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Bragg scattering of electromagnetic wave by microwave produced periodic plasma layers

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O rder N um b er 911749S
Bragg scattering o f electrom agnetic wave by m icrowave
produced periodic plasm a layers
Zhang, Yong-Shan, Ph.D.
Polytechnic University, 1991
UMI
300 N. Zeeb R i
Ann Aibor, M I 48106
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Bragg Scattering of Electromagnetic Wave by Microwave
Produced Periodic Plasma Layers
DISSERTATION
Subm itted in P artial Fulfillm ent of the Requirements
for the Degree of
Doctor of Philosophy (Electrical Engineering)
a t the
Polytechnic University
ty
Yong-Shan Zhang
August 1990
Approved:
Head of Departm ent
Copy N o .
19.
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Approved by the Guidance Committee:
M ajor : Electrical Engineering
Spencer S. Kuo
Professor of E lectrical
Engineering
M em ber
vv v ^
W. C. Wang
Professor of Electrical
Engineering
M inor : Physics
Donald Scarl
Professor of Physics
A dditional Member
P»lPLlu,f
Bernard R-S. Cheo
Professor of E lectrical
Engineering
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•
M icrofilm or other copies of this
Dissertation are obtained from
UNIVERSITY MICROFILMS
300 N. ZEEB ROAD
Ann Arbor, M ichigan 48106
m
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V ita
Yong-Shan Zhang was bom in Nanjing, China on M arch 16,
1953. He
received
his undergraduate
diplom a in
E le c tric a l
Engineering in 1977 and M .S. degree in System Engineering in 1981
from N anjing In s titu te of Tdecom m unications, Nanjing, C hina. He
attended Polytechnic University in 1984.
From September, 1984 to
M ay, 1990 he was offered Research Fellowship and Assistantship in
the E lectrical Engineering Departm ent o f the Polytechnic U niversity.
He received his M .S. degree in Electrophysics in 1988
and pursued
his Ph.D. degree in Electrical Engineering under the guidance of
Professors S. P. Kuo, W . C. Wang, D . Scarl, and B. Cheo.
IV
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Dedicated
to
my wife Lili and my son Ting
and
my parents Mr. De Zhang & Mrs. Lan Qin Zhang; and my
parents in law Mr. Guan-Ron Xian & Mrs. Wei-Zhen Xian.
V
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ACKNOWLEDGEMENT
I am grateful to my dissertation advisor, Prof. S. P. Kuo for his support,
constant encouragement, patience and guidance. I am also grateful to Prof. W.
C Wang for his support, guidance and advices. M y sincere appreciation goes
to Professor D. Scarl and Professor Bernard Cheo for serving in my guidance
committee. Thanks are also due for M r. Antony Ho for his valuable help
with his knowledge in computer systems, and to all friendly colleagues in
plasma lab.
VI
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AN ABSTRACT
Produced Periodical Plasma Layers
ty
Yong-Shan Zhang
Advisor: Spencer S. Kuo
Subm itted in P artial Fulfillm ent of the Requirements
for the Degree of Doctor of Philosophy
(E lectrical Engineering)
August 1990
The feasibility of using artificial atmospheric plasma as a Bragg reflector
in the upper atmosphere to relay electromagnetic wave is studied. The
research includes three parts, (1) the generation of periodic plasma layers and
their reflectivity; (2) the lifetim e of plasma electrons; and (3) the propagation
of high power microwave pulse in air breakdown environment. The
experiments are performed in a Plexiglass chamber of two foot cube which
was fed dry air to a pressure comparable to the upper atmosphere. A pulsed
magnetron w ith peak power of 1 magewatt is used to deliver two microwave
vn
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beams at right angle into the chamber. A set of parallel plasma layers is
generated by die intersecting microwave pulses in die center region of the
chamber. The dependencies of breakdown conditions on die pressure and
pulse length are examined. The results are shown to be consistent w ith the
appearance of tail erosion of microwave pulse caused by air breakdown. A
Bragg scattering experiment, using the plasma layers as a Bragg reflector is
then performed. Both time domain and frequency domain measurements of
wave scattering are conducted. The experiment results are found to agree very
w ell w ith the theory. Moreover, the time domain measurement of wave
scattering provides an unambiguous way for determining the temporal
evolution of electron density during the first lOOps period. The results of
measurement show that the electrons decay initially at the attachment rate.
However, when enough negative molecule ions are produced through the
electron attachment process, die regeneration of electrons via detachment
process is increased and eventually balances out the electron attachment loss.
The net electron loss is then determined by the recombination rate. A
Langmuir double probe is then used to determine the decay rate of electron
density during a later time interval ( 1ms to 1.1 m s). The propagation of high
power microwave pulses is studied experimentally. The mechanisms
responsible for two different degree of tail erosion are identified. The
optimum pulse amplitude of an l.l(is pulse for maximum energy transfer
through the air is also determined. Using a forward wave approximation
model and a software package PDEONE in CRAY, the propagation of a high
power microwave pulse is also studied numerically. The numerical results
are shown to agree very well with the experimental results.
vm
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TABLE OF CONTENTS
■
■
Abstract
P
a 8
e
vn
List of Figures
x
L
Introduction
1
H
Bragg Scattering of Electromagnetic Wave by Microwave
Produced Periodical Plasma Layers.
8
2-1 Experimental Set-up and A ir Breakdown by microwave pulse
8
2-2 Wave Scattering from Periodical Plasma Layers
15
2-3 Bragg Scattering Experiment
24
m . High Power Microwave Pulse Propagation in the Atmosphere
31
3-1 The Experimental Study of Tail Erosion Mechanism
32
3-2 Theoretical Model
40
3-3 Computer Simulation
42
3-4 Discussion
51
IV . Lifetime of Plasma Generated by Microwave Pulse
55
4-1 The Electron Loss Process
56
4-2 Wave Scattering Measurement of Electron Density
58
4*3 Langmiur Probe Measurement
61
4-5 Discussion
66
V . Summary and Discussion
67
References
72
IX
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List of Figures
Figure 1~
OTH radar using artificial plasma patch as a
3
m irror
Figure 2.
Two crossed beams scheme
Hgure 3.
Plasma layers produced in the chamber
9
Figure 4.
Microwave pulse envelope and the induced airglow
10
.
5
(a) Envelope of a l.l|is microwave pulse
(b) Growth and decay of plasma glow measured
by an optical probe
Figure 5.
Dependence of air breakdown threshold field on
12
pressure for two different pulse lengths
Figure 6.
Pulse received after passing through the chamber at
13
different air pressure
Figure 7.
Top view of plasma layers produced in the chamber
16
Figure 8.
Probe measurement of the plasma density
17
distribution along the direction transverse
to the plasma layers. Measurement is from
X
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the central point x=0 of one layer to the midpoint
x=3*24cm to the next layer. The minimum density
102cm-3 is an estimated value
Figure 9.
The Plasma Slabs
19
Figure 10.
Configuration of wave scattering study
20
Figure 11.
The integration contour
22
Figure 12.
Experimental setup of periodical plasma layers
25
generation and Bragg scattering
Figure 13.
Spectrum analyzer CRT display
27
(a) No signal is received when plasma is off
(b) Spectrum of scattered signal when plasma
layers are present
Figure 14.
Time domain measurement of the scattered signal
28
and the microwave pulse used for plasma generation
(a) Growth and decay of scattered signal over IOOjjs
time domain
(b) 1.1 us pulse similar to that of Figure 4(a)
XI
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Figure 15.
The dependence of the reflectivity S of plasma
29
layers on wave frequency. Experimental and
theoretical results. The 0 dB on the vertical
axis is an arbitrary reference
Figure 16.
Experimental setup of high power microwave pulse
33
propagation
Figure 17.
Tail erosion of microwave pulses of four
34
consecutively increasing amplitudes
Figure 18.
Received pulses and corresponding reflected pulses
36
Figure 19.
The dependence of the normalized critical power
37
Pr/Pc on pressure for l.lp s pulse
Figure 20.
The growth and decay of enhanced airglow
39
(upper trace). 3.3jis pulses at two different power
levels Pi [for a] and P2 [for b] are used for causing
air breakdown, where P2 /P i=1-32. The lower trace
of each photo represents the time dependence of
the amplitude of the microwave pulse. The
horizontal scales are lps/d iv.
Figure 21.
Boundary condition and initial condition of the
44
simulation
XU
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Figure 22.
Tail erosion of microwave pulses for four
46
consecutive increasing amplitudes
(computer simulation)
Figure 23.
