JAERI-Conf 95-021

PA37
FREQUENCY UP-SHIFTS OBSERVED IN MICROWAVE-PLASMAINTERACTION
Xiaoxi XU, Yasushi NISHIDA, Noboru YUGAMI
Department of Electrical and Electronic Engineering,
Utsunomiya University,
2753 Ishii-machi, Utsunomiya, Tochigi 321, Japan.

Abstract
Frequency up-shifts and some higher frequency components have been observed in the interaction of a high power microwave (fo=9GHz)
with an unmagnetized inhomogeneous argon
plasma. The. relationship of the frequency upshift with incident microwave power, plasma density and strength ofelectric field have also been
investigated. The induced frequency up-shift isconsidered to be related to a rapidly expanding
plasma which is created by the ponderomotive
force of a strong standing wave.

observed in the z direction. Here Lz is the halfwidth of the density profile along the chamber
axix, nmax is the maximum plasma density during the experiment and zo is the position of themaximum density layer, while in the radial direction there is a quite weak linear density gradient. In the present experiments, the Lz is around
25cm and Lr, the gradient length in radial direction, is around 300cm.

I. Introduction
Recently, the frequency up-shift (blue shift)
has been studied in laser plasma interaction andplasma wake field accelerator [1,2]. Frequency
up-shifts in laser-plasma interaction have been
observed in recent experiments by Wood et al.
and Savage et al [3,4].
The first observation of the frequency upshift in the microwave-plasma interaction without any ionization front has been reported [5,6].
In this paper, we demonstrate that when a highpower microwave is injected into a underdense
plasma a frequency up-shift around 2MHz andsome other higher frequency components from 2
to 8MHz have been observed.
II. Experimental Arrangement.
In the present experiments, a cylindrical,
unmagnetized argon plasma column was created by a pulsed discharge between two directly
heated LaB 6 cathodes in a vacuum chamber(32cm in diameter, 60cm in length) as shown in-Fig.l.
A typical plasma discharge pulse duration is
tw=2ms with a repetition rate of 10 Hz; The typical plasma parameters are: maximum electron
density no:::; 1.2x1012 cm- 3 and electron temperature Te ~ 3 "' 5eV. The estimated electron-ion
collision frequency is Vei ~ 4.5 X 106 sec- 1 , andion neutral collision frequency is Vin ~ 105 sec- 1 .
Within the experimental region of concern, aparabolic density, no = nmax[l- (z- zo)2 / L~], isFig.l Experimental set-up.
Pulsed microwave (/o=9GHz) with a risetime of Tr ~ lOOns, maximum power of 250kW
and a typical pulse width of T ~ 3J.Ls is irradiated synchronously with the discharge pulse
through a rectangular horn antenna (aperturearea= 13.5 x 10.5cm2 ) from the lower densityside of the plasma along the chamber axis (z direction). The ratio of the electric field energy tothe plasma energy is coE5/4ncKTe ~ 0.1, where
Eo is the amplitude of the electric field of theincident microwave, nc = 1.0 X 1012 cm- 3 is theplasma density of critical layer and K is Boltzmann's constant. Because the pulse width of themicrowave is short enough for the ionization orplasma heating, these effects can safely be neglected. The plasma density perturbation andrf signal in the plasma are detected by a plane
Langmuir probe and a cylindrical probe, respectively.
III. Experimental Results
The frequency spectra of rf signals are observed along the center axis of the chamber. ~typical example of the frequency spectra of ffilcrowave pulses is shown in Fig.2. These frequency spectra are observed inside the plasma- 130-

JAERI-Conf 95-021

at z=llcm where plasma density no=O.Snc withtwo different incident powers. Here z is a distance from the horn antenna aperture. The
dashed and solid lines represent the spectra ofrf signals of 37 and 250kW, respectively. It canbe seen that the up-shift is 2.5MHz when P; is250kW, but is 0.5MHz when P; is decreased to37kW.
· The relationship between the upper frequency components and the incident power isplotted in Fig.3. We found that as the incident power of the microwave P; is increased
from 0 to 250kW, the frequency up-shift (fi) andthe higher frequency components (fm, m=2, 3)
can only been observed when P; is higher than
7.9kW, i.e. the threshold power for the presentphenomenon is around 7.9kW. This result is thesame as that we obtained before [5,6].

frequency on plasma density. It can be seen thatwhen the plasma density no is increased from 0to 0.9nc ( nc = 1 X 10 12 cm- 3 ) the up-shifted frequency increases from 0 to 2MHz, and the higher
frequency components increase from 0 to about
8MHz proportionally to the plasma density.
9• ft
• f.
• fs

87I

6'N 5/:I:'' '- I /~ --/~ 4<l 32

10-250kW·--·37kW
f0=9GHz
t=311S;

ii~,.I l ,."' /i-·-·/,.

,,

_J
-- ,,

~/-1

00.6

0.4

0.2

0.8

nolnc

l"'o=0.5n.

Fig.4 Frequency up-shift and higher frequency
components vs. plasma density.

1/5 times

As mentioned in Ref[5,6], the up-shifts are
due to moving plasmas which are created by the
ponderomotive force of the incident wave. So,
the frequency up-shifts should have a relation to
the strength of the electric field of the incident
wave. In order to verify it, a moveable reflecting plate is put near the end wall of the chamber ( Zr =Ocm) for investigating the dependenceof frequency spectra on the intensity of the electric field. The the electric field intensity of theincident wave IEI 2 and frequency spectra are observed at a fix point z=llcm while the reflecting
plate is moved from Zr=O to 9cm with a step-25-20-15-10-5 0 5 1015 2025~f(MHz)Fig.2 Frequency spectra of microwave fordifferent incident power.
987/1'1_L./_J
I--- -----T~z=0.4cm.

