Quasi-Optical Microwave Pulse
Compressor at 34 GHz
A.L.Vikharev*'1, Yu.Yu.Danilov*, A.M.Gorbachev*, S.V.Kuzikov*,
Yu.I.Koshurinov*, V.G.Paveliev*, M.I.Petelin*, J.L.Hirshfield1
^Institute of Applied Physics (Russia)
Omega-P, Inc, and Yale University (USA)
Abstract. We describe a 34.272 GHz pulse compressor based on a three-mirror traveling-wave
resonator, which creates pulse compression using linear frequency modulation of the input pulse,
rather than step-wise phase modulation used traditionally. The results of testing the compressor
prototype at a low power level under different modulation methods and different widths of the
input pulse are discussed. We present also the results of calculations and tests of an electrically
controlled diffraction grating, which can serve as the active switch for such a three-mirror
resonator.
INTRODUCTION
Passive pulse compressors which have been created up to now and are currently
used at frequencies below 14 GHz, are based on resonators and delay lines that store
the microwave energy [1-3]. Compression is achieved as the result of a transition
process which arises when the resonator is excited with a microwave pulse having an
appropriate phase modulation. Creation of new electron-positron colliders that would
provide high-gradient charged particle acceleration (over 150 MV/m) will require,
evidently, a transition to higher frequencies. Hence, an important task is to create
pulse compressors appropriate for the use in frequency ranges beyond X-band. This
paper describes a 34.272 GHz pulse compressor based on a three-mirror travelingwave resonator using linear frequency modulation of the input pulse, instead of the
step-wise phase modulation used traditionally. Further it is planned to test this
compressor with the magnicon under development by Omega-P. As compared with
the X-band frequencies, in the Ka-band the transition to quasi-optical systems is
inevitable: under moderate microwave fields in the oversized storing resonator quasioptical systems provide an acceptable level of ohmic losses and acceptable selectivity
in terms of spurious oscillations.
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
448
THREE-MIRROR RESONATOR
AS A PASSIVE COMPRESSOR
The passive compressor that we have developed consists of a high-Q-factor threemirror resonator and an excitation system, as diagramed in Fig.l. The resonator
consists of two focusing mirrors that provide a high-Q-factor operating eigenmode of
the running-wave type, and the third mirror with fine corrugation on its surface.
1
FIGURE 1. Schematic diagram of the pulse compressor with the excitation system: C - resonator, cor
- planar corrugated mirror, sf - focusing mirrors, 1- rectangular to circular cross-section transducer, 2
- horn converting Hn mode into Gaussian wavebeam, 3 - feeding mirrors.
The corrugation provides coupling of the operating mode with the wave beam
formed by the excitation system. The coupling with the resonator is provided by using
the -1st diffraction maximum of the grating (see Fig. 2). The required period of the
grating is determined by the following expression:
,
(1)
where 9 is angle of wave beam incidence on the grating measured from the normal,
and 0.\ is angle corresponding to the -1st diffraction maximum. The corrugation
amplitude should be chosen basing on the necessity to provide the required Q-factor of
resonator coupling.
FIGURE 2. Separation of the beam (1) incident on the diffraction grating (4) into two: mirror beam (2)
and the-1st diffraction maximum (3).
449
The resonator does not require an additional 3-dB microwave decoupler, as does
the well-known SLED compressor, since it is ring-shaped and the reflection from the
resonator is negligibly small. The structure of the field for the operating mode of the
resonator was calculated using the method described in [4].
In order to have the highest resistance to rf breakdown, the polarization of the
electric field in the resonator is chosen such as to make the component normal to the
surfaces of all the mirrors small and tending to zero within the approximation of the
infinite mirror apertures.
The excitation system includes a horn that converts the main mode of the standard
rectangular waveguide into a Gaussian beam, and a pair of matching mirrors. Those
mirrors provide a distribution of the field which is close to the transverse distribution
of the field of the operating mode (the lowest TEMoon mode) over the corrugated
mirror of the resonator. The radiation at the compressor output is focused again into
the single-mode waveguide.
OPTIMIZATION OF INPUT SIGNAL MODULATION
AND COMPRESSOR PARAMETERS
For the version of the compressor under consideration we consider a linear
frequency modulation of the input pulse, as compared to the step-wise modulation
used in SLED and SLED-II, in order to reduce the band-width requirement for the
high-power amplifier that generates the input signal to the compressor. For effective
compression optimization of parameters of frequency modulation and compressor
parameters are required.
Let us determine compression efficiency as the ratio of the output pulse energy
stored in the accelerating section to the pulse energy at the compressor input:
tn+T
Eout2dt
———
\Ein
(2)
max
where Ein and Eout are complex amplitudes at the input and output of the compressor.
