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Methods to Produce Short-Pulse, High-Power Microwaves
BY
Andrey D. Andreev
B.S., Physics, Tomsk State University, USSR, 1990
DISSERTATION
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy
Engineering
The University of New Mexico
Albuquerque, New Mexico
December, 2007
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UMI Number: 3298168
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Andrey D. Andreev
Candidate
ELECTRICAL AND COMPUTER ENGINEERING
Department
This dissertation is approved, and it is acceptable in quality
and form for publication on microfilm:
Approved by the Dissertation Committee:
, Chairperson
Accepted:
Dean, Graduate School
NOV 1 5 2007
Date
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©2007, Andrey D. Andreev
iii
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ACKNOWLEDGMENTS
I heartily acknowledge Prof. Edl Schamiloglu, my academic advisor and dissertation
chair, for continuing to encourage me through the years of classroom teachings and the long
number o f months writing and rewriting these chapters. His guidance and professional style
will remain with me as I continue my career.
I also thank my professors, Mikhail I. Fuks, Christos G. Christodoulou, and Mark
Gilmore, for their valuable recommendations pertaining to this study and assistance in my
professional development.
The research reported in this dissertation was supported by grants from AFOSR,
ONR, and an Internship with AHS Engineering Services sponsored by Farr Research.
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Methods to Produce Short-Pulse, High-Power Microwaves
BY
Andrey D. Andreev
ABSTRACT OF DISSERTATION
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy
Engineering
The University of New Mexico
Albuquerque, New Mexico
December, 2007
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Methods to Produce Short-Pulse, High-Power Microwaves
by Andrey D. Andreev
Ph.D., Engineering, University of New Mexico, 2007
ABSTRACT
The use of high-power microwaves (HPM) in radars increases the maximum detection
range that depends on transmitted power as P1/4. However, such a simple microwave power
increase leads to a proportional increase in signal-to-noise ratio produced by ground/sea clut­
ters and other interfering effects. One way to reduce this ratio is to decrease the HPM pulse
width, as it depends on pulse duration as ~2/ct. Using shorter HPM pulses also minimizes the
dead time and allows one to detect lower-cross-section targets, as it depends on pulse duration
as ~cT/2.
As an HPM source either a relativistic magnetron with a transparent cathode or nonrelativistic magnetrons equipped by a microwave pulse compression setup with fast waveguide
switches can be used. Both of these sources can produce up to 1 GW and greater of output
microwave power with high pulse repetition rate and frequency stability from one pulse to the
next. The research described in this dissertation is focused on the experimental study o f i) a
prototype relativistic magnetron with a transparent cathode driven by a high-voltage (300-700
kV) nanosecond accelerator SINUS-6, and ii) the prototype of a microwave pulse compressor
using a gas discharge switch driven by a high-voltage (30 kV) pulse generator.
A comparison o f the radial distribution of output HPM power produced by a relativis­
tic magnetron driven by a traditional solid cathode and recently invented transparent cathode
was performed. The transparent cathode was found to improve relativistic magnetron opera­
tion by providing faster start of microwave oscillations at a predetermined mode without mode
competition. Comparison of output microwave pulses produced by the microwave pulse com­
pressor equipped with a mechanically operated switch and a fast gas-discharge switch showed
that the latter one sufficiently shortens the rise time of the output microwave pulse.
Results of this research suggest that: i) the use of a transparent cathode in relativistic
and, probably, nonrelativistic magnetrons provides better mode selection by locking the desired
vi
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magnetron oscillations in a shorter period of time, and ii) the use o f a faster switch (as fast as
possible) in a waveguide of a microwave pulse compressor shortens the rise time of the com­
pressed output microwave pulse.
