J. Plasma Fusion Res. SERIES, Vol.4 (2001) 509-513

Observation of Superthermal Electron Beam and Gavitons in
Broad Resonance Region due to Nonlinear
Microwave-Plasma Interaction
RAJYAGURU Chirag*, FUJI Toshiyukit, ITO Hiroaki, YUGAMI Noboru and NISHIDA yasushi
Energy and Environmental Science, Graduate School of Engineering,
Utsunomiya University, 7 - I -2 Yoto, (Jtsunomiya Tochigi32 I -g5 g5 JA4AN'

Fujitsu General, Japan(Received: 5 December 2000 / Accepted:2j August 2001)

Abstract
Study of generation of superthermal electrons near the critical layer, by resonance absorption
phenomenon, is extended to very high microwave power levels (4 E&l4rn"kT. 0.5). Successive==
generation ofelectron bunches having maximum energy about 2keV, due to nonlinear wave breaking, isobserved. The energy, e, ofthe electrons scales as a function ofincident microwave power, P, according
to e * Io5. Spatial distribution and temporal evolution of high energy electrons reveal that they are
generated near the critical layer. However, lower energy component is also generated in lower density

region indicating the possibility of other electron heating mechanism. Density cavitons are observed to begenerated near resonance region as well as in lower density region, temporal evolution of which, showtransition from supersonic velocity regime to subsonic one.

Keywords:
resonance absorption, wave breaking, high energy electron

1. lntroduction

If RF (radio frequency) field amplitude in resonance region is high enough, ponderomotive forces
become important leading to caviton [9] generation.
Cavitons have been observed experimentally [9,10] andFast electrons, with energies well above the thermalenergies, have been observed in experiments [1,2] aswell as in simulations [3-5] describing the interaction of

intense microwaves and laser beams with an inhomogeneous plasma. This can be attributed to thesubstantial intensification [6] of electric field innumerically [4,lll. Above works do describe somephysical processes behind its formaion and some effects
associated with trapped RF electric field but its temporal
dynamics and other related phenomena in high incident
power regime is still to be uncovered.
In the present paper, we wish to present the firstexperimental observation of superthermal electrons nearresonance region, where incident microwave frequency

becomes equal to the local plasma frequency, due toresonance absorption of incident electromagnetic wave.

For high incident power, wave breaking [7] phenomenon is the most probable candidate to account for the
genration of high energy electrons as incident power ismostly absorbed resonantly [8]. It predicts electronenergy scaling law as e * IP s, wherer e is the maximum

critical layer, using microwaves, to demonstrate thevalidity of cold wave breaking theory even when 4 =fil4xnkT"= 0.5. Superthermal electrons, having energy
as high as 1.8keV are observed near the critical layer at

electron energy and P is the incident radiation power.
*

Corresponding author's e -mail : chirag @ plasma. e es.utsunomiya-u.ac.jp509@2001 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchRajyaguru C et al.,ion of Suoerthermal Electron Beam and Cavitons in Broad Resonance Region

250kW of incident power. The nergy scaling of suchts are in fairly goodelectrons is measured and theby the wave breaking
agreement with those predic
tial distribution andtheory. Two dimentionaleelectrons reveal thatofhighevolution
temporal
rated from near the
hot electrons are successively
ier simulations [5,12].
critical layer as predicted in
2keV) electrons, low
After generation of high energy
in subcritical density
energy electrons are also
er than the criticalregion with plasma density(c). DrimNo. ltigh eirergy €*P' ^j.4density. Cavitons having ve ity transition fromsupersonic regime to subsonic gime have also been
well as in subcriticalobserved in resonance region
region after the generation of igh energy electrons.
Observed cavitons show density
6nln = 357o. where dn and n

fication as large as
the densitv depletionand mean plasma density
high energy electrons and cavi
scale in resonance and subcriti
shows that two different

vely. Generation of

"'0

1m

Fig. 1 (a) Experimental setup. (b) Electron energy dis-tribution function for different incident microwave
power. (c) Energy scaling law of high energy
electrons.