+00
T = \\Ejn(t)\
— 00
/
dt I Ein\
/
/
|
is duration of the input pulse, tn is time at which
max
the pulse starts to fill the accelerating structure, ris time of filling of the accelerating
section. Let us define also the pulse compression ratio
s=-
(3)
T
as the ratio of duration of the input and output pulses.
The power amplification ratio is given by following simple formula
Po=S7J
450
(4)
Conversion of a microwave pulse e(t)=E(t)exp(ico
t) with any smooth modulation
o
in the resonator with input/output decoupling is described by the following equation:
dEout(t]
dt
,
I °
dEjf)
+\I
-
2Q ext
.[,
''
-0),\Eout(t} =
(5)
i
where Qext is the external Q-factor of the resonator and aJ0 is eigenfrequency of the
resonator.
Equation (5) is to be integrated for a pulse with linear frequency modulation given
by formula:
I ^in(0 < t < T) = expuico t + LI tI2}\,
f^
§
w
\ein(t<0,t>T) = 0.
where // is parameter that measures the frequency modulation. In this case the
2
efficiency is a function of the following dimensionless parameters: a = ——,
"ext
Figure 3 shows optimized efficiency and power amplification coefficient as
functions of the compression ratio s. Efficiency of compression in the case of linear
modulation proves to be about 10% lower as compared to the step-wise modulation.
-2.4
FIGURE 3. Characteristics of optimized compressors. Efficiency T| (solid lines) and Pg (dashed lines):
the input pulse is frequency-modulated linearly.
Optimized parameters that correspond to point A in Fig. 3 (ft = 34.272 GHz, s = 4,
77 = 65.89%, Pg = 2.64) are a = 11.78, >ff = 8.61, y = 2.11. Table 1 lists also
dimensional compression parameters.
451
TABLE 1. Optimized parameters corresponding to point A.
T , ns
500
100
80
T,ns
125
25
20
Af'0, GHz
0.003
0.014
0.017
Qext
4/,,GHz
25516
5105
4084
0.007
0.037
0.049
Calculations show that the use of quadratic frequency modulation makes it possible
to improve the efficiency somewhat.
TESTING THE COMPRESSOR AT A LOW POWER LEVEL
We used a high-stability (Af/f = 10~5 - 10~6) klystron-type pulse generator as a
source of input microwave pulses. The source worked in the regime of generation of
rectangular pulses T = 80-120ns. The measured loaded Q-factor of the resonator
proved to be slightly lower than the calculated value and was gm=3500-3700, which
did not make it possible to achieve the maximum possible compression.
The manufactured prototype of the compressor was tested both in the scheme with
step-wise frequency modulation, and that with linear frequency modulation. In the first
case we used an electrically controlled phase rotator based on a p-i-n diode with its
phase switching time T s ~ 1 ns to switch the phase from 0 to 180°. The oscillogram of
the compressed pulse obtained in that scheme is shown in Fig. 4.
At the length of the input pulse 80 ns, s = 4, and Pg = 3, efficiency of compression
was 75%, which corresponds totally to efficiency of the SLED compressor at the same
compression coefficient.
FIGURE 4. Oscillogram of the output pulse in the case of step-wise phase modulation: T=80 nc, s=4,
77=75%, ^=3.
In order to obtain the linear frequency modulation of the microwave pulse we used
the sawtooth generator. Samples of the oscillograms of the output pulses obtained in
this variant of compressor operation are shown in Fig. 5.
452
TABLE 2. Compression with linear frequency modulation; experimental data.
A/g, MHz
120
19.4
3
58
120
28.6
3
71
110
33.2
3.5
62
100
39.3
3.6
65
90
45.4
3.7
65
80
51.0
4
59
a)
1.74
2.13
2.17
2.34
2.41
2.36
b)
FIGURE 5. Oscillogram of the output pulse in the case of linear frequency modulation: a - T=100 ns,
4^=39.3 MHz, s=3.6, 7/=65%, ^=2.34, b - T=80 ns, A^=51 MHz, s=4, 7/=59%, Pg=236.
In the Fig. 5a the input pulse is 100 ns long, in the Fig. 5b it is 80 ns long.
Experimental characteristics of compressed pulses and parameters of compressor
operation are listed in Table 2.
CALCULATION OF THE DIFFRACTION GRATINGS WITH
ELECTRICALLY CONTROLLED PARAMETERS
The quasi-optical travelling-wave resonator with a diffraction grating as a coupling
device, which has been described in previous sections, can be used as an active
microwave pulse compressor. The two regimes of grating operation are depicted in
Fig. 6. To achieve this, in the regime of energy storage the grating should provide
branching of a small portion of the incident power into the diffraction (-1st) beam, to
couple the resonator with the feeding line, as in Fig. 6a. Then, to extract the stored
energy, the grating should switch fast into the state in which a significant portion of
the power is branched into the diffraction beam. As a result, the coupling of the
resonator with the feeding line becomes better, and the energy stored in the resonator
leaves it in a short time, as in Fig. 6b.