Two different degree of tail erosion
47
Figure 24.
(a) Microwave pulse envelop as a function of time
49
and space
Figure 24.
(b) Electron density as a function of time and space
50
Figure 25.
The temporal evolution of the intensity of die
57
scattering signal
Figure 26.
Numerical solution of electron density evolution
59
compared with experimental results
Figure 27.
Numerical solutions of electron density, positive ion
60
density and negative ion density
Figure 28.
Langmuir double probe measurement of temporal
62
evolution of electron temperature Te(t)
Figure 29.
The V -I characteristics of die Langmuir double
64
probe measured at four different times starting
at 1ms after the transmission of microwave pulses.
xm
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Figure 30.
The evolution of electron density from 1.0ms to
65
1.1ms after the microwave pulse
X IV
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Chapter L Introduction
Over the years, there have been continuous research activities in the
areas of modification of the ionosphere1-* and generation of artificial
ionosphere by high power electromagnetic wave?,8. W hile many researches
are aimed at understanding the basic physics, the application of mancontrolled ionosphere for improving communication systems is also under
investigation. One of the prospective application of artificial ionosphere is to
use it as a mirror for the OTH radar.
It is a well known fact that conventional line of sight radars are limited
by their range of detection. This limitation is removed, however, by over-thehorizon (OTH) radars9'10. OTH radars use ionospheric plasma to reflect
obliquely incident radar pulses back to the ground a distance away from the
radar site. The range of detection is, in general, from 1000 to 4000 km which is
far outside the range of line of sight (about 400km). Since the radar pulses are
coming down from the ionosphere, moving targets can be detected, in
principle, at any altitude. The extended range of detection of OTH radars can
also be used to monitor ships and oceans from a land base Moreover, OTH
radar can also be used for air traffic control in areas where the simple line of
sight radars can not reach. The above mentioned attractive applications of the
OTH radar in turn generate a great deal of concern on how to improve the
sensitivity of the OTH radar.
It is believed that the sensitivity of an OTH radar can be improved if
the capability of the OTH radar can be extended with respect to three major
factors. The first one regards the range of the radar. In order to avoid
cluttering in the radar return, a large clearance region which is proportional
to the height of the ionospheric reflector is required. Thus, OTH radar is, in
general, not reliable in a zone from 1000 to 2000 km which is still far outside
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the line of sight range. The next concerns the resolution of the radar which
depends strongly on the radar frequency. Since die peak electron density of
the ionosphere is about lt^ c n r3, the operating frequency of the OTH radar is
lim ited in the range from 6 to 30 M Hz. In addition, the long propagation
length also tends to degrade the resolution of die return. The last concern is
on die stability of the ionosphere, which varies from day to night. This
variation w ill affect the performance and reliability of the radar.
These concerns may be resolved if a reflector can be positioned at a
much lower altitude which is able to reflect radar pulses of much high
frequency. In addition, if the reflector is made artificially, its stability and
location are controllable. Two schemes have been proposed. Both schemes
use a high power rf breakdown approach for plasma generation. The rf pulses
used for air breakdown and plasma maintenance w ill be transmitted by
ground based phased array antennas. In the first scheme, only a single focused
rf beam w ill be employed to produce an ionization patch in the D region of
die ionosphere. The rf beam is required to be focused because the altitude is
w ell above the altitude of minimum threshold. Consequentiy, the cross
section of the beam at the patch altitude w ill be too small in comparison with
the Fresnel size, and a scanning process must be in cooperated in die
operation of the rf beam in order to enlarge and tilt the ionization patch. The
density of the patch is expected to be at the same level as that of the F-peak
(i.e. ne =106cm'3) and thus, the same radar (Le. existing OTH radar) can be
used in the operation. The schematic arrangement of this scheme is shown in
Figure 1. The radar resolution may still be improved since the reflector is
located at a much lower height The major technical difficulties of the scheme
appear to be how to uniformly enlarge and tilt the ionization patch.
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ionosphere
1000-1200 km
2000 km
6-30 M H z ( radar frequency)"
Ile=10E6
Figure. 1 OTH radar using artificial plasma patch as a mirror
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The second scheme can, however, remedy these difficulties. Two
crossed beams are proposed to be used for plasma generation in their
intersection region, at an altitude between 30 and 60 km11-13. The interference
between the fields of the two beams enhances the peak field amplitude and,
thus, reduces the required power level of each rf beam. This, in turn, helps to
reduce the propagation loss in pulse energy before the two beams intersect. In
fact, more energy w ill be delivered to the destination because the pulse tail
erosion problem can be almost completely suppressed, especially when the
intersection altitude is chosen to be near 50km (1 torr pressure)11 where the
breakdown threshold is minimum (so that the most effective ionization
patch can be achieved). Such a low altitude can be used because the ionization
patch w ill be tilted automatically to a large angle (the average of the
propagation angles of the two beams). Moreover, the ionization patch consists
of a set of parallel plasma layers which are the consequence of interference
between the fields of two beams. In the intersection region, field amplitude
varies periodically in space in the direction perpendicular to the plane
bisecting the two beams. Using Bragg reflection to replace conventional
plasma cutoff reflection, the supplemental radar can then be operated in
much high frequency. Using this scheme, the location of the ionization layers
can also be fixed easily. A schematic of the scheme is shown in Figure 2.
There are three major issues related to the crossed beams scheme. The
first one is the effectiveness of the periodic plasma layers as the mirror of the
incident electromagnetic wave. The plasma layers generated by the crossed
beams have very high spatial gradient, and the wave impinging on it is
expected to have partial reflection from each of the plasma layers even the
wave frequency is above the electron plasma frequency. These reflected waves
interfere each other and have constructive interference under the Bragg
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5
30-60km
300 MHz radar frequency
Figure. 2 Two crossed beams scheme
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scattering condition. The Bragg scattering coefficient w ill be derived
analytically and measured experimentally. A comparision between the
analytical result and experimental measurement w ill be made to assess the
first issue. The second issue is the effective transmission of microwave energy
from ground to designated region. When high power microwave pulse
propagating in the atmosphere, the breakdown of air w ill occur if the wave
field is higher than the air breakdown threshold. Once the breakdown occurs,
the electrons w ill build up to cause the tail erosion of the propagating pulse
and the loss of pulse energy. Therefore, the ionizing pulse should be carefully
designed so that it w ill experience minimum energy loss before reaching the
designated area. The successful modeling supported by experiment study and
computer simulation are vital for choosing the optimum parameters for the
ionizing pulse. The third issue is how long w ill the plasma layers remain
after the microwave pulse is off. For practical purpose, one would have to
keep the electron density above the 107cm"3 level for radar detection period
(~lsec). It could be done by repetitive pulses. However, if the plasma decays
very fast, one would have to increase the duty cycle of microwave facility
(i.e.the repetition rate of the pulses). It implies that more power is needed in
the operation. This is then translated as that more expensive microwave
facility w ill be required and more running cost w ill be resulted. On the other
hand, if plasma is shown to have desired long lifetim e, the current
technology is already ready for required specifications. The design of the
system become straight forward and more important, the whole system can be
justified to be economically feasible and competitive. These three major
issues can be summarized as following:
1) the effectiveness of the plasma layers as a Bragg reflector.
2) the propagation of high power microwave pulse (HMP),
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7
3) the lifetime of the plasma.
In the follow three chapters, the results of experimental investigation,
theoretical modeling, and computer simulation of the physics problems
associated w ith the three major issues w ill be described. This work is
summarized and discussed in chapter V, in which the suggestions for further
work are also given.
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8
Chapter n .
Bragg Scattering of Electromagnetic Wave by Microwave Produced Periodical
Plasma Layers.
The intensity of wave scattered off from a periodic structure varies
w ith frequency and incident angle. This is because die components of the
wave reflected from different layers of the periodic structure w ill interfere
each other due to their relative phase differences. Strong scattering through
constructive interference occurs when the Bragg scattering condition
2dsin0=nX, is satisfied. We, therefore, expect to observe strong scattering of
electromagnetic wave by a set of periodic plasma layers. An experimental
investigation for the observation is conducted. The plasma layers are
produced by two crossed microwave beams. The results of measured
scattering coefficient w ill be compared with the theory derived from a simple
model.
