The space charge wave of electron beam excited by the
reactive medium instability in a uniform magnetic field region
is observed to propagate into the increasing magnetic field
region. When the wave passes through the cyclotron resonance
region, it suffers a heavy cyclotron damping

IDEHARA, T.

ISHIDA, Y.

TANAKA, M.

The space charge wave of electron beam excited by the
	reactive medium instability in a uniform magnetic field region
	is observed to propagate into the increasing magnetic field
	region. When the wave passes through the cyclotron resonance
	region, it suffers a heavy cyclotron damping

Community Repository of Fukui

MEMOIRS OF THE FACULTY OF ENGINEERING 
FUKUI UNIVERSITY 
VOL.26 No.2 1978 
Cyclotron Damping of the Space Charge Wave of Beam 
in a Nonuniform Magnetic Field Region 
* * * T. Idehara, M. Tanaka and Y. Ishida 
The space charge wave of electron beam excited by the 
reactive medium instability in a uniform magnetic field region 
is observed to propagate into the increasing magnetic field 
region. When the wave passes through the cyclotron resonance 
region, it suffers a heavy cyclotron damping. 
The instability of the space charge wave of beam due to the coupling 
with the Bernstein wave has been investigated by many authors in a beam-
plasma system confined in a uniform magnetic field. The calculation of 
its growth rate shows that the instability occurs most strongly near the 
cyclotron sub-harmonics w/w ~n+2~ , where w/2n and w /2n are the wave and 
c c 
175 
the electron cyclotron frequencies and n is an integer, because the cyclotron 
damping due to the plasma electrons supresses the instability near the 
cyclotron harmonic frequencies w/w ~n.l) 
c 
On the other hand, it has 
been verified by the experimental study that the emission spectrum ascribed 
to the instability has a series of sharp peaks near the cyclotron sub-
harmonics2) and the amplification factor ki of the obliquely propagating 
* Department of Applied Physics 
1~ 
test wave excited in a beam-plasma system has maximum values near the inter-
section between the cyclotron sub-harmonics and the upper hybrid resonance, 
i.e., W ~ (n+~)wc ~ J w~ + w~ , where wp/2n is the electron plasma 
frequency. 3) ,4) In this letter, we report the experimental result which 
supports the above consideration. That is, the space charge wave excited 
strongly by the reactive medium instability in a uniform field region where 
the cyclotron sub-harmonic condition w/wc ~n+~ is satisfied, suffers the 
heavy damping near the cyclotron resonance region, when it propagate in the 
region of increasing magnetic field. 
The plasma is produced by the dc dischar~ in the TP-D type device5) 
and diffused along the line of magnetic force into the pylex glass tube 
(9.5 cm in diameter and 65 cm in length), its parameters being as follows. 
The density n =3.5~5.3xI09 cm-3, the electron temperature kT =10 eV, p e 
4 -4 the plasma diameter D=30 mm and the pressure of the neutrals CAr) p=7. xlO 
Torr (the collision frequency of electrons with neutrals ven=4 MHz is 
much smaller than the wave frequency w/2n). The electron beam is 
generated by an electron gun placed at the opposite side of the discharge 
region and injected parallel to the line of force into the diffused plasma, 
so that the electron beam-plasma system is formed and the density ~ and 
velocity Vb (or energy eVb ) of the beam are controlled independently of the 
plasma parameters. This device has been used in the experimental study 
which was reported recently.3) The magnetic field is applied to the 
beam-plasma system by ten coils, which are arranged as shown in Fig. 1. 
The current II of two coils denoted by I and 2 is varried independently on 
the current 12 of the other eight coils, so that the distributions of 
1 
:g 
.~ 50 
I.L. 
o----~----~--------~----~--------SO 60 40 20 0 
Distance from the exciter z(cm) 
Fig. 1 The arrangement of coils and the distribution of 
magnetic field intensity. The coil current 12=1.0 A. 
The coil current II is varied independently on 12 . 
11= 1.0, 1.6, 2.0 and 2.4 A for the distributions shown 
by cueves 1, 2, 3 and 4, respectively. The dotted 
line shows the field intensity corresponding to w/2n= 
380 MHz. 
177 
178 
4 
60 40 20 0 