vii
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TABLE OF CONTENTS
1. Introduction and Motivation
1
1.1. Relativistic Magnetron with Enhanced Geometry Cathode
3
1.2. Nonrelativistic Magnetrons with Microwave Pulse Compression
5
1.3. Contributions and Organization of the Research
7
2. Relativistic magnetron with transparent cathode
2.1. Current-Voltage Characteristics of the SINUS-6 Accelerator
10
16
2.1.1. Simplest theory of limiting currents in cylindrical geometry
18
2.1.2. Calibration of the diagnostics
19
2.1.3. Voltage, current, and total electric power measurements
24
2.1.4.1-V characteristic and impedance of vacuum diode
26
2.1.5. Summary o f diagnostics calibration and I-V characteristics meas­
urements
29
2.2. Smooth-Bore Magnetron with a Transparent Cathode
30
2.2.1. Computer experiments with smooth-bore magnetron
31
2.2.2. Microwave measurements with smooth-bore magnetron
36
2.2.2.1. Measurements of microwave power distribution
37
2.2.2.2. Measurements o f microwave frequency
41
2.2.2.3. Measurements of total radiated microwave power
45
2.2.3. Summary of smooth-bore magnetron measurements
47
2.3. Relativistic Magnetron with a Transparent Cathode
48
2.3.1. The Buneman-Hartree condition
50
2.3.2. Optimization of a transparent cathode geometry and position
53
2.3.2.1. Optimization of the cathode geometry
56
2.3.2.2. Optimization of 6-emitter transparent cathode azi­
muthal position
58
2.3.3. Experimental measurements of microwave radiation from the
relativistic magnetron with transparent cathode
60
2.3.4. Summary of the relativistic magnetron measurements
68
2.4. Conclusion
69
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3. Microwave pulse compressor
71
3.1. Theory of the microwave pulse compressor
72
3.2. Design of the microwave pulse compression experiment
76
3.3. Computer simulation of the microwave pulse compression experiment
81
3.4. The microwave pulse compression experiment
87
3.5. Conclusion
90
4. Summary and possible future work
91
5. Appendix
94
5. References
102
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LIST OF FIGURES
Fig. 1. NAGIRA radar system [6]: a) photograph of the radar system at forest clutter 2
trials, b) block diagram, c) image o f a helicopter in a "moving reference frame."
Fig. 2. Different designs of the enhanced geometry cathodes: a) encrusted cathode de-
4
sign [12], b) shaped cathode design [14], c) transparent cathode design [10], d) photo­
graph of the transparent (left) and the solid smooth-cylindrical cathodes (right) [17].
Fig. 3. Two designs o f the microwave pulse compressor [21]: a) H-plane single-arm 6
Tee, b) double-arm (Magic) Tee.
Fig. 4. SINUS-6 accelerator located at ECE Department University of New Mexico: a)
8
Tesla transforming with pulse-forming line inside the oil tank, b) tapered transmission
line, c) radiation shielding with vacuum chamber inside, vacuum pump inside the Fara­
day cage and vacuum measuring system, d) output antenna.
Fig. 5. The microwave pulse compressor: a) waveguide assembly/resonant cavity with
9
the double-arm (Magic) Tee, b) gas discharge tube (GDT) switch inside the sort sec­
tion of X-band waveguide.
Fig. 6. The view on the SINUS-6 high-current electron-beam accelerator located in the
11
Pulsed Power, Plasma and Microwave Laboratory, ECE Department, the University of
New Mexico.
Fig. 7. The basic configuration of the SINUS-6 accelerator [31], [32],
12
Fig. 8. Photograph of graphite cathodes used to generate thin tubular electron beams
14
to measure I - V characteristics, cathode radii are 0.9 cm, 1.1 cm, and 1.5 cm.
Fig. 9. Photograph of smooth-cylindrical and transparent cathode with radius 9.1 mm
14
used in experiment with smooth-bore magnetron.
Fig. 10. Photographs of the 6-vane anode block used in experiment with relativistic
15
magnetron.
Fig. 11. Diagnostics used on the SINUS-6 accelerator: coefficients K define the voltage
ratio provided by the capacitive dividers, (Ci+C 2)/C i, and coefficients N define num-
x
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17
ber of windings in the Rogovski coils.
Fig. 12. Calculation of electron trajectories in a coaxial vacuum diode with smooth-
18
cylindrical cathode and smooth anode tube showing two opposite flows of electrons:
the downstream electrons flow to the right from the cathode, while the upstream elec­
trons flow to the left from the cathode: a) screen-shots of the graphical output of the
Field Precision code [37], b) screen-shots of the graphical output of the MAGIC code
[39].