2.1. Experimental Set-up and A ir Breakdown by Microwave Pulses
Experiments14 are conducted in a large chamber made of 2 foot cube of
Plexiglass and filled with dry air to a pressure corresponding to the simulated
altitude. The microwave power is generated by a single magnetron tube
(OKH1448) driven by a soft tube modulator. The magnetron delivers 1
megawatt peak output power at a center frequency of 3.27 GHz. The
modulator uses a pulse forming network having a pulse width which can be
varied from l.lfis to 3.3gs with respective repetition rates from 60 to 20 Hz.
Two microwave beams are fed into the cube, w ith parallel polarization
direction, by two S-band microwave horns placed at right angles to the
adjacent sides. The plasma layers are then generated in the central region of
the chamber where the two beams intersect Shown in Fig. 3 is a photo of the
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Figure 3. Plasma layers produced in the chamber
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(a) Envelope of a l.lp s microwave pulse
200ns/division
(b) Growth and decay of plasma glow measured
by an optical probe, ljis/division
Figure 4. Microwave pulse envelope and the induced airglow
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plasma layers which are manifested by the enhancement of airglow from the
corresponding locations. A maximum of eight layers can be generated,
thought only seven of them are shown in the photo. Shown in Fig. 4(a) is the
typical envelope of a l.lp s pulse used for plasma generation. Using a focusing
lens to localize the enhanced airglow, its temporal evolution between the two
consecutive pulses is then recorded on die oscilloscope through a
photomultiplier tube. A typical result is shown in Fig. 4(b), which shows the
growth and decay-of the enhanced airglow. Breakdown of air15*19 was detected
either visually, as the first sign of a glow in die chamber, or as die distortion
in the shape of the pulse received by the horn placed at the opposite side of
die chamber. The dependence of the breakdown threshold field as a function
of the pressure is then measured. The microwave field is measured by a
microwave probe which has been calibrated by a known waveguide field.
Shown in Fig. 5 are the Paschen breakdown curves for die cases of l.lp s and
3.3ps pulses. Since a shorter pulse requires a larger ionization rate in order to
generate the same amount of electrons, the threshold field is, therefore,
accordingly increased. This tendency is clearly demonstrated in Fig. 5. It shows
that die breakdown threshold field for l.ljis pulse is always larger than that
for a 3.3gs pulse. The results also show that in both cases, the breakdown
threshold field decreases w ith a decrease in air pressure and reaches a
minimum in the 2 to 1 torr region where <*>=Vc; co and vc are the microwave
frequency and the electron-neutral collision frequency, respectively. W ith a
further decrease in the pressure, the breakdown threshold field increases
again. The increase of the threshold field happens also because the wave is in
the pulse mode. The ionization frequency and collision frequency are
proportional to the neutral density; lower pressure requires a larger field in
order to maintain the ionization frequency.
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E(volts/cm)
a 3.3 j j l s
o 1.1/as
f =3.3 GHz
10
0.01
1.0
0.1
10.0
100.0
p(Torr)
Figure 5. Dependence of air breakdown threshold field
on pressure for two different pulse lengths
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13
a
m
■ —
m
—
m
Ml
m
—
1
—
m
m
m
m
E
rn
(a)
P= 8
ton-
Cd)
P= 4
ton
(b)
P= 6
ton
(e)
P= 2
ton
(f)
P= 1
torr
_
_
_
_
■E3:
(f)
P= 5
ton
Figure 6 (a - f)
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14
(g) P = 0.45
torr
(j)
P = 0.07
torr
JSOnS
(h) P = 0.2
to n
(k)
P = 0.05
torr
Figure 6 (g - k)
200nS
(i)
P = 0.1
torr
Figure 6. Pulse received after passing througth the chamber at
different air pressure
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15
The dependence of the breakdown threshold field on the pressure is
also manifested by a similar dependence of the degree of attenuation in the
ta il portion of a single transmitted pulse through the chamber. The
experiment is performed by reducing the chamber pressure consecutively
from 8 torr to 50 m torr, while the incident pulse is fixed at constant
amplitude. A series of snap shots demonstrating this behavior is presented in
Eg. 6. L i flie high pressure region (> 8 torr ), the breakdown threshold field is
higher than that of the incident pulse, and therefore, very little ionization can
occur; thus, the pulse can pass through the chamber almost without any
distortion (Rg.6(a)). However, as the pressure drops, the breakdown threshold
also decreases before reaching the minimum, and hence, more ionization
occurs and so does more distortion to the pulse (Fig. 6(b)). The distortion
always starts from the tail portion of the pulse (i.e. tail erosion) because it
takes finite time for the plasma to build up and thus, maximum absorption of
pulse energy by the generated electrons always appears in the tail of the pulse.
Consequently, the leading edge of the pulse is not affected. Between 2 to 1 torr,
the pulse appears to suffer maximum tail erosion and hence only the very
narrow leading edge of the pulse can pass through the chamber (Fig. 6(c)). The
tail erosion becomes weak again for a further decrease in the pressure ( Fig.
6(d)) and eventually vanishes (Fig. 6(e)) once the pressure becomes so low (<
0.05 torr) that the breakdown threshold power exceeds the peak power of the
incident pulse.
2.2 Wave scattering from periodical plasma layers
Shown in Figure 7 is a photo of the plasma layers taken from the top of
the vacuum chamber. The spatial distribution of the plasma layers is
measured with a Langmuir double probe. This is done by using a microwave
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Figure 7. Top view of plasma layers produced in the chamber
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17
2-
LOG(N0) CM“;
\
5*
1
— i— i— — i— i—
0.00
0.65
—
1.30
i— i—
—
1.95
i— i— - — i— i—
2.59
3.24
X (CM)
Figure 8. Probe measurement of the plasma density distribution
along the direction transverse to the plasma layers.
Measurement is from the central point x=0 of one
layer to the midpoint x=3.24 to the next layer. The
minimum density 10E2 is an estimated value
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phase shifter to move the plasma layers across the probe. The peak density
distribution for a spatial period is thus obtained and presented in Figure 8.
The result shows that we have indeed produced very sharp plasma layers
with very good spatial periodicity.
W ith die experiment result, we can establish a theoretical model to
simulate the plasma layers by a set of parallel slabs as shown in Fig. 9.
Assuming that the slabs are infinite in length in x and y direction, the
dielectric constant* of the medium is simplified to be an one dimensional
function given by
N -l
_
_
e(z) = 1 + (e !-l)£ [U(z-nd) - U(z-nd-A)]
N -l
B=0
_
_
= 1 + a £ [U(z-nd) - U(z-nd-A)]
n=0
22-1
Where U(p) is an unit step function defined by
(
0 p<0
u(p) = _
.1 p > 0
c. - i
and
<4
cu(aH-iv)
The wave scattering is studied by the arrangement as shown in Fig. 10, where
the incident wave from left of the plasma is polarized parallel to the plasma
slabs. Thus both reflected and transmitted waves are also polarized to the
plasma slabs, and hance, the total wave electric field can be expressed to be
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19
S
H
R
l
\ . --" '
■^
Figure 9 The Plasma Slabs
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20
m
E Direction
Figure 10 Configuration of Wave Scattering Study
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E(x,z,t) = y ei(k<hX• ^ECz)
22.-2
substitute 22-2 into the wave equation, yields
a2
r
21
2
E(z) - ki-Se-E (z) = -
dz2
c2i
_
—
[U(z-nd) - U(z-nd-A)]E(z)
c2 S
22.-3
where the RHS. of-2.2-3 contributes to the wave scattering.
We now set E(z)=EineikozZ + Ei(z) in Eq.(2Z-3), the RHS of Z2-3 is
decomposed into two terms if scattering is not too strong, lE i/E in l is small
and the scattering term contained by Ei on the RHS of Z2-3 can be neglected.
We can then expand the resultant equation into two equations, one for Ein
and one for Ei(z). The one for Ejn leads to the dispersion relation fflo =
and
the other one for Ei is given by
Ei(z) + kijEj = - k ? c £ [U(z-nd) - U(z-nd-A)]EineiW
2 .2 -4
Taking Fourier transform, 2.2-4 becomes
[k 2- ^ ] e ,( k ) = 2 S
22-5
and we have
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22
22.-9
Taking the inverse Fourier transform, along the loop given in Figure 11
we have the solution:
r-*~>
,N-1
ejkz
B .w -a a -E B .