'6N' 5':I:~ 4'!a 32''

I-- --50100. .·::...t"'0'''... 4·".,.., .........

I

0-1''',

1816~
c: 14~ 12.............

150200Ul~ 10Q)
8"0::I
6==Ci
4~ 20250

Incident power (kW)Fig.3 Frequency up-shift and higher frequency
components vs. incident power.

02

3

4

5

6

7

89z. (em)Position of reflecting plate

The relationship between the frequency upshift and plasma density has also been investigated. Figure 4 shows the dependence of the- 131-Fig.S(a) Electric field intensity vs. reflecting
position.

JAERI-Conf 95-021

The electric field intensity 1£1 2, frequency
up-shifts and higher frequency copmonents observed as a function of reflecting position are
shown in Fig.5(a) and Fig.5(b). It is obvious that the frequency up-shifts and higher frequency components have been observed at which
the electric field intensity is strong.

__ ,,1"614'N' 10~ 8!~ i.~.

:I:':aI •• ,! .
! I!\-•·f•~ !i;.

..... fa12!,~\1.i-·- fz

I!~.\/\1w'*j \\// \6"0.f \'i1 l., fl,

4
200

123

• j\,•0•':~0.,..
....

00,....

"' • .J

4

56' >J'.;,' '."'\ ....

' \,.J~r··o v ~.. •::~0j• !i• \I"' ! \i ~x' \ ! l \\{78

while for the transmitted wave, it is found that

w1 = 7 2 (1+,8) [ 1- ,8 ( 1-w~,,~~+,B)')!]

Wo,(3)
Substituting·v = 7.5 x 106 cm/s (experimentalresult) into Eq.(2), the frequency up-shift of thereflected wave is b.fr = ;~~ ~ 4(MHz ), and forthe transmitted wave, the frequency up-shifted
is 6ft = f!~ ~ 2.1(MHz). These results are ingood agreement with the experimental results.
Since the up-shifted frequency signal interacts
with the moving plasmas several times within
one pulse duration of the incident wave, higher
frequency components could be observed in theexperiments.

9V. Conclusion

Z..(cm)Position of reflecting plate

Fig.5(b) Higher frequencies fm (m=1,2,3,4) vs.
reflecting position.
IV. Discussion
Frequency up-shifts have been verified experimentally in the interaction of high power microwave and plasma. As shown above, the observed up-shifted frequency and higher frequency
components depend not only on the incident
power of the microwave and the plasma density
but also on the strength of electric field. According to Refs.[5,6), the frequency up-shifts are due
to moving plasmas arising from ponderomotive
force and the velocity of the expanding plasma
can be written as

where A is the irradiation area of the microwave,
cis speed of light in vacuum and mi is ion mass.
Ti and Te are ion temperature and electron temperature, respectively. If we take Pi= 250kW,
fo=9GHz, Te = 3eV, A= 5 X 10-3 m 2 , r=3 J.lS,
l = 8 X 10-03 m, the velocity of the expanding
plasma is estimated to be v ~ 7.5 x 106 cmfs.
Whet~- the incident wave en_counters such q, moving plasma, a part of it is retlected by the plasma,
and the rest transmmits through the moving
plasma. In the frame of the moving plasma (theprime frame) the frequency of the incident wave
is wb = 1(1 + f3)w0 , where 1 = (1 - f32tl/2,
f3 = v/c. Performing an inverse Lorentz transformation to get back to the lab frame, the wave
frequency for the reflected wave is(2)In summary, the frequency up-shift around
1 ,...., 2MHz and some other higher frequency components in the range of 2MHz to 8MHz havebeen demenstrated again experimentally in theinteraction of microwave ( f0 =9GHz, Pi=250kW)
with underdense plasma. It has been predicatedtheoretically that a frequency up-shift may occur when an electromagnetic wave interacts withan underdense ionization front [7). This mechanism is verified by our experiments of microwaveplasma interaction when there is no ionization
front. It means not only an underdense ionization front but also a moving underdense plasma
can be used to up-shift the frequency of a microwave radiation. In the present case, because astrong standing wave is established in the chamber, the plasma is expanded rapidly by the collective ponderomotive force arising from the electricfield gradient of the standing wave. The reflectedand transmitted waves interact with the moving
plasmas, and the frequency is up-shifted due tothe Doppler effect.
References[1) S. C. Wilks, J. M. Dawson, and W. B. Mori,.
Phys. Rev. Lett. 61, 337 (1988).
[2) E. Esarey, G. Joyce, and P. Sprangle, Phys.
Rev. A 44, 3908 (1991).
[3) W. M. Wood, C. W. Siders, M. C. Downer,Phys. Rev. Lett. 67, 3523 (1991).
[4) R. L. Savage, Jr., C. Joshi, and W. B. Mori,Phys. Rev. Lett. 68, 946 (1992).
[5) X. Xu, N. Yugami, Y. Nishida, submitted toPhys. Rev. Lett.
[6] X. Xu, Y. Nishida, N. Yugami, submitted to
J. of Plasma and Fusion Research.
[7) W. B. Mori, Phys. Rev.· A 44, 5118 (1991).

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