JAERI-Conf 95-021

PA38

Formation of duct in Plasma by High Power Microwave
and Self-Focusing
H. ITO, Y. NISHIDA, and N. YUGAMI
Department of Electrical and Electronic Engineering,
Utsunomiya University,2753 Ishii-machi, Utsunomiya, Tochigi 321, Japan.

Abstract
The first experimental demonstration of ducitng ofhigh power microwave in a preformed density channel is studied. The microwave remains trapped andguided in a preformed density channel. These results
are in good agreement with a numerical model describing the microwave propagation.
1. Introduction
One of the most interesting topics is the application of the laser to plasma based particle acceleratorswith a ultrahigh gradient. A number of ways to excite
plasma waves having gradients as high as several tenof GeV jm have been proposed so far. A laser driven
accelerator that has a number of attractive features
is the laser wakefild accelerator (LWFA) [1,2]. But
LWFA has the fault that the acceleration distance isseverely limited to the diffraction length, or ReyleighLength zR = 1rr6/ Ao, where Ao is the laser wavelengthand r 0 is the laser spot size at focus. The self-guiding[2] of an intese electromagnetic wave in a plasma has
been proposed to overcome its limitation. This phenomenon is particularly interesting for processes requiring a long interaction length such as x-ray lasers[3] and laser-driven accelerators. More recently numerous theoretical works on this subject [4,5] havebeen performed and experimental results [6,7] havealso been presented.

where w0 is the incident-wave frequency, Wp =(47rnelel 2 /me) 112 is the plasma frequency and ne isthe electron density. With the preformed density
channel along the pass of electromagnetic wave, it
propagates in this channel over distances exceeding
Reyleigh length. The latter results from the increaseof the refractive index due to the relativistic quiver
motion of electrons. Because the refractive index has
the largest peak on the axis where the intensity ofelectoromagnetic wave has a maximum, the distribution of refractive index is the same as that of an optical fiber. Such relativistic self-guiding occurs when
the inident-wave power P exceeds a critical power[8,9] given by Pc = 16.2(wjwp) 2 GW.
3. Experimental Set up
The experimental arrangement used in the present
studies is shown in Fig.l. A cylindrical, unmagnetized argon plasma is produced in a stainless-steel
chamber of 60 em length by 32 em diameter covered
with a number of multidipole permanent magnets fora plasma confinement.

2. Theory of optical guiding
One approach to the guiding of an intense electromagnetic waves uses the effect depending on selfinduced modulations of the plasma refractive index.
In a plasma there are two types of optical guiding
mechanisms. One is the self optical guiding due tothe ponderomotive force of an intense electromagnetic
wave and the other is the optical guiding due to therelativistic effect. The former utilizes the dependenceof refractive index on the plasma, which is given by(1)

Fig.l Experimental apparatus

The plasma is produced by a pulsed discharge with
discharge duration of 2 msec and 10 Hz repetition between the LaB 6 cathode and the chamber wall. The
plasma density is measured by both a cylindrical and- 133-

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a plane Langmuir probe. The typical plasma parameters are the maximum electron density n 0 ~ 2.0 x 10 12cm- 3 , electron temperature T. ~ 3 ......, 5 e V in an ar4 Torr.
gon gas pressure Po = 3 '"'-' 4 X
The pulsed microwave with frequency fo =w 0 /27r = 9 GHz and a maximum power of 250 kW
and the pulse duration of 1 Jl-Sec in FWHM is irradiated from a rectangular horn antenna (aperturearea= 13.5 x 10.5 cm 2 ) with a metal lens located at alower end of plasma density toward a higher density
area along the chamber axis.

w-95-021

z = 19 '"'"' 20 em, while the field amplitude has maximam on the axis. Therefor, we can say that themicrowave pulse is focused at z = 19 '"'"' 20 em.
Figure.3 (b) shows the halfwidth of the field radial profile as a function of the incident power. Fig.3(b} indicates that the half width has a minimum atthe maximum power P = 250 kW. It is evident fromFig.3 (b) that the half width tends to decrease withincreasing the incident power.
3r----------,
0 P=250WV02.5

4. Experimental Results

P=250WI..... P=150WI

0.8- - . P=50WI

y~ 0.6!.!;!
w 0.4

0.2

0.2

1015 20z (em)(a) r=O em

2530

0.5................

o~~~~~~~~0........._..,_._._........_.........._~~

016 17 18 19 20 21 22z (em)

50 100 150 200 250

P (kW)(a)(b)

Fig.3 (a) Half width of radial field profile ar as a function of
the axial distance (z). (b) Half width Ar as a function of theincident power. Solid circles, open circles, triangles, andsquares are the axial positions z
17 em, z
18 em, z19em, and z
20 em, respectively. Solid lines represent
theorical calculations.

====5. Discussion
In order to interpret the observed behavior, wecalculate a transverse profile of the microwave in thedensity channel. We assume that the microwave pulse
is weak enough to neglect the relativistic effect. We
use a propagation model approximated by that in an
opticl fiber with refractive index N 1 inside and N2
outside. Because the microwave field is axially symmetric, we can look for the fundamental TE mode
solution of Maxwell's equations. In a slab geometry,
this solution [10) is given by(2)where k; = Nlk6-k 2 , p 2 = k 2 -Nik6 and ko = wo/c,
c is the speed of light and a is the channel radius.
Applying the continuity condition of magnetic fieldHy, we obtain the characteristic equations

05

....