453
FIGURE 6. Scheme of compression basing on the quasi-optic resonator: 1 - diffraction grating/switch;
2 - focusing mirrors; 3 - input pulse; 4 - output pulse; a - resonator in the regime of energy storage; b resonator in the regime of output of the compressed pulse.
This can be done by changing the properties of the diffraction grating; specifically,
by using gas-discharge plasma to change the distribution of the electromagnetic field
on the grating, thus changing its electrodynamic structure.
Operation of such gratings was modeled by the FDTD method [5]. To provide
electric reliability of the grating, we chose the TE polarization of the electromagnetic
waves, in which the vector of the electric field is parallel to the grating grooves. In this
case there is no noticeable increase of intensity of the electric field on the periodic
structure.
The calculations aimed at choosing the type and configuration of the grating that
would provide almost total reflection (insignificant branching into the diffraction
beam) in the absence of plasma in the switching elements, and at the lowest possible
intensity of the electric field at these elements. We considered different types of
gratings: those formed by dielectric tubes over a metal plane, by variously shaped
metal profiles, by dielectric plates with gaps, etc. For the sake of convenience of
calculations and measurements the angles of incidence and diffraction were chosen to
be 45° and 17°.
The calculations revealed that it is unreasonable to use gratings that incorporate
dielectric tubes, since the electric field becomes stronger at their side surfaces; this can
result in development of a multipactor discharge and lower electric reliability. The
gratings that consist of a relatively thick dielectric plate with channels within (which
serve as gas-discharge tubes) seem to be more electrically reliable. The thickness of
the plate is chosen such that the boundary between the vacuum and the dielectric is at
the minimum of the electric field of the standing wave, as shown in Fig. 7a. As a
result, the occurrence of multipactor discharge is not very probable here. The intensity
of electric field in the channels is equal approximately to the intensity of the field in
the standing wave.
The channels in the grating shown in Fig. 7 are placed with a double period and
have slightly different dimensions to provide weak branching into the diffraction
wave. In this case the "reflection coefficient" (R2), equal to the ratio of intensity of the
mirror wave to intensity of the incident wave (see Fig. 2), is close to unity. When
plasma is produced, a strong periodic inhomogeneity appears in half of the channels,
and a significant portion of the energy is branched into the diffraction wave, as in Fig.
7b.
454
a)
b)
FIGURE 7. Distributions of the instantaneous electric field (1) and mean-square field (2) during
reflection of the plane wave from the diffraction grating made of quartz: (a) - in the regime of energy
storage in the resonator (R2 = 0.99); (b) - in the regime of energy extraction from the resonator (R2 =
0.5). In the figures the field within the quartz is shown in a darker colour. The part of quartz with two
grating periods is shown as black. The plasma inside the quartz is shown as black also.
Technically, manufacture of the quartz grating that has been described is
comparatively complicated. That is why in order to check the possibility to create a
controlled diffraction grating at a low power level experimentally, we calculated for a
grating made of polystyrol,
STUDY OF OPERATION OF THE ACTIVE
DIFFRACTION GRATING
The scheme of the setup for studying controlled diffraction gratings is shown in
Fig. 8. The horn (6) sent the radiation produced by the microwave generator (1)
towards the grating, which consisted of a plane metal mirror (3) and a periodic
structure (2). The voltage produced by the high-voltage pulse generator was fed to the
elements of the controlled grid via a set of ballast resistors (5). The level of power in
the reflected (9) and diffraction (10) beams was determined by means of horns (6) and
detectors (7); the signal from them was registered with a digital oscillograph. These
experiments were aimed only at checking the basic possibility to change the ratio of
beam intensities by using plasma in the grating, so the simplest conical horns (that did
not provide 100% energy transmission) and a relatively low-power generator of highvoltage pulses (voltage 50 kV, current ~100 A, pulse duration -50 ns) were used.
The electrically controlled grating used in the experiments at the low power level is
50x25 cm2 and is made of two sheets of polystyrole with grooves in one of them,
which communicate at one end, to pump the gas into and out of them. At the both ends
of the grooves, metal electrodes are glued in.
455
7
1
6
6
9
6
8
7
10
2
4
3
00000000000000000000000000000000000000000
00000000000000000000000000000000000000000
5
FIGURE8.8. Scheme
Scheme of
of the
the setup
setup for
for studying
studying the
the controlled
FIGURE
controlled diffraction
diffraction grating:
grating: 11 -- microwave
microwave
generator;22--diffraction
diffraction grating;
grating; 33 -- plane
plane metal
metal mirror;
55 -- set
of
ballast
resistors;
66- -horn;
generator;
mirror; 44 -- PVG;
PVG;
set
of
ballast
resistors;
horn;7 7
st
detector;88--incident
incident beam;
beam; 99 -- mirror
mirror beam;
beam; 10
- -detector;
10 -- diffraction
diffraction -1
-1stbeam.
beam.