2itc21>=0
2_
k -k z
e-Xk-kzXnd-4 ) d k
22-10
or
r+~
,N-1
_gPn_ ^
E i (z) = « ^ - £ e
^ 2 n=0
k+ k z
2
J e-j{k-k2Xnd+|) ^
(k - kzf
2 “
22-11
and
E r = j a a | Ein_ s m M y 1 ^ ^ + 5 )
2c2
k2
S
22-12
notice that
N-l
£
n=0
gjkz(2nd+8) _ gjM .] _e2jkz<N
l^ jk z d
22-13
we have
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A
-k .
Im{k}
I
Re{k}
z<0
Figure 11 The integration contour
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E, = -fo-Q sin M ) sin(Nkzd) ^ (N -ijd + 8] £;„
2c2
kf
sin(k2d)
the ratio of the reflected power to the incident power is
Pr _ Er 2 -/flLptt£
12/ c4
Pin Ein
.
sin(k28) 2 sin(Nk2dJl2
k§ . . sin{kzd)
23. Bragg Scattering
Presented in Fig. 12 is a block diagram of the experiment setup. In
addition to die facility used for plasma generation (located to the left of the
Plexiglass chamber), a sweep microwave generator (4-8 GHz) is used to
generate a test wave which is incident into the chamber through a C-band
horn. The incident angle of the test wave w ith respect to the normal of the
plasma layers is 45 degrees, hence, the S-band horn #2 located at a right angle
to the adjacent side can be used as die receiver of the Bragg scattering test
wave. In order to separate the Bragg coherent reflection mechanism from the
cutoff reflection mechanism, the test wave is swept in a frequency range
much higher than the plasma cutoff frequency. Consequentiy, the test wave
w ill be received by the S-band horn #1 even while the plasma is present. The
amplitude of this undesired signal is reduced by using a directional coupler,
nevertheless, it represents a large noise to the real scattering signal. To
resolve this problem, a standard noise cancellation technique is used. The
microwave components used for noise cancellation are shown in the diagram
(Fig. 12). An HP spectrum analyzer (8569B) is used for recording the scattering
signal. It is noted that the attenuation of the directional coupler is frequency
dependent. Only test waves w ith frequencies leading to mare than 15 db
attenuation of the directional coupler are used in the experiment.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to vacuum pump
dry air in
H3
H2
phase
shifter
HI
oscillator
F=3.3GHz
microwave
directional coulper
generator
scope
trigger out
pulse
spectrum
analyzer
generator
trigger in
Figure 12. Experimental setup of periodical plasma layers generation and Bragg scattering
Consequently, the perturbations of the noise signal due to the presence of the
plasma, which in principle is in the same intensity level as the scattering
signal, is reduced by 15 or more db and w ill not affect the measurement of the
Bragg scattering signal
Presented in Fig. 13 are the outputs of the spectrum analyzers for two
cases. Fig. 13(a) shows that no signal is received when there is no plasma.
However, an appreciable scattering signal is detected, as shown in Fig. 13(b)
whenever the plasma layers are produced. The frequency of the test wave is
4.01 GHz, which is much higher than the cutoff frequency. A clear signature
of Bragg scattering has been demonstrated. The temporal evolution of the
scattering signal has also been measured. The result for a test wave with
frequency 5.5 GHz is presented in Fig. 14(a). For comparison, one of the two
microwave pulses ( both are l.lp s ) used for plasma generation is shown in
Fig. 14(b). As one can see, the scattering signal continues to persist for about
IOOjis after the breakdown pulses are turned off. This result indicates that the
coherent scattering process can be very effective even when the plasma is well
below (= 2 order of magnitude) the cutoff frequency of the test wave. By
sweeping the test wave frequency, such a dependence is determined
experimentally in a relatively small frequency range (4.3 GHz to 7.8 GHz) and
presented in Fig. 15. For comparison, the reflection coefficient (Eq. 2.2-15) is
also plotted as a function of the test wave frequency in Fig. 15. The frequency
dependencies of output intensity of the sweep generator and the antenna gain
of the receiving horn (S-band hom#2) have been examined and taken into
account in calibrating the intensity of the scattering signals. Though a
maximum eight layers can be produced, only three of them have significant
overlap along a line of sight. Therefore, only these layers can significantly
contribute to the Bragg scattering process. Besides an uncalibrated absolute
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:■=
4 .-v « r -> :
SE* -31 iSr.
. SP6H 5 fH r/
3 aa
RES BU 100 iH :
ATTtN 10 as
\.R .3 ■
sIP .3 S»c
(a) No signal is received when plasma is off
> :
S F ttt 3 m :
3 :S
■ PSS B J ICC
wTTHN 1'0 5 s
ph;
S J5 .5 sec
(b) Spectrum of scattered signal when plasma
layers are present
Figure 13. Spectrum analyzer CRT display
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(a) Growth and decay of scattered signal
over 100p.s time domain
(b) 1.1 jis pulse similar to that of Fig.2a
Figure 14. Time domain measurement of the scattered signal
and the microwave pulse used for plasma generation
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20Log(E r/E i)
22.0
-
42.0
-
62.0
-
82.0
REFLECTITY
-
-
102.0
5.27
6.27
7.27
FEEQUENCY (GHz)
Figure 15. The dependence of the reflectivity S of plasma layers
on wave frequency. Experimental and theoretical
results. The 0 dB on the vertical axis is an arbitrary
reference.
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magnitude, the two functional dependencies are shown to agree w ith each
other very well. It is noted that the separation d between the two adjacent
plasma layers is related to the wavelength Xo of the microwave pulse and the
angle <f>between the propagation directions of die two intersecting pulses,
with the relationship d=Xosin(<j>/2). Using the Bragg condition 2dsin9=nXs the
optimum frequency for Bragg scattering is given by
fs=nfosin((j>/2)/sin6
Z3-1
In the present experiment <j>=90° and thus fs=nfo, this indicates that the
frequency of the test wave, which satisfies the Bragg condition for the current
experimental arrangement, is equal to the frequency and its harmonics of the
breakdown pulses. Consequently, die breakdown wave can not be filtered out
and represent a very strong noise, which prevents any meaningful test of
Bragg scattering at these frequencies, and in fact, also in the neighborhood
frequency regions. Although the optimum frequency region for Bragg
scattering is not examined, nevertheless the consistency between prediction
and experimental results may lead us to conclude, based on the maximum
theoretical reflection coefficient, that plasma layers can indeed be an effective
Bragg reflector, especially if more layers can be produced for scattering
purposes.
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Chapter m
High Power Microwave Propagation in the Atmosphere
The propagation of high power microwave pulses through the
atmosphere has been a subject with considerable scientific interest20*-26. This
is because air breakdown produces ionization phenomena that can radically
modify wave propagation. Ionization gives rise to a space-time dependent
plasma which attenuates the tail of the pulse but hardly affects the leading
edge because of the finite time for the plasma to build up. A mechanism
which is called "tail erosion" plays the primary role in lim iting transmission
of the pulse20-24. Moreover, the nonlinear and non-local effects brought
about by the space-time dependent plasma also play important roles in
determining the propagation characteristic of the pulses25. Basically, there are
two fundamental issues to be addressed. One concerns the optimum pulse
characteristics for maximum energy transfer through the atmosphere by the
pulse. The second concern is maximizing the ionizations in the plasma trail
following the pulse. In general, these two concerns are interrelated and must
be considered together. This is because in order to minimize the energy loss
in the pulse before reaching the destination, one has to prevent the
occurrence of excessive ionization in the background air. Otherwise, the
overdense plasma can cutoff the propagation of the remaining part of the
pulse and cause the tail of the pulse to be eroded via the reflection process.
This process is believed to be far more severe fy causing tail erosion than the
normal process attributed to ionization and heating. Once this process occurs,
the remaining pulse w ill become too narrow to ionize dense enough plasma.
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3-1. The experimental study of tail erosion mechanisms
Experiments have been conducted w ith a large chamber made of
Plexiglass filled with dry air at various pressures. A microwave pulse is fed
into file cube by an S-band microwave horn placed at one side of die chamber.
A second S-band horn placed at the opposite side of the chamber is used to
receive the transmitted pulse.The chamber is shielded w ith microwave
absorbers so that the microwave reflection from the walls and nearby
structures can be minimized. Shown in Figure 16 is the block diagram of the
experimental setup.
