J. Plasma Fusion Res. SERIES, Vol.2 (1999) 133-137

Generation of Electromagnetic Waves and Alfv6n Waves
during Goalescence of Magnetic lslands in Pair Plasmas
HARUKI Takayuki. SAKAI Jun-ichi, NEUBERT Torstenr and NAMBU Mitsuhiro2
lnboratory for Plasma AtrltOh].tn-t-, ,*"!,'Toyama University, Toyama 930-8555 Japan.tf !:gineering,Danish Meteorological Institute, Copenhagen, Denmark

2Tokyo Metropolitan Institute of Technology, Hino, Tokyo 191-0065 Japan(Received: 8 December 1998 / Accepted: 12 February 1999)

Abstract
We show that the strong magnetic flux can be generated during coalescence of magnetic islands inpair plasmas. It is also shown that the charge separation with a quadrupole-like structure is produced near
the localized magnetic flux. There appear strong wave emissions with electromagnetic waves and Alfv6n
waves during the decay of the magnetic flux and the charge structure.

Keywords:
pair plasma, coalescence of magnetic islands, magnetic flux generation, electromagnetic wave, Alfv6n
wave

1. Introduction

astrophysical plasmas.

In the present paper we show that the strong

Electron-positron (pair) plasmas are thought to besources of intense electromagnetic radiation from manymagnetic flux can be generated during coalescence ofmagnetic islands. Also we find that the charge
separation with a quadrupole-like structure is produced
from the localized magnetic flux generation. During theobjects in space, such as pulsar magnetospheres, active
galactic nuclei (AGN) and the early universe. It is wellknown that magnetic reconnection in plasmas is one ofimportant energy conversion processes from magnetic
field energy to plasma kinetic energy as well as highenergy particles. The coalescence instability [] is an
ideal magnetohydrodynamic (MHD) instability in which
parallel currents attract each other and to coalesce into

decay phase of the magnetic flux and the charge
structure, there appear strong wave emissions ofelectromagnetic waves and Alfv6n waves.

2. Simulation Results
The simulation code used here is 2-D fullylarger units through magnetic reconnection. A lot ofworks on the coalescence dynamics in electron-ion
plasmas have been published both in MHD model andcollision-less model. Pritchett [2] reported a new effecton the magnetic flux generation during coalescence ofmagnetic islands in electron-ion plasmas, and showedthat during the nonlinear stage of the merging process of
two magnetic islands, a quadrupole out-of-the-planemagnetic field structure with a size of the ion skin depth
is formed. On the other hand, study on magnetic
reconnection and coalescence dynamics [3] in pairrelativistic electromagnetic particle-in-cell (PIC) code.
Firstly, we show the simulation results for a thin current,of which width is order of electron skin depth. Next, weshow the results for a thick current sheet with width oftwice electron skin depth (See Fig.4).
Figures 1(a) and (b) show coalescence of magneticislands at apet = 21.08 and ao.t = 31.62 in the x-yplane. Two magnetic islands formed by repeating@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Researchplasmas has begun under some motivations inr33

Haruki T. et al., Generation of Electromagnetic Waves and Alfvdn Waves during Coalescence of Magnetic Islands in Pair Plasmas

separation with a quadrupole-like tructure is formed(See Fig. 2(c-2)) near the region of the magnetic flux
generation. This charge structure corresponds to theregion where f. is negative. Figure 2(c-3) shows thecoalescence of small magnetic islands develop finally toa single large island.

Figures 1(c) and (d) show the electron spatial
distribution at awt = 21.08 and ar"t = 31.62 in the .r-yplane. There are three clouds as seen in Fig. l(c). As
seen in Fig. l(d), these clouds collide each other anddecay of the charge structure.

Figure 3(a) shows the dispersion relation of theelectric field E, along the magnetic field B,, which is
obtained by performing a 2-D Fourier analysis of thefield data taken in the x-direction on y = 45A. We findthat there occur the electromagnetic waves with highfrequency. Figure 3(c) shows the time history of the

become a single large cloud.

Figure 2 shows three snapshots of the magnetic
flux 8., the vector plots of magnetic field and theelectric charge density at apet = 28.46,31.62 and 36.89

in the x-y plane. The left column shows the timedevelopment of the magnetic flux 8.. The middle
column shows the vector plots of magnetic field B, - Br.