<I

10.5~ 0.6!.!;!
w 0.4~ 1.5

....

<I

2~~~ 1.5

Eocos(kyy)exp(-jkz) (IYI :Sa),
Ex = { Eo cos(kya)x exp[-p(IYI- a)]exp(-jkz) (IYI >a),P=250 WIP=150 WI
P=50WI

0.8~2The density channel is formed by inserting thePolyimide film sheet with 240 mm length by 15 mm
width and 125~tm thickness at the center of the chamber filled with the plasma. In the present experiment,
the sheet is inserted from the higher density to 15 em
position from the edge of metal lens. We may estimate that the radius of density channel is about 1em.
When the microwave pulse is injected into thisdensity channel, Fig.2 shows an axial profile of observed electric field pattern as a function of incident
power. We observe that with increasing the incident
microwave's power the microwave pulse propagates
deeper along the density channel and that the electricfield also becomes stronger. The electric field tends
to be confined around the axis ( r = 0 em) as the microwave pulse propagates along the channel. We canmeasure that the spatial separation of three peaks(ex, {3, 1) appeard in Fig.2 (a) is about 2.2 em. Threepeaks can be visible as the incident power increases.
We know that the wave length of the fundamental TE
mode in the wave guide (WRJ-10: 2.29 x 1.02 cm 2 )is >. 9 = 4.8 em. If we assume that the observed wave
in the experiment is the fundamental TE mode, we
suppose that the stanting wave of the mode is formed
in a density channel.

2.5

6 P=150WV

101520 25z(cm)(b) r=4 em

30(3)Fig.2 Profiles of the nomalized field E as a function of theaxial distance. Radial positions (a) r = 0 em, (b) r = 4 em.

Figure.3 (a) shows the half width of the radial field
profile ~r as a function of z. The half width ~rchanges along the channel and has minimum around

This numerical caluculation enables us to determine
the transverse profile for propagation of microwave inthe plasma channel.
We assume that the channel radius is a = 1 emfrom the experimental result. Because the plasma
density of channel outside is overdense, we may put- 134-

JAERI-Conf 95-021

N 2 = 0. We carry out the calculation as a functionof the refractive index N 1 . Figure.4 shows the transverse profile of the microwave calculated for abovementioned conditions and the observed experimentalresults. Note that experimental and numerical values
are normalized. Solid lines and dashed lines are results calculated for the .cases of N1 = 1 (in vacumm)and N 1 = 0.5, respectively. One can see that there isa fairly good agreement between experimental andnumerical results. The experimental result at thelower density (Fig.4 (a)) is more agreement with the1,0.5 than that of N 1
numerical result of N1
while at the higher density (Fig.4 (b)) the observationshows better agreement with N 1 = 1. These resultsobtained for Fig.4 can understand as follows. As themicrowave propagates along the plasma channel, theelectric field of microwave in the channel is maximum
around z = 19 em. Therefor, the refractive index
of channel increases, since electrons in the channel
are pushed out of the channel by the enhanced ponderomotive force. As a result, the refractive index
of channel changes gradually along the plasma channel. We can say the results indicate that the ductingof the microwave is formed and that the microwave
propagates along the channel.

==0.8

0.8

p.8

i 0.8~!!::!

w 0.4

w 0.4

0.2

0.2

3243 4r/a(b)z= 19cm
25ria(a) z= 17 em

5Fig.4 Normalized radial field profiles. Each curve represents
numerical results. The parameters are channel radius a = 1,refractive index N2 = 0, and Nt = 0.5 (dashed line), N 1 = 1
19 em.
17 em, (b) z(solid line). Axial positions (a) z==The variation of refractive index is very importantand the motion of the electron has to be taken intoaccount. The plasma is modeled using no relativistic cold fluid equations. Using the momentum andcontinuity equations, we can estimate that 6nfnc is
directly proportional to the incident power. The half
width has ~r ::::::: 1/ky. Using equation (3), the half
width is approximated by ~r ::::::: 1/ky ,.... 1/N1 . Because the channel refractive index is given by N 1 =(1- nfnc) 112 ,.... VP, where we put n = nc- 6n, thehalf width is given by

6. Conculsion
We have demonstrated that the ducting of the microwave is formed and the microwave pulse remains
trapped and guided in the plasma channel at the fundamental TE mode. The comparisons of the experimental observations with the theorical calculations
produce good agreement for both the transverse profile of the electric field and the dependence on theincident power of the half width Ar. We have shownthat the experimental result can be explained by theconcept on the "otical guiding " .
Acknowledgem ent
We would like thank Mr. X. Xu for his corporation
on establishing the experimental device. This work
was supported by a Grant-in-Aid for Scientific Research from Ministry of Education, Science and Calture, Japan.
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(4)
On writing in this result on Fig.3 (b) by solid lines,
the experimental and the theorical results are in goodagreement. But this comparison can only be qualitative.

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