Fusion Res.
Res. SERIES,SERIES, Vol.
Vol. 6 (2004) 000-000
406–409
J. Plasma Fusion

Improvement with High Frequency Field ofDischarge Plasma by an Electron Beam
SUGAWA Masao, UTSUNOMIYA Shohei1, MAEHARA Tsunehiro and SUGAYA Reiji
Department of Physics, Faculty of Science, Ehime University,
Matsuyama 790-8577, Japan1
Matsuyama Shinonome Junior College, Matsuyama 790–8531, Japan(Received: 9 December 2003 / Accepted: 27 February 2004)

Abstract
We study the plasma discharge process of Ar gas by an electron beam injection parallel to the magnetic field. On
the lower magnetic field, waves with low frequency become strongly unstable, the discharge plasma diffuses
perpendicularly to the magnetic field by unstable waves and disrupts rapidly in the short time. The unstable waves are
identified as the lower hybrid wave. By the external application of high frequency (hf) field near the frequency ofBernstein modes, unstable waves are suppressed, so that the plasma discharge is improved. The suppression of
unstable lower hybrid waves occurs, as the frequency of pump hf field is only lower than the frequency of theBernstein mode. Numerical analyses due to the nonlinear theory explain reasonably the experimental ones.
Keywords:
plasma discharge, electron beam, lower hybrid waves, Bernstein modes, ponderomotive force, nonlocal nonlinear analysis

1. Introduction

2. Experimental procedures and results

The feature of the beam plasma discharge is theproduction of high energy electron in a magnetic mirror field
whose energy is higher than the injected electron energy. A
project of space experiment with particle accelerator has
attempted to produce artificial aurora by injecting electron
beams from a space shuttle into the ionosphere of the earth.
We studied experimentally the beam plasma discharge in low
gas pressure and showed that the gas break down wasexplained by the cyclotron damping of the plasma wave
generated via the two stream instability. As the gas pressure
has relatively increased, we have reported that the plasma
discharge by an electron beam showed cascade-likely
temporal evolution [1]. As the magnetic field is weak, wehave observed that the generated plasma disrupts rapidly inthe short time ( - 100 µs). Then unstable waves with the lowfrequency were strongly excited. The disruption of theplasma discharge is attributed to the occurrence of unstablewaves, that is, the generated plasma diffuses radially by
unstable waves with the low frequency [2].
We investigate numerically and experimentally thedispersion relation of unstable waves, identify unstablemodes as lower hybrid waves.
By the external application of high frequency (hf) field,
we attempt to suppress unstable waves and to improve theplasma discharge. We analyze numerically the process of the
suppression of unstable waves with low frequency, as the hf
field is externally applied.

Experiments were performed in a linear vacuum
chamber of diameter 15 cm and 150 cm length. The argon
gas pressure in the chamber was maintained at the value
5 # 10 - 5 - 5 # 10 - 4 Torr. The electron gun (diameter = 1.2cm) was set at the end of the chamber, the accelerating
voltage was 500 –1500 V, and the beam current was 2 – 20mA. The discharge space were in a uniform magnetic field.
The unstable waves were detected by the radially and axially
movable coaxial probe. Plasma parameters were measured by
the radially and axially movable Langmuir probe. A 450 µs
electron beam pulse was injected into argon gas at 3 # 10 - 4Fig. 1 Temporal evolution of light intensity detected by aphotomultiplier, where ~ ce /2r =280 MHz, beamenergy V b =1 keV, gas pressure p - 3 # 10- 4 .
Parameters are same in Figs. 2–6.

Corresponding author’s e-mail: sugawa@phys.sci.ehime-u.ac.jp1406©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchSugawa M. et al., Improvement with High Frequency Field of Discharge Plasma by an Electron Beam

Fig. 2 Temporal evolution of frequency spectra of unstablewaves with the low frequency for no hf field.

Fig. 3 Temporal evolution of frequency spectra of unstablewaves with the low frequency for pump rf field.

Fig. 4 Temporal evolution of the radial profile of the electron density.