Fig. 13. The measured signals registered by the oscilloscope in the screen room: a) the
20
accelerating voltage diagnostic (with additional 20 db attenuator), and b) the electronbeam current diagnostic. Rk=l.l cm, Ra=2.5 cm, Lk-C= 1 1 .5 cm, Pg= 1 1 0 psi.
Fig. 14. t. ,-parameter of the 18.3 m coaxial cables.
21
Fig. 15. /-parameters of the 18.3 m coaxial cable with 20-db attenuator HP 8491A.
21
Fig. 16. Single pulse of the FPG-30-2 pulse generator on a 50 Q load: a) the load is 22
floating; b) the load is grounded to the SINUS-6 accelerator body.
Fig. 17. Measured voltage pulses used to calibrate the voltage divider: a) the voltage
23
calculated from the signal measured by the current-viewing resistor, b) the voltage
measured at the output of the voltage divider K=2500 (Fig. 11).
Fig. 18. Measured oscillograms of accelerating voltage and electron-beam current in
24
the gas pressure range from 20 psi to 200 psi with the step of 10 psi. Rk=l.l cm,
Ra=2.5 cm, Lk-c—11.5 cm.
Fig. 19. Measured 3D oscillogram+s of accelerating voltage and electron-beam current 24
in the gas pressure range from 20 psi to 200 psi with the step of 10 psi. Rk=l.l cm,
Ra=2.5 cm, Lk-c—11.5 cm.
Fig. 20. The maximal values obtained in the accelerating voltage pulses (a) and in the
25
pulses of electron-beam current (b), measured at different gas pressures (Fig. 18).
Fig. 21.1-Y characteristic obtained from the measured maxima of voltage and current 27
(Fig. 20)
and the measured data taken from [30].
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Fig. 22. Impedance of the electron beam obtained from the measured maxima of volt­ 27
age and current (Fig. 20).
Fig. 23. I-V characteristics measured at different radii of the solid cathode: a) all three
27
together, b) Rk=0.9 cm, c) Rk=l.l cm (please compare with Fig. 21) and d) R k=1.5 cm.
The measured results are compared with theoretical dependence of the FedosovBelomytsev current IFB(4), (5) and the Bogdankevich-Rukhadze current Im (l)-(3).
Fig. 24. The electron flow structures obtained at accelerating voltage 600 kV and ex­ 32
ternal magnetic fields: a) 0.3 T; b) 0.33 T; c) 0.36 T; and d) 0.38 T.
Fig. 25. Calculated spectrograms of microwave oscillations obtained at: a) 600 kV and
33
0.33 T; b) 600 kV and 0.36 T.
Fig. 26. Calculated frequencies of microwave oscillations at accelerating voltage 600 kV 33
and different external magnetic fields.
Fig. 27. Calculated intensities of microwave oscillations at accelerating voltage 600 kV 34
and different external magnetic fields.
Fig. 28. Dependence of the number of rotating electron spokes on accelerating voltage
34
and external magnetic field.
Fig. 29. The electron flow structures obtained at accelerating voltage 600 kV and ex­ 35
ternal magnetic field 0.4 Tesla at different angular dimensions of single emitters of the
6-emitter transparent cathode: a) 10 degrees, and b) 50 degrees.
Fig. 30. Diagram of microwave measurements by a near-field probe.
36
Fig. 31. Photograph of the Tband near-field probe with 40 dB directional coupler,
37
high-power load, HP8492A-10 dB coaxial attenuator, and HP8437B crystal detector.
Fig. 32. Calculated r-parameters of the 40 dB directional couples used to measure mi­ 37
crowave power.
Fig. 33. Diagram of the experimental measurements o f radiated microwave power: 1 — 38
near-field probe, 2 - 90° E-band, 3 - 40 dB directional coupler, 4 - high-power load, 5
- waveguide to coaxial cable adapter, 6 - 10 dB coaxial attenuator, 7 - crystal detector,
8 - coaxial cable, 9 - oscilloscope TDS644A.
xii
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Fig. 34. Measured pulses o f accelerating voltage, total emitted electron current and mi-
39
crowave signal (50 dB attenuation) at -500 kV, -0.75 Tesla, H-plane orientation and
0° position of the near-field probe: a) near-field probe is closed by cupper mesh, b)
near-field probe is open.