In order
order to
to obtain
obtain homogeneous
homogeneous plasma
plasma during
In
during aa high-voltage
high-voltage breakdown
breakdown ininthe
the
experiments
performed,
the
gas
pressure
was
maintained
at
a
low
experiments performed, the gas pressure was maintained at a low pressure
pressure level
level
(~1Torr).
Torr). After
After the
the process
process of
of switching
switching in
(-1
in such
such aa controlled
controlled grating
grating had
had been
been
analyzed,
the
following
was
revealed.
In
the
absence
of
plasma
in
the
tubes
analyzed, the following was revealed. In the absence of plasma in the tubes the
the
intensity of
of the
the diffraction
diffraction beam
beam is
is low
intensity
low and
and the
the incident
incident power
power isis reflected
reflected into
intothe
the
mirror beam.
beam. When
When the
the plasma
plasma appears
appears in
mirror
in the
the grating
grating channels
channels in
in aa high-voltage
high-voltage
breakdown, the
the intensity
intensity of
of the
the mirror
mirror beam
beam decreases
breakdown,
decreases and,
and, atat the
the same
same time,
time, the
the
intensity
of
the
diffraction
beam
grows,
as
seen
in
Fig.
9.
After
the
high-voltage
intensity of the diffraction beam grows, as seen in Fig. 9. After the high-voltagepulse,
pulse,
overthe
the plasma
plasma diffuses
diffuses and
and the
the reflection
reflection coefficient
isisover
coefficient becomes
becomes close
closetotounity
unityagain.
again.
It
should
be
noted
that
in
these
experiments
the
time
of
switching
was
about
It should be noted that in these experiments the time of switching was about 100
100ns,
ns,
which is too long to obtain compressed pulses of duration several tens of nanoseconds
which
is too long to obtain compressed pulses of duration several tens of nanoseconds
long. However, the use of a more powerful high-voltage pulse generator and smaller
long. However, the use of a more powerful high-voltage pulse generator and smaller
dimensions of the grating will make it possible to shorten the switching time.
dimensions of the grating will make it possible to shorten the switching time.
I, a.u.
/, a.u.
1
2
0
200
600
800
ns 600
200time,
400
400
800
time, ns
FIGURE 9. Time dependence of intensity in the reflected (1) and diffraction (2) beams when plasma
FIGURE
Time
dependence of intensity in the reflected (1) and diffraction (2) beams when plasma
appears in9.the
grating.
appears in the grating.
456
CONCLUSION
A passive quasi-optical compressor with linear frequency modulation on the bases
of the three-mirror resonator was demonstrated. The results of the studies show that a
developed version of a high-power passive quasi-optical compressor should be able to
demonstrate the parameters shown in Table 3.
Diffraction gratings as the third mirror of the resonator are promising for creation
of electrically controlled wave beam switches. An active grating made of a dielectric
with low losses was demonstrated. Preliminary estimates show that a compressor with
such an active grating is capable of operating at high pulse powers with parameters as
listed in Table 4.
ACKNOWLEDGMENTS
This work was supported by the Division of High Energy Physics, US Department
of Energy.
TABLE 3. Parameters of passive quasi-optical rf pulse compressor.
operating frequency
34.272 GHz
distance between mirrors
350mm
apertures of mirrors
250x150 mm2
input and output modes
TEn
inherent Q-factor
70000
coupling Q-factor
3500
duration of the input pulse
100ns
duration of the output pulse
25ns
compression ratio
4
efficiency, in the case of the rectangular envelope of
66%
the input pulse frequency-modulated linearly
TABLE 4. Parameters of active quasi-optical rf pulse compressor.
operating frequency
34.272 GHz
distance between mirrors
350mm
apertures of mirrors
~ 20 x 20 cm2
input and output modes
Gaussian beam
105
unloaded Q-factor
loaded Q-factor (power feed/output)
40,000/3000
duration of input pulse
600ns
duration of output pulse
20-30 ns
power gain
15-30
________efficiency________
50%
457
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1.
2.
3.
4.
5.
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Balakin V.E., Syrachev I.V., VLEPP RF Power Multiplier, Proc. 3-rd Int. Workshop on Next Generation
Linear Collider, Branch INP, Protvino, Russia, 1991, pp. 1990.
Shintake T. C-band RF System for Linear Collider, Proc. Of the 3-rd Int. Workshop on Pulsed RF Sources for
Linear Collider, Shonan Village, Japan, 1996.
A.G.FOX, T.Li.. Bell SystemTechn J., 1961, Vol. 40, No. 2, pp. 453-464
Yee K.S., IEEE Trans. Antennas and Propagation, v. AP-14, 302 (1966).
458