J. Plasma Fusion Res. SERIES, Yol.2 (1999) 36O-362

Nonlinear Wave Phenomena in an Electron-Beam Plasma:Observations of Electric Field Fluctuations
YAMAGIWA Keiichiro, TAKEDA Tsuyoshi, KAMIYA Takashi and HORIKAWA Masayuki
Dept. of Physics, Faculty of Science, Shizuoka University, Shizuoka 422-8529, Japan(Received: 2l December 1998 / Accepted: 13 May 1999)

Abstract
A double electric probe was applied to detect local electric fields of unstable waves excited in anelectron-beam plasma. In the investigation (beam density n6 < 0.37o of the plasma density zs), the wave

field energy was less than lU%o of the plasma thermal energy and nonlinear phenomena, the generation ofa series of rf-bursts. were observed.

Keywords:
unstable electron-beam waves, electric fields, double probe

1. Introduction

cyclotron frequency (a".l2n = 25OMHz) is larger thanthe plasma frequency (oo"lzn = 150MHz). As is wellknown, in a plasma of finite transverse dimensions anelectron beam interacts with two possible plasma waves,
Trivelpiece-Gould modes. For al". ) rlo", one is theplasma wave in a lower frequency band (< ab"). The
other is the upper hybrid wave (= (ap"2 + a""21tt21.In thepresent study we focus on observations of the beamplasma interaction in the lower frequency band. We
inject a pulse electron beam (beam diameter 45 mm)with duration of 7 x l0-6 s into the target plasma along
the external magnetic field. The beam current 16 passing[] on nonlinear
phenomena of Langmuir waves, considerable progresshas been made in this area [2]. There has also been a
Since Zakharov's pioneering work

growing interest [3-7] in nonlinear phencrnena of
unstable beam modes. Yajima and Tanaka [5] predicted

the existence of soliton modes of unstable waves in anelectron-beam plasma. The present authors haveexperimentally studied on evolution and formation of
nonlinear structure of the unstable electron-beam waves
16,71.

In this work we will report observations of electricfields of the unstable beam waves and compare thethrough the plasma is measured by a collector located atwave field energy with the plasma thermal energy.
Finally we will briefly discuss the stabilization

the opposite end from the beam gun. Local electricfields E(r) are detected by a double electric probe [8]mechanism of the beam modes in the nonlinear stase.

which is connected with a wide-band differential circuit(HPl14lA: DC - 200MHz). Langmuir probes are also
used for observing local density fluctuations n(t). The
realtime data picked up are captured by a fast digitizing
oscilloscope (HP54510A: lGSa/s, 2ch, 8kWch). Plasma
parameters are as follows: plasma density no = 3 x l}ta

2. Plasma Device and Experimental Setup
A target plasma is produced in argon gas of 1 x
10-5 Torr by a dc discharge in a so called magneticmultipole device [6,7]. An additional magnetic field (=90G) is externally applied parallel to the axis of theplasma chamber to observe the one-dimensional
behavior of the beam modes. where the electron

m-3, electron temperature T. = 2 - 4eV, beam density n5= (0.2 - 3) x 10-3 n6, and beam velocity v6 = (5 - 8) x v1
@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research360

Yamagiwa K. et al., Nonlinear Wave Phenomena in an Electron-Beam Plasma: Observations of Electric Field Fluctuations

21zz = 58 [cmlE

Lu _1-2

Time [S0ns/div]
Fig. 1 Realtime data of electric fields F(t) at z= 58cm. Here beam density nolno=9.945o7o, beam velocity vrlh=8.4.

(v1; electron thermal velocity).
z = 58 [cm]

3. Experimental Results and Discussion
3.1 Unstable beam waves and their wave
energy.aU'When an electron beam is injected into the target
plasma, unstable waves are spontaneously excited andgrow linearly along the beam stream. After the initialdevelopment of the waves, nonlinear wave packets [6,7) are generated and the wave energy becomesmaximum. Finally the instability is stabilized as thebeam electrons lose their energy mostly in the beamplasma interaction.
An example of local electric fields E(t) observed at
58
cm is shown in Fig. I, where the beam density
z=normalized by the plasma density n6lns = O.O457o andthe beam velocity normalized by the thermal velocity v6lvr = 8.4 (i vt= 4.9 x 106m/s ). The position z is thedistance from the beam gun. In this case, the phasevelocity vo= 4.6 x 106m./s, and the group velocity ofwave packets ve= 3.3 x l06m/s. These velocities are
dependent on the beam velocity v5, but not much on thebeam density n6. Figure 2 shows the Fourier spectrum A(l) of the realtime data in Fig. l. The beam plasma
system is unstable in a frequency range lower than theplasma frequency (t't= 150MHz). Details on the"/2nnonlinear properties of the wave packets were alreadyreported in the reference [7].
Figure 3 shows the wave energy eo < E > / 2nsksT"
as a function of the beam density ndns. In the presentexperiment (na < 3 x l0-3ns) , wave energy Er< E2 > | 2
is no more than lOVa of the plasma energy noksT.

c.9c
EPc)

(t)oct)50 100 150 200

0Frequency f [MHzlFig. 2 Fourier spectrum of realtime data shown in Fig. 1.