electric field energy E2. which is obtained by
performing the inverse Fourier transformation by use of
the data of Fig. 3(a). As seen in Fig. 3(c), theThe right column shows the spatial distribution of theelectric charge density (p+ - p_). As seen in Fig. 2(a-l)

electromagnetic waves can be generated after formationof the strong charge separation, and the emissions growthere is no magnetic flux before coalescence ofin the decay phase of the charge structure.
Figure 3(b) shows the dispersion relation of themagnetic field B. along the magnetic field 4. Fig. 3(d)shows the time history of the magnetic field energy Bl.
There is strong emission with low-frequency, whichbranch corresponds to the Alfv6n waves. Three solid

magnetic islands. But the strong localized magnetic flux
generation with a pair polarity is observed inFig.2(a-2).
Recently Sakai et al. [4] investigated the generation
mechanism of magnetic fields during collision of thinplasma clouds. Figure 2(a-3) shows that the magnetic

flux can diffuse in space and decay. Also the charge(c)(a)
100- -Mz a/+-6020o+-+ tt-F++-l\r!'\,\\- ,.,f @>-\:,\\

t1/z-1t.ll-\-,-\\f\'\\\-<-/r-\\\-r.g-/l*r\--+..<---<<<<<{z-40t '?
+r2080o

4080
(d)

(b)
100120t.trtt-+--\\\-tt
ar.tttttr++-1\ttitt*

y6020o40 X

8012004080

r20---l> - 1.45000
Fig. 1 For a thin current sheet with a width of electron skin depth, the vector plots of the magnetic field B" - Bv at(a) rop"f = 21.04 and (b) roo.t = 31.62 in the x-y plane. The electron spatial distribution at (c) aro"f = 21.08 and(d) aro"t= 31.62 in the x-yplane.
134

Haruki T. et al., Genention of Electromagnetic waves and Alfv6n Waves during Coalescence of Magnetic Islands
in pair plasmaslines in Fig. 3(b) mean theoretical curves with (l) al""/flux with different polarity appears lengthwise, becauseo0" = 0.5, (2) (D""/ @p" = 0.4, and (3) a"./ oJp. = 0.3,
which are obtained fromdispersion relation of theAlfv6n waves (g)t = |^th"eY.

of wide width of a current sheet. The structure of thecharge separation becomes more complicated than theprevious case, as seen in Fig. 4(c-l).

The strong emission in

the simulation result lr fr'.#6'O between tl ) and fzl ln
Fig. 3(b). We conclude that a""/ trto" = 0.45 is areasonable value to fit the theoretical dispersion curve.

3. Summary
We found from the simulation results that thestrong magnetic flux is generated and the charge
separation with a quadrupole-like structure is produced
during coalescence of magnetic islands in a current
sheet. It is found that the electromagnetic waves are

Figure 3(d) shows that the Alfv6n waves grow in thedecay phase of the strong localized magnetic flux.
Figure 4 shows three snapshots of the same
physical quantities as in Fig. 2 at apet = 36.89, 42.16
and 47.43 for a thick current sheet with a width of twice
electron skin depth. As seen in Fig. 4(a-l), the magnetic

1002(llfi))(lemitted in the decay phase of the charge separation andstrong Alfv6n waves are emitted in the decay phase of(c'3)
80

y60

60r00

20r0t)

20X

ffi-0.6 -0.4 .0.2 0.0 0.2 0.4 0.6-=1.54ilil"%

Fig.2Thetimedevelopmentof themagneticfluxQat(a-1) ato.t=28.46,(a-21 31.62and(a-3) 36.89.Thetime

development of magnetic islands at (b-1 ) ,or.t = 28.46, (b-21 31 .62 and (b-3) 36.89. The time development of thespatial distributionof theelectricchargedensity(p--p_l at(c-1) a,"t=28.46, i.c-2], 31.62and(c-3)36.89.
135Islands in Pair Plasmas
Haruki T. et al., Generation of Electromagnetic Waves and Alfv6n Waves during Coalescence of Magnetic12) P.L. Pritchett, Phys. Plasmas 2,2667 (1995).

the strong localized magnetic flux.

[3] J. Zhao, J.I. Sakai and K.I. Nishikawa, Phys'
Plasmas 3, 844 (1996).

Acknowledgment

t4l J.I. Sakai, Y. Kazimura and T. Haruki, submitted toWe thank the Cosel company for the support.

Phys. Rev. E.

tll

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opel

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oy' otpe
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Fig. 3 The dispersion relation of (a) the electromagnetic waves and (c) the Alfuen waves propagating along the magnetic
field 8,. The time history of (b) the electric field energy E'? and (d) the magnetic field energy 8,2.

136

IHaruki T. et al., Genention of Electromagnetic Waves and Alfv6n Waves during Coalescence of Magnetic Islands in Pair Plasmas

(a-1)
t60
140t20t00rffr00

20100

20160

t40
120l(x)20(b-3)160140vlzt)
100 E
2060lft)

20

100

20x

ffio*=l'3eo*-rm,
Fig. 4 For a thick current sheet with a width of twice electron skin depth, the time development of the magnetic flux 4at {a-1} alp" = 36.89, (a-21 42.16 and {a-3} 47.43.The time development of magnetic islands at {b-1}aro"t= 36.89,lt,-21 42.16 and (b-3) 47.43.The time development of the spacial distribution of the electric charge density lp.- p-l
at (c-1) ar*t = 36.89, (c-2) 42.16 and (c-3) 47.43.

t37