J. Plasma Fusion Res. SERIES, Vol.2 (1999) 129-132

Emission of Electromagnetic Waves from Langmuir
Waves Generated by Gold Electron Beam Instability
in Pair Plasmas
GYOBU Daisuke, SAKAI Jun-ichi, EDA Masanori, NEUBERT Torstenr and NAMBU Mitsuhiro2Inboratory .for Plasma As.trophysics, Faculty of Engineering, Toyama University, Toyama 930-8555 Japan'Danish Meteorological Institute, Copenhagen, Denmark

2Tolcyo Metropolitan Institute of Technology, Hino, Tokyo 19I-0065

Japan(Receoved: 8 December 1998 / Accepted: 12 February 1999)

AbstractUsing a two-dimensional electromagnetic and relativistic particle-in-cell (PIC) code, we show thathigh-frequency electromagnetic waves can be emitted by the plasma maser from Langmuir waves
generated by cold electron beam instability in pair plasmas. It is confirmed that the presence of amagnetic field is essential for the plasma maser mechanism.

Keywords:
pair plasmas, plasma maser, beam instability, Langmuir wave, electromagnetic wave

1. Introduction

2. Simulation Results

Plasma maser [] is a new nonlinear process forgeneration of various kinds of waves in plasmas, among
other processes like cyclotron maser instability [2],dimensional electromagnetic and relativistic PIC code

It is well known that an electron beam along amagnetic field in the y-direction becomes unstable toexcite Langmuir waves. Solid lines in Figs. 1(a) and1(b) show the time history of electric field energies
Ej and E2, for a case of {Do"l d)" = l0 with the beam of v5= O.7 c, n6lno = 0.1, while the dotted lines show the time
history for a case without the electron beam. As seen inFigs. l(a) and 1(b), both components of the electricfields are strongly excited due to the beam instability.
The solid line in Fig. l(c) shows the time history of theelectric field energy E2,, while the dotted line shows thecase without the beam. As seen in Fig. 1(c), the electricfield E grows after the electric field energy associatedwith the beam instability becomes large.
The enhancement of the electric field E, is related

whether electromagnetic waves can be generated by theplasma maser from Langmuir waves excited by cold
electron beam (26 = 0) instability [7] in pair plasmas.

to the plasma maser mechanism. Before discussing this,we investigate the phase space y - v, for the beamelectrons. Fig. 2 shows the phase space y - v, for theCherenkov emission [3], free-electron laser [4], andparametric three-waves interaction [5]. The mostimportant characteristics of the plasma maser process isthat the process requires the external magnetic field.
Recently Gyobu et al. [6] showed by using a 2-D EM
PIC code that electromagnetic waves (R-mode) can beemitted from Langmuir waves generated by the electron
beam (TlT,o = 2) instability in pair plasmas, where I isthe background temperature and 16 is the beamtemperature.
In the present paper we investigate by using a two-Corresponding author's e-rnail: gyobu@ ecs.toyama-u.ac.jp
129@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Gyobu D. et a/., Emission of Electromagnetic Waves from Langmuir Waves Generated by Cold Electron Beam Instability in Pair Plasmas

beam electrons at (opet = 21.08. The beam electrons arebunched in the phase space due to Langmuir waves
generated by the electron beam instability.
To investigate the behavior of the electric field E.,

we perform a 2-D Fourier transformation in thedirection parallel to a magnetic field. Fig. 3(a) shows thedispersion relations for Ez in the y-direction (al vs tx).
The results show that there appear two branches ofelectromangetic wave excitation. The first is seen near
the frequency 2.5 ap. with maximum amplitude. The
second excitation is seen around crr = 1.0 @r" and krcl
ar" = 2.0. This is so-called Cherenkov emission due toe3-1A>c4oal120Fig. 1 Time history of electric field energies (a) Ei. (b)El, and (c) E?. Solid lines show a case with aro"/
Q" = 10, vt = 0.7c, and nolno = 0.1. Dotted lines
correspond to a case without the electron beam.

(a)vlL
Fig. 2 The (y - v) phase space distribution
particles al oe.t = 21.8.

(b)

3.5

3.0

I

3.5

t'f#

3.0

2.5

2.5,t

2.O
1.5of beam

2.O
1.5

l.o

1.0

0.5

0.5

o.o

4 4-2

0 2 4

0.0

44-2

6k"/rp"0246
kc/or*(") +.0
4.2
4.4
trlao

4.6-4.8-5.0-5.20p"t

Fig.3 (a) The dispersion relation lor E, la vs (,). (b) The dispersion relation (arvs (,) for E, cutting the low frequency
region of at< 1.74 aro". (c) Time history obtained by the inverse-Fourier transformation from (b).
130

Gyobu D. el a/., Emission of Electromagnetic Waves from Langmuir Waves Generated by Cold Electron Beam Instability in Pair Plasmas

the resonance with electron beam. But the first branch

be excited by the trigger of the Langmuir waves due tocould not be explained by the usual emission

the cold electron beam instability. We investigate further

mechanisms. We cut the low frequency = region of oJ <the characteristics of the excited electromagnetic waves.