Torr in the magnetic field 100 G. The visible light intensity
was measured by a photomultiplier with S-4 sensitivity. The
temporal evolutions of all these were investigated. The
external hf field with the frequency 300 MHz ( ~ 0 /~ ce - 1.1,
where ~ 0 and ~ ce are the frequency of hf field and theelectron cyclotron frequency) was applied to one ofaccelerating electrodes of the electron beam.
Figure 1 shows temporal evolutions of the light intensity,where the time of the injection of an electron beam is 45 µs.
After the rapid increment of the light, it is seen that theintensity of the light decreases in the short time (- 50 µs),
then almost disappears.
The hf field near the electron cyclotron frequency isexternally pumped. Then the maximum value of the lightintensity (t - 90 µs) increases by approximately one and ahalf times that of no hf pump. Although after 90 µs the lightintensity decreases with time, the light does not disappear
between the beam pulse (450 µs). It is seen that the plasma
discharge keeps up between the beam pulse, and is muchimproved.
Temporal evolution of unstable waves with the low
frequency are shown in Fig. 2. Waves with the low frequency~/~ ce - 0.32 are strongly observed. Here, although spatial
feature is not shown by figures, unstable waves is moststrongly excited in the neighborhood of the center of theplasma column, unstable waves are observed in the broad
range of the radial position.
Figure 3 shows temporal evolutions of unstable waves
for the pump of the hf field. Unstable waves with frequency~/~ ce - 0.32 decreases by approximately 10 dB than that ofno pump of the hf field, also spatial reduction is seen.
Figure 4 shows the temporal evolutions of radial profiles ofthe electron density generated by the discharge. At the earlytime (80 µs), the plasma via the gas break down is generated
only in the injected beam region, then the maximum locationof the density is the position in the center ( r = 0 cm ). Whenthe plasma discharge begins to disrupt, the maximum
location of the density move away from the center, and theradius of the plasma become larger, as seen by the radial
profiles of t = 90 µs and t = 100 µs. Further as the timeproceeds, the maximum location of the density moves to thelarge radial position in the outside. Also, with the time
elapsed, the electron density n e rapidly decreases at the firsttime and then gradually decreases with the time. Thesebehaviors are similar as temporal evolutions of the lightintensity. These results show that the discharge plasma
diffuses radially from the center to the outside with the timeelapsed. It is considered that the radial diffusion and2407

Sugawa M. et al., Improvement with High Frequency Field of Discharge Plasma by an Electron Beam

Fig. 5 Dispersion diagram of unstable waves, whereelectron density ne = 2.0 # 1010 cm- 3 , T e - 5 eV, beam
density ratio nb /n p =0.01.

Fig. 6 Numerical growth rates versus frequency of pumphf field for various normalized pump field intensities,
where electron density ne = 2.0 # 1010 cm- 3 , T e - 5 eV,beam density ratio nb /n p =0.01.

disruption of the plasma are attributed to the unstable waves.
We attempt the identification of unstable waves. The wave
number k parallel to the magnetic field of these waves isestimated to 0.27 cm - 1 . Also the velocity of an electron beamv b is 1.9 # 10 9 cm/s (energy 1 keV). Then observed waves(frequency ~ - 84 MHz) satisfy ~ = k v b . Therefore, thisunstable wave is excited by the coupling with a slow spacecharge wave of an electron beam. On the other hand, thewave number perpendicular to the magnetic field is estimatedto 1.35 cm - 1 . This estimation is obtained from theassumption due to that the radial profile of the wave
amplitude depend on the 0th Bessel function J (k 9 r p ) , wherer p is the plasma radius.

electron beam, I n is nth modified Bessel function, Z is theplasma dispersion function and other notations are standard.
The numerical dispersion relation ~ - k 9 diagram isshown by the solid curve in Fig. 5, and the experimental one
is plotted by the circle. The experimental plot satisfies thedispersion relation of the lower hybrid wave. Therefore, This
unstable wave is identified as lower hybrid waves.
The hf field with the frequency ~ 0 near the electron
cyclotron frequency of the electron cyclotron harmonicmodes (Bernstein mode) is externally applied. Then lower
and upper sideband waves (frequency ~ 1 and ~ 2 ) appear
around the frequency ~ 0 by the coupling between unstable
lower hybrid waves with the frequency ~ , the relation~ 1, 2 = ~ 0 ! ~ satisfies, and amplitudes of both sideband
waves have nearly equal magnitude. These sideband fields
interact with the pump hf field and a ponderomotive force
acting on the low frequency unstable waves is generated.
It is considered that this ponderomotive force suppresses
unstable waves [4]. We attempt the numerical analysis ofunstable waves in the presence of the applied hf field. The
analysis is performed by taking the boundary condition
perpendicular to the magnetic field as the cylindrical beamand plasma column i.e., the nonlocal theory. The treatment issimilar to that in ref. [4], and the ponderomotive force due tothe pump hf field and fields of both sideband waves is taken
in nonlinear terms. The obtained nonlinear dispersion relation
is given byn1
n2f++= 0,(2)~ T k1 r0~ T k1 r0mn ,,~0- ~ - m n , ,~0+ ~3. Numerical results of theory andcomparisons with experiment
At the first, we calculate the dispersion relation of thelower hybrid waves by using f (~, k) =0. Here, the dielectric
function f is given by [3]f = 1 + |e+ |i+ |b ,(1)