at two different time
I density region clearlyisms are acting simul-

analyzer of 23mm length and 1Omm diameter, capableof measuring electron energy upto 3keV, is employed

for measuring the electron energy distribution function.
All three electrodes of the energy analyzer (two grids
and one collector) are covered with a copper cup toshield from microwaves and other noises. Acylindricalprobe with a tip of lmm length and 0.25mm diameter isused to measure the spatial distribution of microwave
field. Pulsed microwave has a central frequency, al2n =9GHz (corresponding to cut-off density, ft" = | xl0r2cm-3) and maxmimum power, 250kW. The pulse

The paper is organized as follows: Experimental
2 and results arearrangment is described in
the results anddescribed in Sec. 3. Section 4
gaind
ns
due
to nonlinearbycalculates energy
lated in Sec. 5

2. Experimental Setup
The experimental arran

100

Ircident Power (kW)taneously.

wave breaking. The paper is

l0

yai

ment is shown sche-matically in Fig. 1(a). Cylindri , unmagnetlzed argon
ss-steel chamber ofplasma is produced in a stai
. Outside surface of thel00cm leneth and 32cm divacuum chamber is covered, for improved plasma
ngements, made from
confinement, with line cusp
rface magnetic fieldpermanent magnets having
ed by a pulsed disstrength of 4kG. Plasma is
m Hexaboride)
charge between four LaB6 (groundedwall acting as
bercathodes and theItage and dischargeananode. Typical discharge
respectively, with theduration are 180V and 1
plasma parameters are,repetition rate of 10H2. Typi
axial density gradient
fr.=2x l0l2cm-3, T.=ZeY
pressure is adjusted
scalelength, L,= 44cm. Atgon
Plasma density
valve.
xaneedl
10-3Torrbyto 3 - 5
a disk probe with area
and temperature are measured
is and rotatable in theof 0-96mm2, movable along
spatial resolution andazimuthal plane. To get

duration is variable from 1-3ps, full width at half
maximum (FWHM), with rise and fall time of 100ns
and repetition rate of 10H2. Present experiment isperformed with l.5ps. Microwaves are launched into
plasma from rectangular horn antenna, with aperturearea of 14.8 x 11.7cm2. This antenna contains a metaltime response, disk probe isused to measure spatial

distribution and temporal eution of high energy

electrons as well as cavi

Electrostatic energy

different incident power. It is identified clearly different,with bumps in tail showing presence of superthermalbeam, than that observed in earlier works [8,13] withlens for making ray trace of incident microwave parallelto the propagation direction. Thus, the microwave canbe considered as a plane wave and this has been
confirmed in air without plasma. The antenna is locatedat lower end of the plasma densitY.

3. Experimental Results
When high power microwave pulse is injected into
plasma, it is observed that high energy electrons areejected from the layer close to the critical layer' Theelectron energy distribution function measured by theelectrostatic energy analyzer is shown in Fig. l(b) for510

Rajyaguru C et aI., Observation of Superthermal Electron Beam and Cavitons in Broad Resonance
Resionnonthermal sholder. The scaling law of high energy
electron emission as a function of incident power isobtained as shown in Fig. l(c). It can be seen veryclearly that the maximum electron energy depends on
the incident microwave power as t x p0.4t. This is ingood agreement with that predicted by the wave
breaking theory as e n F.5 [7]. The power dependence

and calculation of electron energy for present
experiment will be given in the next section. The energy
scaling law and the nature of the distribution function
indicate that high energy electrons are produced mainly
due to nonlinear wave breaking.

tr45
()

For getting better physical insight of mechanisms
acting in the resonance region, spatial distribution ofhot

C)

3+o
o

electrons are measured and depicted in Fig. 2(a) and (b).