Tail erosion is a common phenomenon appearing in the propagation
of a high power microwave pulse (HMP). This phenomenon is demonstrated
by the snap shots presented in Figure 17, where l.lp s pulses, w ith four
consecutively increasing amplitudes, are transmitted into the chamber of 1
torr pressure from one side and received at the opposite side. The first pulse
has amplitude below the breakdown threshold, and hence, nothing is
expected to happen. Consequently, the received pulse shape as shown in
Figure 17 (a) is undistorted from that of transmitted pulse. Once the
amplitude exceeds the breakdown threshold, more tail erosion occurred to
the larger amplitude pulses,as is observed by the subsequent three snap shots
[Figures.l7(b) - 17(d)]. This is because the increase of the ionization rate with
field amplitude allows more electrons, which attenuate the pulse, to build up.
Now let's focus on the last two pictures [Figures. 17(c) and 17(d)]. Pulses have
been eroded strongly in both cases. However, a clear distinction between the
two cases is noticed. In one case corresponding to the third picture
[Figures.l7(c)], the erosion to the tail of the pulse is not complete. In other
words, the received pulse width extends to the original width. In the other
case [Figure. 17(d)], a large portion of the pulse is more or less eroded
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
screen room
to pump
directional
coupler
magnetron
oscillator
3.27 Ghz
F T -
microwave
absorber
transmitting
hom
dry air
receiving
horn
- F I
crystal
detector
attenuator
§
a
crystal
detector
generator
trigger
crystal
detector
power
photomultiplier
tube
□
Figure 16. Experimental setup of high power microwave pulse propagation
u>
Figure 17. Tail erosion of microwave pulses of four
consecutively increasing amplitudes
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completely during the finite propagation period. Obviously it is a different
mechanism responsible for the second case. The ionization frequency
becomes so large in the second case that the electron density exceeds the cutoff
density of the wave before the whole pulse passes through. The overdense
plasma screen reflects the remaining portion of the pulse and causes even
more severe tail erosion, h i summary, two mechanisms responsible for the
tail erosion are identified27. One is due to attenuation by the self-generated
underdense plasma. The other one is caused through reflection by die self­
generated overdense plasma screen. These two processes are also verified by
the reflected power level measured for each case. As shown in Figure 18, the
snap shots [Figures 18(b) and 18(d)] presented on the RHS of the Figure are the
reflected pulse shape corresponding to each received pulse on die left [Figures
18(a) and 18(c)]. As shown by the last set of pictures [Figures 18(c) and 18(d)],
strong reflection and complete erosion are observed consistendy.
In order to avoid cut off reflection, the power of the pulse should be
lower than a critical power Pr which is defined as the minimum required
power for generating an overdense plasma screen. When an overdense
plasma screen is formed the shape of the reflected pulse changes drastically
and can be monitored easily. Thus, the critical power Pr can be determined.
This critical power varies in general w ith the pressure. Measurements are
made to determine this functional dependency as shown in Figure 19, where
P=Pr/Pc is the critical power normalized to the breakdown threshold power
Pc which has been presented in Fig. 5. Due to the limited available microwave
power, only region of 0.2 to 10 torr is examined. Outside this pressure region,
the breakdown threshold power becomes too high to be exceeded by the
maximum output power of our microwave source. Nevertheless, this is the
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36
Figure 18. received pulses and coresponding reflected pulses
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3.50
P r/P c
3.00
2.00
1.50
0.00
2.00
4.00
6.00
8.00
10.00
P (torr)
Figure 19. The dependence of the normalized critical power
Pr/Pc on pressure for l.ljis pulse
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38
pressure region of main concern because air breakdown has its lowest
threshold.
The study indicates that an increase of pulse amplitude may not help to
increase the energy transfer by the pulse. This is because two tail erosion
mechanisms are at play to degrade the energy transfer. A demonstration is
presented in Figure 20, where the growth and decay of airglow enhanced by
electrons through air breakdown by 3.3ns pulse are recorded for two different
power levels, h i Figure 20(a) the power level is below the critical power and
the airglow grows for the entire 3.3ps period of the initial pulse width. As
power is increased beyond the critical value, the initial growth of the airglow
becomes faster as shown in Figure 20(b). However, it is also shown in Figure
20(b) that the airglow saturates at about the same level as that of Figure 20(a).
Moreover, die airglow already starts to decay even before die 3.3ps period. In
other words, cutoff reflection happening in the second case limits the energy
transfer by the pulse. The additional energy added to the pulse is wasted by
reflection. A practical way to solve this problem is either to lower the
amplitude of the pulse or to narrow the pulse width so that the propagation
loss can be minimized. However, the ultimated way is to determine the
optimum parameters for the pulse in order to achieve effective ionization..
Unfortunately, this question can not easily be answered by the chamber
experiments. This is because the effect of pressure gradient and large
propagation distance can not be incorporated in the investigation.
Nevertheless, the understanding of the fundamental behavior of tail erosion
and the set of experimental data obtained should be very useful for guiding
the development of a practical theoretical model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
(b )
Figure 20. The growth and decay of enhanced airglow (upper
trace). 3.3jis pulses at two different power levels Pi [for a] and
P2 [for b] are used for causing air breakdown, where
P2/P i =1.32. The lower trace of each photo represents the time
dependence of the amplitude of the microwave pulse. The
horizontal scales are lps/div.
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3-2 Theoretical model
The high power wave propagation in air breakdown environment can
be described by the Poynting equation for the wave
V~£- (E X B )+ A (E2+B2)/8 ic= -J-E
4n
dt
32-1
the rate equation for the electron density
9t
= (V i-va) n - m 2
32-2
and the momentum equation of electrons
|^v T=
“- ^f - - tV+Vj+Va
(v+Vi+va)V
) V=
= -- ^f - - -v vvV
3.2-3
where r is the recombination coefficient, v, Vi, and va are collision frequency,
ionization frequency, and attachment frequency respectively, and v=v+Vi+va
We now express the wave field and the velocity response of the
electrons as
E = Eoe-i®1+ c.c.
—*
V = Voe-i<Bt + c.c.
32-4
^
where Eo and Vo are the vector phaser amplitudes.
Substitute 3.2-4 into 3.2-3, yields
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Thus, the induced current density is derived to be
- 2 (7+£ +k0> J = - enV=e-*>tnsi.—
------ e 0+ c.c.
(v + p +©2
2
^ ----- (v + ^ + i© )^ + c.c.
4j i (©2+v 2)
*
= e-i©t
where we have neglected
32.-6
terms in the denominator of 3.2-6 for a slowly
time varying function Eo.
Taking time average of J-E over one cycle of the wave, we obtain
(?-e ) =-----^ -----(v+ll-)E§
87t(ffl2+v2)
2dt
$2-7
The time average of Eq. 3.2-1 then becomes
Bo+ 1h— —£ ]e?
©2+v2
8 jc(© 2+ v 2)
3.2-8
Defining
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\
(02+ V 2/
32.-9
and
s = £ E qBq=^-Eo(l- cdM ^ + v2))1^
3.2-10
where P and S are the energy density and power flux of die wave respectively.
We finally reduce the Poynting equation to
3.2-11
where P = v c o ^ + v 2) ^
Vg= c[l- c o ^ + v 2)]172
Equation 3.2-11 is coupled w ith Eq. 3.2-2 through the ionization
frequency Vi. These two equations give a self consistent description of pulse
propagation in an air breakdown environment.
3-3 Computer Simulation
In terms of the normalized variables:
n=SL’ P=£ ’ X = V \^ t,z '
Equations. 3.2-11 and 3.2-2 become
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43
^ = -J S 'n P -iTyi5p
dx
VVa
3z
3.3-1
and
? = ^ { 3 .8 2 x l0 2[? /4+3.94P1/4]exp[-7.546^1/2]-l|n
3.3-2
where die recombination loss term in 3.2-2 is neglected and the ionization
frequency28 is given by
vi=3.82xl02[p3/4+3.94P1/4]exp[-7.546/P1/2]
3.3-3
Considering a pulse whose initial envelope is given by
Po=P{T,o)=Poe-(^)1()
33-4
where ^0~ Vvcvato/2 is the normalized pulse width, to is pulse width and for
this simulation to = l-ljx s.
To solve the Eqs. 3.3-1 and 3.3-2 numerically, we used a software
package developed by Richard F. Sincovec and N ile K. Madsen29 for nonlinear
partial differential equations. This package is an interface routine which uses
centered difference approximations to convert one dimensional systems of
partial differential equations of die form
< £ = F ( t ,x ,u ,< £ < £ *)
dt
dx dx2
33-5
into an explicit system of first order differential equations of the form
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
cto
t= -to /2
\ft
to
t=to/2
Figure 21 Boundary and initial condition of the simulation
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
f i = F (t ,x ,u )
at
33-6
Then it utilizes the widely used ODE integrator subroutine30"32 to solve these
partial differential equations by calculating the tim e derivatives of the
functions at mesh points from neighboring spatial points and integrating in
time domain to get the solution. This program is written in FORTRAN and
can be run on Cray in Pittsburgh Super Computing Center.
