate of fundamental (0), 2nd (1)and 3rd (2) ICH waves versus frequency of pumprf field, where plasma density no = 2'O x 1010cm-3,
7" = SeV, beam density ratio no/no = 0.01, beamenergy Vu = 300eV.

168