The dark spots in Fig. 2 indicate the loations where
maximum flux of high energy electrons is observed.
These locations and the one clearly visible at r

Q:s

= -2cmX

in Fig. 2(b), move deeper (towards the higher density) indro

axial direction and radially outward direction-505

respectively with increase in incident power. This isbecause of the deformation of plasma resonance region

Radial Distance (cm)in a strong high frequency field [14]. Interestingly,

Fig.2 Two dimentional contour map showing spatial
distribution of emitted high energy electrons foranother location can also be seen, more clearly in Fig.
2(a), around z=37cm and r= *6cm, where hot electrons
are generated. Observation of hot electrons ar rwo
different positions motivated us to investigate theirincident power of (a) 2b0kW, (b) EOkW.

temporal evolution. Accordingly, the temporal evolution(c)of high energy electrons at r = 6cm is shown in Fig.
3(b). It is clearly observed that hot electron bunches arewave onl g wave off.g

successively generated near the critical layer (7- 44cm)
for all times (40 to 540ns) during which incident
microwave is present. However another bunch of

s]

ol23
40 ns

Time (ps)electrons is observed at alater time around l80ns near z- 37cm, as compared to that observed near resonance0.

region, revealing that some other mechanism is also
operative in the lower density region.

140 ns
240 ns0. I

To explore the subcritical density region more

qJ

carefully, we have measured plasma density profile atdifferent times after microwave is launched indicating
caviton with density depletion as large as 6nln=35Vo as
shown in Fig. 3(d). The temporal evolution of caviton isshown in Fig. 3(c). Caviton is observed near resonancelocation as well as in subcritical density region, moving
with supersonic speed, slowing down gradually to
subsonic speeds. However caviton, observed near the

340 ns:'520ns30 35 40 45 50

Axial Distance (cm)30 35 40 45

Axial Distance (cm)50

Fig. 3 Temporal evolution of high energy electrons

measured by disk probe with applied bias voltageof -300V and cavitons at r= 6cm. (a) Microwave
electric field for 2b0kw (*), 1SokW ( o ), 50kW (O)and the density profile at r = 6cm (solid line).
(b) Temporal evolution of high energy electron
bursts at r= 6cm for incident power of 2bOkW.
(c) Temporal evolution of cavitons (O and x) r7y;16high energy electrons (o and +). Dotted line

resonance region, is observed to move faster than that inshows the sound velocity. (d) Typical caviton
structure observed in present experiment. Solidvertical line shows the location of the criticalsubcritical layer. It is also evident from Fig. 3(c) thatcaviton is formed after the generation of superthermal
electrons in the resonance region as well as in thedensity.
511

Rajyaguru C et al.,ation of Superthermal Electron Beam and cavitons in Broad Resonance Region

the spatial profile
subcritical region. Figure 3(a)of microwave field in plasma at r = 6cm as well as

plasma density in low inci
Enhanced electric field cregion can be seen clearlY to i
power. Presence of large
37cm in subcritical densitYt power (- lkw).

role modifying electron energy

stribution function andill be described in thegeneration of caviton which

nt at the resonancetime scale of ion motion. One can estimate maximum
energy of electrons as e = eE^u*Lx - eEaL, For the
optimum angle of incidence, using definition of E6
above formula can be written as/ '\t2lr \t =rf.'\"!cl\^o)T, \r"J l=l

with increase inelectric field at z =can play significant

As 4 * P (incident power), it can be seen that electron
5
energy depends on incident power as t * P0 as
predicted by the wave breaking theory. Substituting thepresent experimental parameters as 4 - 0.5, T"= 2eY
and electron rest mass energy mcz = 5l2keY, one gets €= 2.6keY which agrees very well with the experi-

next section.

4. Discussion
This section discusses

ing results quali-

mentally observed maximum electron energy of 1.8keV'
Now we discuss the phenomenon responsible forgenerationof high energy electrons near the region
thearound z = 3'7cm in Fig. 3(b). Although the exact
mechanism is not very well understood at present' somethe energy distribution
tatively. The observed naturefunction and the energy scali law as a function of theof wave breaking
incident power, are clear evi
electrons. In
phenomenon to produce thecollisionless plasma,case of high power radiation
linear mode conversion of inci nt radiation to plasma
wave is low efficiency proce ll4l. Also, it has been
ifications decrease theobserved that strong densitY
oscillating two stream
effect of other phenomena li
and ion acoustic decay instabi tes [8]. Thus, the inten-of the possibilities are considered. As the subcriticalregion, where high energy electrons are generated, isquite distant from the resonance region, possibility ofparametric instability can be ignored.