1.746 @pe from Fig. 3(a), as seen in Fig. 3(b) and 3(c),Fig. 4 shows the hodograph of the electric field E,- E,
associated with the excited electromagnetic waves. FromFig.4 we conclude that the excited electromagnetic
waves along a magnetic field show almost linear-then we perform the inverse-Fourier transformation toobtain the time histories for the excited high-frequency

waves. As seen in Fig. 3(c), the high-frequency
electromagnetic waves with olror" - 2.5 along amagnetic field can be excited only after about 20 rrro"/.

polarization.

We investigate further the emission process of

We may conclude from the above observations that theelectromagnetic waves parallel to a magnetic field canelectromagnetic waves by Langmuir waves. The plasma
maser theory predicts that there appears no plasma

maser mechanism when external magnetic field isabsent. Fig. 5 shows three different simulations: (1)thermal noise case with no electron beam and nomagnetic field, (2) the case with beam (vo = 0.'7c, nrlno= 0.1) and no magnetic field, (3) case with beam (vo =0.7c, n,olno = 0.1) and with magnetic field (a)r"/0)"" =0.1). As seen in Fig. 5, there is no strong enhancementof the electric field Ez for the case (2), compared withthe case (3). Therefore, we conclude that the presentemission mechanism is the plasma maser process,aT263sN
fY1

because it is essential for the presence of the external

magnetic field as predicted by the plasma maser theory.

There are many emission mechanisms ofelectromagnetic waves from Langmuir waves. We try to

explain the characteristics of the electromagnetic
radiation around d)/ap. = 2.5 observed in the present
simulation. The cyclotron maser originates from therelativistic electron mass change and the free energy forthe electromagnetic radiation exists in the direction
perpendicular to a magnetic field. On the other hand, in-l0xlO3-lOxl0

Fig. 4 Hodograph of (E, - E,l for high-frequency (o >1.74 ./N.p.l electromagnetic waves propagating

along a magnetic field.

-2.O

-2.2
-2.4
dNrI]bt)

-2.6
-2.8

-3.0
-3.2
-3.4
20

40

60

80lm

0prt
Fig. 5 Time history of electric field energy E]on effect of external magnetic field. (1) Thermal noise case with no electron
beam and no magneticfield. (2) Casewith cold beam (vo=9.7", nbln.=O.11 and no magneticfield. (3) Casewith
cold beam (vo = 9.7 nbln. = O.1l and with magnetic field (ar""/ar"" = 'l9).

",

l3l

Gyobu D. et a/., Emission of Electromagnetic Waves from Langmuir Waves Generated by Cold Electron Beam Instability in Pair Plasmas

3. Conclusions

the present simulation, the free energy exists in theelectron beam parallel to a magnetic field. Thus, we canrule out the cyclotron maser mechanism. Next, theCherenkov maser satisfies the Cherenkov condition

We found that high-frequency electromagnetic
waves can be excited for both directions parallel andperpendicular to a magnetic field. We confirmed thatthese electromagnetic waves can be generated by theplasma maser from Langmuir waves excited by the cold
electron beam instability.

between electrons and electromasnetic waves d) = K

7, where Q and I

representi ,h" fr"qu"ncy andwavenumber for electromagnetic waves. As is shown byFig. 3(a) in the present simulation, it is difficult tosatisfy the Cherenkov condition because d)lkx- l.2c >>Acknowledgmentv", where c, ye are light velocity, electron thermalvelocity, respectively. Accordingly, the Cherenkov
emission mechanism is not likely to operate in ourWe thank the Cosel company for the support.

simulation. The third possibility is the free electron laser
including the Langmuir waves driven by electron beam.
This requires several matching conditions to be satisfied
among the frequencies and wavenumbers of Langmuir

tll M. Nambu, Laser Part. Beams l,427 (1983).
t2l C.S. Wu and L.C. Lee, Astrophys. I. 230, 621

References(r979\.

t3l A.F. Alexandrov, L.S. Bogdankevich and A.A.
Rukhadze, Principles of Plasma Electrodynamics

and electromagnetic waves. However, the simulation
results does not satisfy these matching conditions.

(Springer Verlag, Tokyo, 1984).

l4l R. Fedele, G. Miano and V.G. Vaccaro, Phys.

Finally, the standard three-wave interaction requires thematching conditions {) * a = Q', F +t = i' , where rrr,

Scripta T3O, 192 (1990).

/ shows the frequency, wavenumber of Langmuir

t5l V.L. Ginzburg and V.V. Zheleznyakov, Astron. zh.,waves, respectively. We may rule out the three-wave

3s,694 (1958).
D.
t6l Gyobu, J.L Sakai, M. Eda, T. Neubert and M.

interaction because the above conditions are notsatisfied in the simulation. Accordingly, we must

Nambu, J. Phys. Soc. Jpn.68, (1999) in press.
Ul J. Zhao, K.I. Nishikawa, J.I. Sakai and T. Neubert,

conclude that the standard emission mechanisms can notexplain the generation of high-frequency

Phys. Plasmas I, 103 (1994).

electromagnetic radiation around d)la*= 2.5 observedin the present simulation.

t32