Fig. 35. Measured pulses o f discharge current o f magnetic coils and detector signal.
39
Fig. 36. Measured pulses o f accelerating voltage, total emitted electron current and mi-
40
crowave signal (50 dB attenuation) at —500 kV (a) and —450 kV (b), —0.75 Tesla, Hplane orientation and 45° position of the near-field probe.
Fig. 37. Measured pulses o f a) accelerating voltage and b) detector signal (60 dB at- 41
tenuation) at magnetic field 0.315 T, H-plane orientation and 0° position of the near­
field probe.
Fig. 38. Diagram of the experimental measurements of microwave frequency: 1 —near-
42
field probe, 2 - 90° E-band, 3 —40 dB directional coupler, 4 - high-power load, 5 waveguide to coaxial cable adapter, 6 - 20 dB coaxial attenuator, 7 —power splitter, 8 —
crystal detector, 9 - coaxial cable, 10 oscilloscope TDS644A, 11 - microwave cable, 12
—power splitter, 13 —crystal detector, 14 - oscilloscope TDS7404.
Fig. 39. Photograph of first power splitters connected to the output of FIP8492A 20
43
dB coaxial attenuator.
Fig. 40. Photograph of second power splitters located inside the Faraday cage.
43
Fig. 41. Measured pulses o f detector signals at —550 kV, —0.315 T, at H-band orienta- 43
tion and 0° position of the near-field probe.
Fig. 42. Frequency spectrograms calculated from measured pulses of microwave signal 44
at magnetic field 0.315 T, accelerating voltage -550 kV, and H-plane orientation and
0° position o f the near-field probe.
Fig. 43. Time-frequency spectrograms calculated from measured pulses of microwave 44
signal at magnetic field 0.315 T, accelerating voltage —550 kV, and H-plane orientation
and 0° position of the near-field probe.
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Fig. 44. Diagram of the experimental measurements of radial distribution o f micro­ 45
wave power: 1 —output antenna of accelerator, 2 - near-field probe.
Fig. 45. Measured radial distribution of detector signals at accelerating voltage —550 kV
46
and magnetic field —0.315 Tesla.
Fig. 46. The calibration curve showing HP8437B crystal detector response to the input 46
microwave power at frequency 7.56 GHz.
Fig. 47. Photograph of 3-emitter transparent cathode used in experiments with relativ­ 48
istic magnetron.
Fig. 48. Photograph of solid cathode used in experiments with relativistic magnetron.
48
Fig. 49. Photographs o f two components of the anode block of a prototype of a rela­ 49
tivistic magnetron.
Fig. 50. Computer simulations of the 6-vane relativistic magnetron (Fig. 49) with solid 49
cathode (Fig. 48): structure o f the electron flow showing 7t-mode o f the magnetron os­
cillations; electric field oscillation inside first resonator of the magnetron; spectrum of
the electric field oscillations inside the first resonator o f the magnetron.
Fig. 51. Operational domain for 71-mode magnetron oscillation calculated for the mag­ 53
netron with the solid cathode used in this research (Fig. 47-Fig. 50) (a) and for the classi­
cal A6 magnetron (b).
Fig. 52. Different radii of a solid cylindrical cathode in a relativistic magnetron.
54
Fig. 53. Different geometries of a transparent cathode in a relativistic magnetron: a) 3
54
emitters (Fig. 47), b) 6 emitters (Fig. 2(d)), c) 3 blades, and d) 6 blades.
Fig. 54. Different azimuthal position of emitters of a transparent cathode: a) 6 emitters
55
positioned at 0° relative center of the first resonant vane, b) 6 emitters positioned at 20°
relative center of the first resonant vane.
Fig. 55. Electron flow configurations in the A6 relativistic magnetron at different time
moments and three different geometries of the cold cathode.