We believe that the strong microwave field(transverse electric fileld) component existing at z =37cm, as seen in Fig. 3(a), is responsible for non-nce reglon can, mostsified electric field in
breaking. Maximum
probably, be limited by wa

resonant excitation of plasma waves as the density atz = 37cm. This possiblity can not be ignored as theplasma density at z= 37cm is only l5Vo lower than that

amplitude of the electric field i the resonance region is
given by E^u* = Edlsnonl [l l, where Ed, the highto the vacuum
frequency field at resonance,Lr)tt2 and Snons = (eE6lfield, Es, by E6 = EsQG)/Q

at the resonance region. Various effects due totransverse RF field maxima have been investigated in
116,11l. Because of plasma inhomogenity, generated
plasma waves will have, in general, broader wave-, the amplitude
loation rises to its
maximum value very rapidl Consequently, energy
lon requlres contracconservation in the resonanceis leads to the situation
tion of the resonance width.
one oscillation period of
where electron displacement,
width given by A;
electric field, equals to thehigh energy
ejecting
wave
the
and
Snonrl.
=Il5l
resularelectron
that
maY
One
burst.
electron
is an
there
until
(throughperiod)wi
continuetheburstsma2Lr)tt2. Due to resonanceof the electric field at theappreciable energy loss due
particles. If these particles
amplitude at the resonan

maximum [5], after a time -radiation still exists, a

accelerated particles
generation of high energy e
the present experiment near t

breaking time is very shortbursts of high energy electcase. than the caviton format(1)

number spectrum as compared to the one in the resonance region which is confined in small resonancewidth. Here, one can imagine electrons making"swings" from the potential wells of waves withdifferent wavenumber gaining and loosing the energy'
leading to the resultant turbulent heating (nonresonant
heating) of the electrons. As the incident power is very
high, the plasma wave amplitude will be sufficiently
large, despite of its nonresonant excitation, to heat the

departure of accelerated
ve the plasma, the field

electrons. Electrons are accelerated to energies at least >300eV as temporal evolution measurements were taken

reaches again to its),Snon1, os the incident

series of bursts ofleading to successive

by applying retarding bias of -300V.

bursts as observed inresonance. As the wave
strong radiation [7], theobserved previously [9]. But in the present cas€, we see

appear earlier, in present
which occurs at the ion

observed near the resonance layer' moves with velocity
as high as 48 times greater than the sound speed.

Caviton moving with supersonic velocity has beencaviton generation at two different spatial locations
moving with different veloctiy' However, the one

5t2

Rajyaguru C et al., Observation ofSuperthermal Electron Beam and Cavitonsin Broad Resonance Resion

Whereas the one observed in the subcritical layer moves

initially with 8 times the sound speed slowing down
gradually to sound speed. This behaviour can be
attributed to the presence of hot electrons, greatly
modifying the local plasma pressure resulting inenhanced "kick" to the plasma density, in turn, leading
to higher velocities which ultimately slows down withdecrease in its amplitude. Mechanism responsible for thegeneration of caviton is not clear at present but strong

Calculation of maximum electron energy on the basis ofwave breaking model shows good agreement withexperimental observations. Spatial distribution andtemporal evolution of the high energy electrons also
show that the lower energy electrons > 300eV are
generated at a later time at a different location than theresonance region. Cavitons moving with a supersonic tosubsonicvelocity are observed.

transverse electric field near z = 37cm can playsignificant role in generating strong density modifications. This behaviour has been observed in earlier

Acknowledgement
We are deeply indebted to prof. N.E. Andreev andProf. M.I. Bakunov for their fruitful discussions. We
greatfully acknowledge Prof. p.K. Kaw for his valuablesuggestions. This work is partly supported by a Grant_
in-Aidfor Scientific Research from the Ministry ofworks [4,16,17].
Relation among the caviton in subcritical density
region, possible excitation of plasma wave and presenceof high energy elecrons need more careful examination
for a better clarification of the present observations.
Efforts are going on to measure two dimentional spatial

Education, Science, Sports and Culture of Japan. We arealso grateful to the cooperation Research Center,
Utsunomiya University, for partly supporting the present
experiment.

distribution of caviton as a function of microwave
power. Above measurement can be made after different
time from the microwave pulse to get the time resolved
bahavior. We can also make some density fluctuation
measurement and plasma wave measurements to see

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513