The boundary condition and initial condition for the pulse energy are
best shown as in Figure 21. The initial condition of electron density is n=ngfor
all z; and die density at the boundary w ill be determined from P(t, z=0) with
the restriction of it< l. The differential equations are solved in a two
dimensional surface determined by z and t axes. The number of the mesh
points are chosen so as to minimize the numerical error. For die results
shown here, we have N m=1000, N t=1000.
Figure 22 shows the different degree of tail erosion for four different
intensity of incident pulse intensities (P<n=l' Pa2=4/ Pc3=7' P«=9) propagating
over a same distance (x=66cm) as the experiment, where the vertical axis
represent pulse amplitude (Ai=Pn2). Comparing these plots w ith the
corresponding experiment results presented in Fig. 17, good agreement is
observed.
Similar to the experimental observation, die numerical results (Fig. 22)
of tail erosion phenomenon also reveals two distinct features. In order to
stand out these two features, the transmitting pulse intensities corresponding
to Figures 22(b) and (d) are presented together in Figure 23 for comparison.
The pulse envelope represented by trace A shows a linear decay starting from
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46
1.20
2.00
1.00
1 .5 0
LlI
-1 0 .6 0
1.00
0 .4 0
0.20
-1 5 .0 0
-1 0 .0 0
-5 .0 0
0 .0 0
5 .0 0
1 0 .0 0
1 5 .0 0
0.00
-1 5 .0 0
tim e
-1 0 .0 0
-5 .0 0
0 .0 0
5 .0 0
1 0 .0 0
1 5 .0 0
TIME
3 .0 0
2 .5 0
2.00
Ll I
Q
1 .5 0
— i 1 .5 0
2
1.00
1.00
0 .5 0
0 .5 0
30 I n m i i i ii i i n i r n i r n n 1 n n 1 1 1 »i1i n n n t i t t h i i p n 11 m i
-1 5 .0 0 -1 0 .0 0
-5 .0 0
0 .0 0
5 .0 0
1 0 .0 0
1 5 .0 0
tim e
-1 5 .0 0
-1 0 .0 0
-5 .0 0
0 .0 0
5 .0 0
1 0 .0 0
1 5 .0 0
t im e
Figure 22. Tail erosion of microwave pulses for four
consecutive increasing amplitudes (computer simulation)
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6 .0 0
5.00
4.00
CL 3.00
2.00
1.00
0 . 0 0
—j
t
1111 m
- 1 5 .0 0
-i j
i i
i i
-1 0 .0 0
111 i i
J111 u
- 5 .0 0
1111 p
11
0.00
5.00
oo
time
Figure 23. Two different degree of tail erosion
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the front portion of the pulse (in this case the incident pulse intensity Po=4).
This decay is solely due to the absorption of the pulse energy by the plasma,
and the electron density generated by the pulse never reaches the cutoff
density. In contrast, the pulse envelope represented by trace B shows a sharp
drop in the amplitude rather than a gradual decay (in this case the incident
pulse intensity Po=9). This is because the electron density already reaches the
cutoff level before the pulse completely passes through the incident
boundary) and the cutoff reflection causes more severe tail erosion as shown.
This again confirms w ith the experimental results shown in Figure 18, where
two received microwave pulses with above-mentioned two different features
of tail erosion has been recorded.
The good agreement between the numerical simulation and the
experimental results suggests that Eqs 3.2-2 and 3.2-11 represent a very good
theoretical model for describing high power microwave propagation in air
breakdown environment. Thus, the numerical solutions of these two modal
equations can provide additional information about die spatial variations of
the pulse energy and electron density which are not easy to be measured
experimentally.
Shown in Figures 24 (a) and (b) are the three dimension drawings of
pulse amplitude and electron density versus space and time for the case of
pulse amplitude Po = 15, and the initial electron density n = It^cm -3. It shows
that the the electron density w ill rise very rapidly at die boundary to reach the
cutoff density n = 1, and thus to form a high density thin layer. This high
density electron layer w ill absorb and reflect the remaining portion of the
pulse. Therefore, only the leading edge of the pulse which is about one-fifth
of the initial pulse width of the pulse passes through the high density layer
and propagates continuously in the forward direction. Since the transmitting
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49
Figure 24. (a) Microwave pulse envelop as a function of time
and space
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
Figure 24. (b) Electron density as a function of time and space
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
pulse has lower amplitude and much narrower width than those of the
incident pulse, the electron density drops sharply after the thin layer and
maintains at a relative constant level following the tail of the pulse.
3.4 Discussion
The experimental and computer simulation results of high power
microwave pulse propagating in a large chamber provide very useful
inform ation about the high power microwave propagating in the
atmosphere. The validity of Eqs. 3.2-11 and 3.2-2 are demonstrated by good
agreement between experimental result and numerical simulation. The
theoretical model established for high power microwave propagation in air
breakdown environment can be used to investigate the high power
microwave propagation from ground to certain altitude die Eqs. 3.2-11 and
3.2-2 can be solved from x=0 to the designated altitude (e.g. 50km) with
pressure p as a function of altitude. However, this w ill require tremendous
computer memory and computing time even if running the program on Cray
at Pittsburgh Super Computing Center. One way to overcome this problem is
to use a frame transformation to convert the the two equations into a local
time domain description.
Consider the following frame transformation:
3.4-1
z= z
3.4-2
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52
/
where t is the local time of the pulse. The partial differential operators in the
two frames are related by
9 -
i
at
l
di
F
*
- 1 d z " v ^ t ,z")
/
1
. Jo
a _
az
3.4-3
a
i
az
v*
a
i
a t'
fz
1 - 1 d z v ^ t ,z")
.
Jo
where vg =
Equations. 3.2-11 and 3.2-2 are then transformed into
s
_
a?V8P =-
Ip -J dz'v^/vg(t,z'j |
3.4-5
and
-n = [(Vi-va)n -r n2}
at
- (
dz"v^/v|(t,z")
Jo
3.4-6
where P=P/Pc> n=n/nc, and r = n ic
Defining
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53
G(z’,t')
f
=
dz"(VgAr|)
JO
3.4-7
it leads
dz'
G = Vg/v| = - 1
& g
—n
** v|
- * 9t'
^
2
3.4-8
with the aid of 3.4-6 3.4-8 can be integrated to obtain
G = 1 - expl
^
V i" Va^ " r ^ dz"
3.4-9
Substituting 3.4-9 into 3.4-8 for vg, 3.45 and 3.46 can then be expressed
explicitly to be
_a..«
7vgp = - IP + r ^ [(vi - va)n - r n2]iP
dz
2v|
3.4-10
and
1 7=
n = [(v i * v a)n - r n2]-exp[ f -j£J(vi - v a)n - r n2]dz"]
dt
L
/o2
v
l
3.4-11
In terms of the normalized variables * = t'VvaV and x = z’Vvav/c, 3 .4 - 1 0
and 3.4-11 become
Aytup ) = - f(v/va)i/2+ % v v )1,2h
dx
I
2
^
t i ^
1-n
W
)
3.4-12
and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
= Vva/v{(vi/va - l)n - (r/va^ 2)
•exi
j
I Jo ^(vaA')1/2(l - n)*3/2[(vi/va - l)n - (r/VaJn^dx
3.4-13
We now simplifying the notations by letting T -» t,n—*n, and r—^ 3.412 and 3.4-13 become
^ il
-nP) = - j(v/va)1/2 + 1 (va/v)1/2^ |P n
3.4-14
and
= (va/vf^A-n-exp
i(va/v)1/2f [An/{l - nf^dz'
Jo
3.4-15
where A = (viMi -1 ) _(r/Va)n
= 3.82xl02[p3/4+3.94P1/4]exp[-7.546/P1/2] -1 - (r/va)n 34_16
Equations. 3.4-14 and 3.4-15 can be solved for long distance propagation
with much less computer time than solving Eqs. 3.2-2 and 3.2-11 directly. This
is because the solutions of the transformed equations w ill be found at the
mesh points of the number N XN Z, which is much smaller than N tN z, .where
N t is the number of time steps in the pulse duration which is many orders
smaller than N t the number of time steps in the pulse propagation time. In
addition, Eqs. 3.4-14 and 3.4-15 are coupled ordinary differential equations
which can be solved by using ODE software package directly.