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56
Fig. 56. Frequency spectrograms obtained during calculations o f the A6 relativistic
57
magnetron operation with different cathodes (Fig. 55) in the broad range of magnetic
field, 0.3-0.65 Tesla.
Fig. 57. Calculated electric field oscillations inside the first resonator of anode block.
58
Fig. 58. Calculated frequency spectrograms of electric field oscillations inside the first 59
resonator of anode block.
Fig. 59. Photographs of the C-band (left) and X-band (right) near-field probes, H-plane
60
orientation of the probes.
Fig. 60. The measured dependences of accelerating voltage, total emitted current, and
61
detector signal on the magnetic field. These dependences were obtained using the
magnetron with solid cathode (Fig. 48).
Fig. 61. Oscillograms obtained with the solid cathode (Fig. 48), H-plane orientated C-
62
band near-field probe.
Fig. 62. Oscillograms obtained with the solid cathode (Fig. 48), E-plane orientated C-
63
band near-field probe.
Fig. 63. Oscillograms obtained with the transparent cathode (Fig. 47), E-plane orientated
63
C-band near-field probe.
Fig. 64. Oscillograms obtained with the transparent cathode (Fig. 47), H-plane orien­ 64
tated C-band near-field probe.
Fig. 65. Total emitted current measured as a function of the radial position o f the near­ 65
field probe (Fig. 44).
Fig. 66. Measured radial distribution o f microwave power delivered by magnetron with
66
solid and transparent cathodes at H-plane and E-plane orientations of the C-band
near-field probe.
Fig. 67. The radiation pattern produced by 7t-mode of magnetron oscillations (TE31) 67
mode (a) and the radiation pattern produced by some other radiation mode (TEu, for
example) (b).
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Fig. 68. Measured radial distribution of microwave power for the magnetron with
67
transparent cathode at H-plane of three different near-field probes.
Fig. 69. Scheme o f the microwave power compressor.
71
Fig. 70. Photograph of the microwave pulse compressor.
72
Fig. 71. Simplified diagram of the microwave pulse compressor: 1 —input waveguide, 2
73
- diaphragm, 3 —resonant cavity. Ai, A 2 , Bi, B2 —electric field components of elec­
tromagnetic waves traveling in opposite direction relative diaphragm at both sides of
the diaphragm.
Fig. 72. Photographs of the gas discharge tube (a) and high-voltage pulser igniting the
77
gas discharge inside that tube (b).
Fig. 73. Measured
-parameters of the tapered waveguide section.
78
Fig. 74. Diagram (a), and photograph (b) of the waveguide assembly designed to the
78
input microwave power measurements, and measured pulses (oscillograms) o f the in­
put microwave power (c).
Fig. 75. Measured oscillograms o f discharge current (a) and photograph of actual gas
80
discharge in the gas discharge tube (b).
Fig. 76. HFSS model of the microwave pulse compressor shown in Fig. 70.
81
Fig. 77. The oscillograms showing the microwave power gain obtained at frequency 82
8.26 GHz.
Fig. 78. Calculated r-parameters of the smooth-waveguide resonant cavity (Fig. 76) and 83
measured %-parameter of (a) the resonant cavity with the smooth waveguide and (b)
the resonant cavity with the same length waveguide and the gas switch at the center
(Fig. 5(b)).
Fig. 79. Electric field distribution inside the HFSS model o f the microwave pulse com- 84-85
pressor (Fig. 70) at frequencies a) 7.5 GHz, b) 8.54 GHz, and c) 9.82 GHz. The or­
thogonal plane shows the gas switch position.
xvi
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Fig. 80. Measured /-parameters of the resonant cavity with closed gas switch and 40 dB
86
attenuator at output of the Magic Tee (Fig. 77(a)) (a) and Network Analyzer HP 8720D
used in these measurements (b).
Fig. 81. Microwave power gain at frequency ~7.56 GHz obtained using the gas switch.
88
Fig. 82. Microwave power gain at frequency ~6.2 GHz obtained using manual switch
88
(Fig. 83).
Fig. 83. The manually operated switch HP X930A.
88
Fig. 84. Microwave power gain at frequency ~9.85 GHz obtained using the same man-
88
ual switch (Fig. 83).