VR
32 ~ 2pe S~ - n ~ ceW~!Z f| e = 2 2 S1 +p exp (-m e) I n ( m e) W,k v te S k v te n = - 3 k v teWTRVX
22 ~ pi S~ - n ~ ciWexp (- m i ) I n ( m i ) W,
| i = 2 2 S1 + ~ Z fk v tik v ti pk v ti SWTXRV2 ~ 2b S ~ - k v b 3 ~ - k v b - n ~ ciW!Z| b = 2 2 S1 +p exp (- m b) I n ( m b) W,k v tb n = - 3 f
k v tbk v tb SWTX
k 92 v t2ama=, ( a = e, i, b),2 ~ ca

1n 1, 2 =

2

14pi

2r0

2
C 2n C n2 , n , 12, 2 # f1 - r 2 p rr00~ ~r0~2ci

20

1

2

22 U0 - p,,e 2 p 1, 2 L n (p 12, 2 ) dr ,2r2# J , (k 9 n r)

where ~ pe , ~ pi and ~ pb are plasma frequencies of theelectron, ion and electron beam, respectively, ~ ce (= ~ cb ), ~ ciare electron and ion cyclotron frequencies, respectively,
v te , v ti and v tb are thermal spreads of the electron, ion andelectron beam, respectively, v b is a drift velocity of theU0=
p 12, 2 =3408

1, 21, 2

1, 21, 2(e/m e ) z 0,
cs2

~ B k1, 2 r0 r 2, mn~ 1, 2r02

1, 2, , 1, 2

= 2 (2n1, 2 + , 1, 2 + 1).

Sugawa M. et al., Improvement with High Frequency Field of Discharge Plasma by an Electron Beam

4. Conclusions

where f is the local linear dielectric function shown by eq.
(1), (~ ,k), ( ~ 0 , k 0 ), ( ~ 1 , k1 ) and ( ~ 2 , k 2 ) are the unstable,pump hf, lower and upper sideband modes, z 0 is the wave
potential of hf field, c s is ion acoustic velocity, C n and C n
are the normalized factor. With respect to the wave potential
for the finite mode of each wave, n1, 2 and , 1, 2 are radial andazimuthal mode numbers of each mode, r0 is the plasma
radius, J , is , th Bessel function, L,n is nth and , - order
generalized Laguerre polynomials, and other notations arestandard. Also ~ B is the frequency of Bernstein modes as thenormal modes in plasma. We have calculated the growth
rates of unstable lower hybrid waves for the pump hf fieldfrom eq. (2). The growth rates of unstable waves as afunction of the frequency of the pump hf field are shown inFig. 6 for various applied normalized potential U 0 of the hf
field. It is seen that growth rates of unstable waves arereduced, when the frequency ~ 0 of pump waves is less than
the frequency ~ B of the Bernstein mode, the growth rate ofwaves is decreases with increasing of the intensity of thepump wave, and then waves damps for U 0 = 5.0 . Also, when
~ 0 is higher than ~ B , growth rates of unstable waves
increase. Therefore, although the pump of hf field enables tosuppress the unstable lower hybrid waves, the suppression isvery sensitive to the pump frequency.
Bernstein modes with ~ B /~ ce - 1.08 can exist
experimentally under the present plasma condition. Thesenumerical behaviors explain reasonably the suppression of
unstable lower hybrid waves in the experiment on the pumphf field.

On the condition of the lower magnetic field in theplasma discharge process of neutral gases by an electron
beam, the plasma disrupts rapidly in the short time. Then the
low frequency waves are strongly excited. These unstablewaves are diffused the plasma perpendicularly to themagnetic field, and introduce to the disruption of the plasma
discharge. The unstable waves are identified as the lower
hybrid waves by comparing the dispersion relation. Thepump of the hf field enables to suppress unstable lower
hybrid waves, the plasma discharge is well improved. The
suppression of unstable waves is due to the ponderomotive
force of the pump hf field and fields of both sideband waves.
This suppression occurs, as the frequency of the pump hf isonly lower than the frequency of Bernstein modes. Numericalanalyses are carried out by the nonlinear theory. Numericalresults explain reasonably the experimental ones.

1, 2

References[1] M. Sugawa, S. Utsunomiya, S. Isobe et.al., Jpn. J. Appl.
Phys. 37, 2681 (1998) .
[2] S. Utsunomiya, Y. Kagayama, M. Sugawa et al.,Proceedings of the 25th International Conference on
Phenomena in Ionized Gases, (Nagoya, Japan, 2001)
Vol. 1, p. 237.
[3] A.B. Mikhailovskii, Theory of Plasma Instabilities(Consultants Bureau, New York, London 1974) Vol. 1
Chap. 7.
[4] G. Praburam, H. Honda and M. Sugawa, J. Phys. Soc.
Jpn. 62, 4262 (1993).

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