Distance from the exciter z(cm) 
Fig. 2 The propagating wave patterns of the space chsrge wave of 
beam in nonuniform magnetic field. Patterns 1, 2 and 
4 correspond to the distributions of field intensity 1, 2 
and 4, respectively. The wave frequency w/2TI is fixed 
at 380 MHz. Arrows show the cyclotron resonance points. 
magnetic field intensity shown in the figure are obtained. The dotted 
line shows the magnetic field intensity corresponding to w /2n=380 MHz. 
c 
The test wave is excited by the coaxial probe situated in the center 
of the beam-plasma. system (z=O) and detected by the other probe movable 
axially. By using the interferometer system, the propagating wave 
patterns along the field (along the axial direction z) are observed in the 
various distributions of the field intensity. The results are shown 
179 
in Fig. 2. The curve 4 is the wave pattern corresponding to the uniform 
magnetic field shown by the curve 4 in Fig. 1, where the wave and the 
electron cyclotron frequencies are 380 MHz and 308 MHz, respectively. 
As shown in the previous paper~) it is seen that the space charge wave of 
beam is amplified by the reactive medium instability (w=kl~b' kll is the 
wave number parallel to field) along the streaming of beam" and shows the 
stable propagation after it saturates at a sufficiently high level. 
From the value of kll obtained from this pattern and the value of the 
perpendicular wave number k" obtained from the radial propagation pattern, 
the propagation angle 8 with respect to the magnetic field (=tan ... l k..L/k" ) 
is about 760 • The patterns denoted by 2 and 1 correspond to the 
nonuniform magnetic fields shown by the curves 2 and· 1 in Fig. 1, where 
the wave frequency w/2n is fixed at 380 MHz. It is seen that the space 
charge waves amplified to high level in a uniform field region are damped 
strongly near the cyclotron resonance region denoted by arrows (that is, the 
points where the dotted line intersects the curves 2 and 1, in Fig. 1). 
The similar experiments are done for the various distributions of 
field intenSity. The regions where appreciable dampings are observed 
are plotted in Fig. 3 as the function of the position z where the cyclotron 
res 
180 
........ 
E 
u 
'N30 
Cl 
.~ Q. 
E 
c 
"'0 
<1140 ~ 
~ 
Q) 
.£:. 
+-' 
15 
e50 0 
+=i 
·in 
0 
a. 
~ 
/ 
50 40 30 
Position of the cyclotron resonance 
zres(cm) 
Fig. 3 The regions where appreciable dampings are observed as the 
function of the cyclotron resonance points z for the 
res 
corresponding distribution of the field intensity. 
resonance occurs for the corresponding distribution. 
shows the res,onance point w=w for each distribution. 
. c 
damped away before it reaches the resonance region. 
The solid line 
The waves are 
The dotted line 
shows the point where the relation of wc=w - kllvt is satisfied, where vt 
is the thermal velocity of plasma electrons. It is reasonable that 
181 
the points where the dampings of waves are most strong (denoted by hollow 
circles in Fig. 3) lie in the region surrounded by the solid and dotted 
lines. 
In conclusion, the results mentioned above may support the previous 
experimental results,3),4) where the amplification of the space charge 
wave of beam due to the reactive medium instability occurs most strongly 
near the cyclotron sub-harmonic frequencies. Moreover, it may 
suggest that the energy transfer from the beam electrons to the plasma 
electrons does occur effectively for the appropriate configuration of 
magnetic field intensity. 
This work is partially supported by the Grant-in-Aid from the 
Ministry of Education in Japan. 
References 
1) M. Seidl, Phys. of Fluids 4 (1970) 966. 
2) T. Idehara, K. Ohkubo and S. Tanaka, J. Phys. Soc. Japan 27 (1969) 
187. 
3) T. Idehara, M. Takeda and Y. Ishida, J. Phys. Soc. Japan 38 (1975) 
1125. 
4) T. Idehara, M. Takeda, N. Miyama and Y. Ishida, J. Phys. Soc . Japan 
39 (1975) 213. 
182 
5) K. Takayama, M. Ohtsuka, Y. Tanaka, K. Ishii and Y. Kubota, 
in Proc. 7th Intern. Conf. on Phenomena in Ionized Gases (Gradevinska, 
Knjiga, Beograde, Yugoslavia (1966) Vol. I, p. 420. 


Cyclotron Damping of the Space Charge Wave of Beam in a Nonuniform Magnetic Field Region

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