Fig. 85. Oscillograms of the compressed microwave pulse obtained using the gasdischarge switch (Fig. 5(b)) and the manually waveguide operated switch (Fig. 83).
xvii
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89
1. INTRODUCTION AND MOTIVATION
Among all applications o f high-power microwaves (HPM), enhanced radar systems are
particularly well suited to take advantage of the short pulse, high power output [1]. Using higher
microwave power in those systems increases the maximum detection range that depends on
the transmitted power P as P1/4. It turns out, however, that the simple microwave power in­
crease leads to a proportional increase of the signal-to-noise ratio produced by ground/sea
clutter and other interferences. One of the ways to reduce the signal-to-noise ratio is to reduce
the width of the microwave pulse, as the signal-to-noise ratio depends on the pulse duration
T
as ~ 2/cT [2], Using shorter microwave pulses in enhanced radar systems also minimizes the
dead time [3], which is the time when the receiver is turned off while the transmitter operates,
and allows one to detect smaller-cross-section targets, as the range resolution o f a radar 8 de­
pends on the pulse duration as ~cx/2 [1]. The pulse duration should not, however, be too short
because the shorter the pulse, the wider is the frequency band of the microwave signal and,
when the pulse is too short, some of the received microwave power can be out o f the fre­
quency band of the microwave receiver of the radar. Thus, the microwave pulse width should
be sufficiently long to have the bandwidth about that o f the wideband receiver [1].
All the advantages of the short-pulse, high-power microwave application in enhanced
radar systems (increased detection range and signal-to-noise ratio, and decreased dead time and
range resolution) have already been demonstrated by the NAGIRA radar (Fig. 1), built about 15
years ago in the Russian Federation [4], and comprehensively tested in the U.K. [5], [6]. The
NAGIRA system is based on a SINUS-6 high-current electron-beam accelerator, where a Tesla
transformer charges a coaxial oil-filled pulse-forming line (PFL) to ~700 kV, and the PFL is
discharged then by triggering a gas switch into a tapered transmission line ( l ’l'L) that matches
the impedance of the PFL with the impedance of the backward-wave oscillator (BWO), which
is the source of high-power microwaves. The BWO produces a ~10 nsec pulse of microwave
power with maximum of ~ 500 MW with a pulse repetition rate (PRR) up to 150 Hz in Xband. After TEoi-to-TMu mode conversion, the microwave power goes through the extracting
waveguide of the BWO that terminates at a feed hom with a vacuum window through which
the Gaussian shaped microwave beam is extracted [1].
1
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Fig. 1. NAGIRA radar system [6]: a) photograph o f the radar system at forest clutter trials, b) block diagram,
c) image o f a helicopter in a "moving reference frame".
In order to upgrade the performance of an enhanced radar system (Fig. l), the transmit­
ted microwave power should increase up to and above the Gigawatt level. It should be noted,
however, that beside the high microwave power and the short pulse duration, there are some
other very important factors determining the enhanced radar system operation. First is the
pulse-to-pulse stability of the microwave frequency, which is very important because target
motion is detected by subtracting subsequent pulses o f a received echo signal from clutter
(Fig.
1(c)) [2]. Therefore, the accelerating voltage and electron-beam current, as well as magnetic
field magnitude, which determine operation of the BWO in the enhanced radar systems, must
be very precisely controlled to achieve frequency stability [1]. The big issue is also the compact­
ness of the HPM source (Fig. 1(a)) allowing the use of the enhanced radar systems on different
mobile platforms [7]. In view of some of the above-mentioned reasons and a couple of other
factors, the more powerful high-current electron accelerator SINUS-7 operating at maximum
accelerating voltage of —2 MV, total electron-beam current o f —20 kA, pulse width o f —50 ns,
and maximum radiated microwave power of —3 GW from the X-band BWO [8] is probably
less well-suited for use in the short-pulse, high-power enhanced radar systems.