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55
Chapter IV .
Lifetime of Plasma generated by microwave pulse
The plasma generated by microwave pulse w ill inevitably decay after
the end of the pulse. For practical purposes such as OTH radar, one would
require the electron density in the plasma to be above certain level at all the
time of the system operation. One way to keep die electron density level in
the plasma is to send repetitive pulses into the plasma. The time interval
between two pulses should be shorter than the decaying time of the plasma at
the desired density level. The other alternative is to deposit energy
continuously into the plasma with cw wave. The questions arise about the
optimum repetition rate and energy of the sustaining pulses for the first
approach, and the minimum power of cw wave for die second approach. In
order to address these questions, one must know the decay process of the
plasma created in the air.
The plasma decay process has been investigated by many researchersfor
different species of gases w ith different methods33-35. The most relevant
works are those reported by A. P. Napartovich36 et al in 1975 and A. L.
Vikharev37 et al in 1984. A.P. Napartovich et al made the measurement of
electron density in the plasma produced in the air by DC pulse. His method of
measurement is simply applying a constant voltage on the plasma volume
and calculating the electron density change from the decaying current.
A.L.Vikharev et al measured the electron density produced by two crossed EM
pulses (5|is-60ps pulse length) at 37.5 GHz. He used an open resonator to
enclose the plasma volume and monitored the resonance frequency change
with time to deduce the electron density change.
In the present work38, the wave scattering method is used to determine
the electron density decay rate during the first lOOps after the end of
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56
microwave pulse. The method does not involve any enclosing boundary
such as resonator walls or electrodes which w ill have boundary effect on the
electron distribution, neither does it require an external voltage which
apparently w ill affect the motion of the charged particles in the plasma.
4.1 The Electron Loss Process
In general, there are three processes work together to cause the decay of
the plasma. They are electron diffusion, electron-ion recombination, and
attachment of electrons to the neutral molecules. For the case of 1 torr
background pressure, electron-neutral collision frequency is about GHz. The
free electron diffusion coefficient D is estimated to be about 3x104 cm2/sec.
Thus, the diffusion time for free electron to walk randomly from the center of
the chamber to the side walls is calculated to be about 20 ms. If file ambipolar
effect is taken into account, the diffusion time becomes even larger and is in
the order of seconds. Therefore, we simply ignore the diffusion effect on the
electron decay rate in the present study. The electron decay process can be
modeled by the following equations,
= "Valle 4" VdUju - CUlellpi
—Valle " Vdllni ■ Pllpinnj
dllpj
.
^ — anetipi - pnnitipr
^
413
where ne, nni, npi are electron density, negative ion density, and positive ion
density respectively; and va, Vd, a, P are attachment frequency of electron to
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Figure 25. The temporal evolution of the intensity of the
scattering signal
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the neutrals, detachment frequency of negative ion; recombination coefficient
of positive ion and electron, recombination coefficient of positive ion and
negative ion- These three coupled equations w ill be solved to compare with
the experimental results.
4.2 Wave Scattering Measurement of Electron Density
As given by Z2-15, Bragg scattering coefficient S of wave intensity is
directly proportional to it*,2* Hence, the Bragg scattering experiment w ith the
produced plasma layers described in Sec.HI provides a way for a
nondestructive measurement on the temporal evolution of plasma electron
density. Using a cw test wave of frequency 6.17GHz, The temporal evolution
of the intensity of the scattering signal is measured in Figure 25. which is
similar to Figure 14(a) using the different test wave frequency. An accurate
measurement of electron density as a function of time can thus be made from
the data contained in this Figure.
Since the carrier frequency of microwave pulses is 3.27 GHz, the peak
electron density ionized by the microwave pulses is in the order of 1011 cm-3.
Thus, the electron-ion recombination rate is always smaller than the electron
attachment rate whose maximum value at 1 torr pressure of air is about
1.4x105 cm -i. We therefore expect that the initial decay rate (i.e. the maximum
decay rate) of the electrons determined by the electron attachment rate is
somewhat bounded by this value 1.4x10s sec-1. It is indeed so as obtained from
Fig. 26 that the electron decay rate right after the breakdown pulses ( i.e. the
initial decay rate) is evaluated to be 6xl04 sec-1. It also shows that the electron
density after 70(is is reduced by a factor of about 30. Similarly, the electron
decay rate is also reduced over a factor of 10 from the initial decay rate. In this
density level (=3xl09cm-3) the decay rate is consistent with the recombination
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59
12.00
11.00
©
z
O
s
10.00
9.00
8.00
0.00
20.00
40.00
60.00
t (microsecond)
80.00
100.00
Figure 26. Numerical solution of electron density evolution
compared with experimental results
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1 2 .0 0
LOG(Ne)
11.00
10.00
9.00
8.00
0.00
20.00
40.00
60.00
t (microsecond)
80,
100.00
Figure 27. Numerical solutions of electron density, positive ion
density and negative ion density
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
loss rate. This is realized by the fact that when enough negative molecule ions
are produced through the electron attachment process, the detachment rate
for electron regeneration is increased and eventually balances out the electron
attachment loss rate. Thus, the dominant electron loss mechanism is shifted
to the recombination process. On the other hand, the attachment process also
plays the role to reduce the recombination and diffusion losses of electrons.
Through the three-body attachment process39 the excess of free electrons is
first stored by attaching themselves to the low mobility neutral molecules and
then released to be the source of free electrons of the system whenever there
is a need for the balance among all the process involved. When such a
balance is reached eg. 70ns point of Fig. 10(a), free electron density w ill only
decay at a relatively slow rate determined by the recombination process and
the ambipolar diffusion process.
Using the model equations 4.5-1 - 4.5-3 described in Sec. 4.1, the
experimental observation can also be reproduced by the numerical result as
shown in Figures 26 and 27 where a, p the coefficients of the equations are
chosen40'41 for best fitting between numerical and experimental result. Thus,
the detachment rate and recombination rate coefficients are also obtained.
4.3 Langmiur Probe Measurement
W ith the available power (=10mw) of sweep microwave generator and
the detecting facility ( HP spectrum analyzer 8569B), the Bragg scattering
measurement is no longer sensitive to the electron density at the level after
100|is decay from its peak (e.g. Fig. 14(a), Fig. 25). The evolution of electron
density at later time is then determined by a Langmuir double probe42'43'44.
The main purpose of Langmuir probe measurement is to confirm that the
decay of electron density after the balance of process is reached is indeed
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1.00
0.80
0.60
<D 0.40 -
0.20
0.00
5.00
10.00
____
15.00
20.00
t ( microsecond )
Figure 28 Langmuir double probe measurement of temporal
evolution of electron temperature Te(t)
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63
caused mainly by the recombination process. As an additional payoff, the
probe measurement can also provide the inform ation on electron
temperature. The difficulty with Langmuir probe measurement lies on the
presence of negatively charged molecules so that the ion density is not quite
the same as the electron density. The presence of negatively charged
molecules also complicates the relationships among the electron density,
electron temperature, and ion density etc. inside, a sheath. For instance, the
sheath potential changes its sign when the density of negatively charged
molecules becomes much larger than that of free electrons. It can be
monitored experimentally by the direction of current flow through a
grounded single probe. We, therefore, report only the results in the time
interval in which the percentage of negatively charged molecules is
effectively low . Shown in Figure 28 is the Langm uir double probe
measurement of temporal evolution of electron temperature Te(t) during the
first 18ps right after the passing through of the microwave pulses. It shows
that electron temperature is heated by the microwave pulses to about le V and
decreases quickly after the microwave is turned off. The decay rate is about
105sec-1 which is consistent with the electron energy loss rate via electronneutral collision. The corresponding evolution of electron density can be
drawn from the result of Fig. 14(a), or Fig. 25
The V -I characteristics of the Langmuir double probe at four different
times starting at 1ms are presented in Fig. 29. These Curves having a same
slope at lp=0 indicate that all the species of the gas have already reached
thermal equilibrium and have a temperature =300°k. However, these curves
saturate at different current levels. It indicates that ion density still varies
with time. Based on the saturation levels of these curves, the evolution of
ion density w ith tim e is determined. In this time interval (1ms,1.1ms)
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64
2.50E—003
Ip (microamper)
2.00E—003
1.50E-003
1.00E-003
5.00E—004
0.00
20.00
40.00
60.