0.08

aa

F-(D 0.06

o-:<oc\tda0,04

UJoo0.02

ao a00.1

0.20.3

Beam Density ns / no [%]3.2 Evolution of a single rf-burst andgeneration of bursts: test wave experimentFig. 3 Wave energy normalized by the plasma thermalenergy h< E'> /2noks7. as a function ofthe beam

The test wave experiment is reproducible. When asmall rf-burst signal with a time-width of 50ns isdensity nolno.

36rYamagiwa K. et al., Nonlinear Wave Phenomena in an Electron-Beam Plasma: Observations of Electric Field Fluctuatrons.f = 150MHz

0.1

U'=c
=oooL

i.... -. t... - -.t -..

Z=14cm{-".rlllh.""i'rlrlr :.\iq,

Z=l6cm(gcPrllllllr,;i,"!

rq...'.l|Ifll:..i.

oco| ,illilililtn,'lru[' l'..
i::4-r(UJ+t(,

Z=22cm'J

Pi""'ril,ltltll'tttthlh'irttr.-i.'..--i---,

'6coo

(,

0.01,Jlrlllrtlllh

iiii

I

3o

Z=19cm....rlr!tmH[['l!!:.:]i:' " : "' ...

trI

EU

ii

0.1

0.03':Z=25cm

0.3

Beam Density nblno [o/o]Fig. 5 Logarithmic plotting of the initial growth rcte Klh
as a function of the beam density nalno, The
empirical line with a gradient of 1/3 is also shownin this figure.

lZ=28cm

Time f [50ns/divJ

Fig. 4 Nonlinear evolution of a single burst wave andgeneration of a series of burst waves. Here beam
velocity vr/v-, = 5 and beam density ntlno = O.28Yo.

present study, the wave energy was less than l07o of theapplied to the control grid of the beam gun, a single
burst wave is excited and propagates downstream.

unstable for a single rf-burst, and generates a series ofburst waves along the beam stream. Finally it becomesstable as the beam electrons lose their energy in thebeam-plasma interaction.

plasma energy. The electron-beam plasma is linearly

Figure 4 shows how a single burst wave initially grows,
saturates and generates new burst waves. The number ofburst waves is proportional to the beam density. Finallythe system becomes stable in the same manner as above-References

tll V.E. Zakharov, Sov. Phys. JETP 35, 908 (1972).
t2l M.V. Goldman, Rev. Mod. Phys. 56,709 (1984).

mentioned.

In Fig. 5 the initial growth rate ky'ke of those burst
waves is plotted on a logarithmic graph as a function of
the beam density n6lns. The solid line in the figure is anempirical one with a gradient of l/3, which shows theinitial growth rate ky'ko is proportional to (n,olns)tt3.
Their magnitudes also agree with the calculated values
from the linear dispersion relation of the beam modes.

[3] A.Y. Wong and P.Y. Cheung, Phys. Rev. Lett.52,

The rf-burst waves seem to be soliton-like

t6l K. Yamagiwa, M. Tanaka, T. Itoh and T.

excitation discussed by Yajima and Tanaka [5]. They
are developed differently from Zakhalov's Langmuir
solitons, because the number of burst waves and thet7l K. Yamagiwa, T. Itoh and T. Nakayama, Journal de1222 (1984); P.Y. Cheung and A.Y. Wong, Phys.
Fluids 28, 1538 (1985).

t4l T. Intrator, C. Chan, N. Hershkowitz and D.
Diebold, Phys. Rev. Lett.53, 1233 (1984).

t5l N. Yajima and M. Tanaka, Prog. Theor. Phys.
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Nakayama, Proc. 1996-ICPP (Nagoya) l,774.
Phys. IV France 7,C4-413 (1997), invited paper ofICPIG (Toulouse, 1997).
t8l K. Yamagiwa and Y. Takeda, J. Phys. E: Sci.

identities are not conserved.

4. Conclusions

Instrum. 20, 332 (19E7).

A double electric probe was successfully applied todetect electric fields of the unstable beam waves. In the362