Vp (mv)
00
100.00
120.00
Figure 29. The V-I characteristics of the Langmuir double
probe at four different times starting at 1ms
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7.60
7.50
7.40
E
O
7.30
O
\ v
7.20
•
z:
7.10
7.00
1.00
1.02
1.04
1.06
1.08
t (ms)
Figure 30. The evolution of electron density from 1.0ms to
1.1ms after the microwave pulse
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electron density can be assumed to be in die same order of magnitude as the
ion density- The evolution of electron density is thus determined and plotted
in Fig. 30. The decay rate of 500 sec-* is indeed consistent w ith the
recombination rate at this density level.
4.4 Discussion
We have shown that in die density region of interest the decay rate of
electron density is governed by die electron-ion recombination rate. Based on
this decay rate, repetitive pulses w ith a repetition rate about 250 sec"l w ill
suffice for maintaining the electron density to a level (107cm-3), which is high
enough for the OTH radar applications. Moreover, the pulses used for
maintaining the plasma can be much shorter than the first pair of triggering
pulses which have to start the ionization from relatively low background
electron density. Therefore, the required microwave power and energy for
plasma generation and its sustainment can be shown to be within the state of
the art of current technology.
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67
Chapter V . Summary and Discussion
Plasma layers generated by two intersecting microwave pulses are used
for the study of Bragg scattering. The experiment is conducted in a large
chamber w ith a microwave absorber so that the microwave reflection from
the w all can be minimized. Hence, the experiment can be considered to be a
laboratory simulation of conceptualized plasma layers generated by high
power radio waves in the upper atmosphere, as investigated theoretically by
Gurevich.
We first determine the characteristic of air breakdown by powerful
microwave pulse. This is mainly because the plasma generated near die wall
adjacent to the microwave horn causes erosion of the tail of the incident
pulse and the pulse becomes too short, by the time it reaches the central
region of the chamber, to cause appreciable ionization. However, this
problem is easily overcome when the scheme of two intersecting pulses is
used for plasma generation. In this approach, each pulse has its field
amplitude below the breakdown threshold to avoid the ta il erosion.
However, the fields in the intersecting region can add up and exceed the
breakdown threshold. This scheme is most effective when the two pulses
have the same polarization and are coherent. In this case, the wave fields
form a standing wave pattern in the intersecting region in the direction
perpendicular to the bisecting line of the angle <|> between the intersecting
pulses. Thus, parallel plasma layers with a separation d=Xo/2sin(<j>/2) can be
generated. This result is shown in Fig. 3.
Since there are no electrodes involved in the current experiment of air
breakdown, we can determine the breakdown threshold field as a function of
the air pressure within the accuracy of microwave probe measurement. Two
Paschen breakdown curves for the cases of 1.1 and 3.3jis pulses are
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68
determined as shown in Eg. 5. The appearance of a Paschen minimum can be
explained as the result of breakdown by a short pulse which is equivalent to a
dc discharge w ith short separation between electrodes (i.e. short electron
transit tim e). The result that the breakdown threshold by a longer pulse
(3.3jis) is lower than that by shorter pulse (1.1ns) agrees w ith the explanation.
The characteristic of the curves is also confirmed phenomenologically by the
various degrees of tail erosion of the same pulse passing through the chamber
at different pressure, as shown in Eg. 6.
An optical probe has been used to monitor the growth and decay of
airglow enhanced by microwave generated electrons. Two processes are, in
general, responsible for the airglow. One is through the electron-ion
recombination and the other one is through impact excitation of natural gas.
Since only weakly ionized plasma is generated, the second process is believed
to be dominant. However, the second process requires that the electron
energy exceed 2eV. Therefore, the decay rate of airglow intensity shown in
Fig. 4(b) accounts for not only the decay of the electron density caused by the
dissociative attachment loss but also for the decay of electron temperature
caused by energy loss to the neutrals and the loss of fast electrons.
We then conducted the Bragg scattering experiment w ith the produced
plasma layers. Both temporal evolution of the scattering signal from a test
wave and the spectral dependence of the scattering coefficient have been
examined. Good agreement between theoretical and experimental results on
the spectral dependence of the scattering coefficient has been achieved
(Fig.15). It should be noted that, due to the dimension of the chamber and
microwave beams, only three plasma layers have significant overlap along a
central line of sight used as the incident path of the test wave for Bragg
scattering. Nevertheless, a remarkable effectiveness of Bragg scattering has
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69
been demonstrated by the chamber experiment. It is further realized that
more layers and much larger cross sectional area for each layer w ill be
produced in the actual installation. One would expect that much more
plasma layers can be incorporated for Bragg scattering. Since the scattering
coefficient is proportional to the square of die number of layers at play,
effective Bragg scattering can still be achieved at even much lower plasma
density (=107cm-3 for practical application) than that of current experiment
(~109cm_3)/ where the radar frequency is also more than one order of
magnitude lower than that of the test wave used in the current experiment.
An experiment investigating the propagation of high power
microwave pulses through die air is also performed. We have identified two
mechanisms which are responsible for two different degree of tail erosion.
One is attributed to absorption by the self-generated underdense plasma. The
other one is caused by reflection by the self-generated overdense plasma
screen. Our study indicates that an increase of pulse amplitude may not help
to increase the energy transfer by the pulse. This is because the two identified
tail erosion mechanism are at play to degrade the energy transfer. A
demonstration is presented in Figure 20, where the growth and decay of
airglow enhanced by electrons through air breakdown by 3.3ns pulse are
recorded for two different power levels. In Figure 20(a) the power level is
below the critical power and the airglow grows for the entire 3.3ns period of
the initial pulse width. As power is increased beyond the critical value, the
in itial growth of the airglow becomes faster as shown in Figure 20(b).
However, it is also shown in Figure 20(b) that the airglow saturates at about
the same level as that of Figure 20(a). Moreover, the airglow already starts to
decay even before the 3.3ns period. In other words, cutoff reflection
happening in the second case limits the energy transfer by the pulse. The
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70
additional energy added to the pulse is wasted by reflection. The way to solve
the problem is either to lower the amplitude of the pulse or to narrow the
pulse width so that die propagation loss can be minimized. The optimum
pulse amplitude for maximum energy transfer through the air has been
determined for 1.1ns pulse used in the present experiment. Since the effect of
pressure gradient and large propagation distance can not be incorporated in
chamber experiment, the determination of optimum parameters of the pulses
for achieving die most effective plasma generation is deferred until a practical
theoretical model developed under the guide of present study is established.
A practical issue concerning the applicability of present study to the
OTH radar is the lifetim e of plasma electrons generated by the microwave
pulses. The theoretical result (2.2-15) shows that the scattering coefficient is
proportional to the square of the electron density and insensitive to the
electron temperature Therefore, the electron decay rate after the breakdown
pulses have passed through can be evaluated from Fig.26. It shows that the
initial decay rate is about 6x10^ seer* which is consistent w ith the dissociative
attachment rate. It also shows that the electron density after 70 ps is reduced
by a factor of about 30. Similarly, the electron decay rate is also reduced over a
factor of 10 from the initial decay rate. In this region the decay rate is
consistent w ith the recombination loss rate. This is realized by the fact when
enough negative molecule ions are produced through the electron
attachment process, the detachment rate for electron regeneration is increased
and eventually balances out the electron attachment loss rate. Thus the
dominant electron loss mechanism is shifted to the recombination process.
Using Bragg scattering, the evolution of electron density can be measured
only for lOOps. h i order to be sure that the loss of electrons is indeed caused
mainly by the recombination process which has acceptable low rate, a
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Langmuir double probe is used to measure the evolution of electron density
at much later time (i.e. 1ms to 1.1ms). The result of probe measurement
confirms die conclusion of Bragg scattering measurement.
Based on the results of our chamber experiments, it seems to us that
the implementation of a Bragg reflector in the upper atmosphere 0=50km) by
two intersecting microwave pulses transmitting from ground for potential
OTH radar applications is technically feasible45.
In the following, a list of topics is suggested for the further research in
the area of using the artificial ionospheric Bragg reflector for the OTH radar
applications.
1) The sustainment of plasma by cw or pulsed microwave;
2). The dependency of plasma lifetime on the gas pressure and the
repetition rate, pulse duration and power of sustaining pulses;
3). The dependency of the reflection coefficient of plasma Bragg
reflector on the polarization of the incident w ave;
4). System considerations: heater wave beams design (frequency,
repetition rate, duty factor, pulse amplitude, and size of the
transmitters), and plasma layers control for radar signal scanning.
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72
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