2
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A good alternative for the BWO in the enhanced radar systems can be either relativistic
magnetrons or nonrelativistic magnetrons equipped with a microwave pulse compression
setup. Both of these sources can produce up to 1 GW and higher output microwave power
with sufficiently high pulse repetition rates and frequency stability from one pulse to the next
However, as it was noted above, the key operational parameter allowing any HPM source to be
used in the enhanced radar systems is the short pulse duration or - even more specifically - the
sufficiently short rise time of a transmitted microwave pulse, because shortening the micro­
wave pulses duration itself has never been a big problem for any HPM source [9]. Therefore,
certain effort is required to shape the output HPM pulse in terms o f shortening its rise time
and providing optimal pulse duration. In the case o f a relativistic magnetron, the shortening of
the microwave pulse rise time can be achieved by using transparent cathodes [10]. In the case of
a nonrelativistic magnetron with the pulse compression setup, the shortening of the microwave
pulse rise time can be achieved by using fast, nanosecond-duration switches, and choosing the
optimal configuration/geometry of the pulse compression setup [11],
1.1. Relativistic Magnetron with Enhanced Geometry Cathode
During the past five years or so, a number of novel-shaped cathodes (enhanced ge­
ometry cathodes) have been suggested for replacing traditional smooth-cylindrical cathodes in
relativistic magnetrons. Most o f those suggested cathodes were based on purely computational
efforts; however, some preliminary experiments with an enhanced geometry cathode embed­
ded in a conventional relativistic magnetron have been performed as well. All these efforts
were inspired by searching for ways to shorten the startup time of magnetron oscillations at a
desired magnetron-operating mode and improve the stability of relativistic magnetron opera­
tion. Furthermore, there was interest in providing better mode selection by locking the desired
type of magnetron oscillations at a single-frequency over a rather long period o f time.
There are basically three designs of the enhanced geometry cathodes: i) the traditional
smooth-cylindrical cathode encrusted with selective emission regions (encrusted cathode) de­
veloped by the University of Michigan [12], [13] (Fig. 2(a)), ii) the shaped cathode design (Mickey
Mouse cathode) proposed by AFRL [14] (Fig. 2(b)), and iii) various transparent cathode designs
introduced by the University of New Mexico [10], [15], [16] ((Fig. 2(c, d))).
3
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Emission
Regions
t
a) Encrusted cathode design [12].
b) Shaped cathode design [14].
c) Transparent cathode design [10].
d) Photograph of the transparent (left) and the solid
smooth-cylindrical cathodes (right) [17].
Fig. 2. Different designs o f the enhanced geometry cathodes.
The encrusted cathode design (Fig. 2(a)) began with the idea to prebunch the rotating
electron cloud into the desired number of rotating electron spokes by forming an appropriate
number of azimuthally periodic emitting regions on the surface of a traditional smoothcylindrical cathode. Authors of this invention use the Projection Ablation Lithography [12] to
form the emission sites, although other methods o f smooth-cylindrical cathode encrustation
can be utilized as well. The preliminary experiments with the 6-vane relativistic magnetron
equipped with the encrusted cathode resulted in observation of faster startup and higher effi­
ciency of microwave generation [12]. Suppression of unwanted magnetron operating modes
during startup was also observed in PIC simulations of the 6-vane magnetron operation [13].
The shaped cathode design (Fig. 2(b)) was also proposed to improve the operational pa­
rameters of the AFRL A63 relativistic magnetron by forming the desired number of rotating
electron spokes inside the magnetron environment [14] to shorten the startup time o f the de­
sired type o f magnetron oscillations and to lock the desired operating mode o f a magnetron
4
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during the pulse. The basic idea behind the shaped cathode is, as is the case with the encrusted
cathode, to mark out certain areas of the smooth-cylindrical cathode in order to enhance ex­
plosive emission plasma formation at those regions. However, while the encrusted cathode still
uses a solid cylinder with the emission regions marked out by whatever method can be used to
periodically scratch the surface of a solid cylinder (Fig. 2 (a)), the shaped cathode is redesigned
from the solid cylinder by moving the emission regions upward toward the anode o f the mag­
netron (Fig. 2(b)). Extensive computer simulations o f the AFRL A63 relativistic magnetron with
the shaped cathode have been performed and a dramatic increase in the range of magnetic
fields in which the magnetron functions, as well as an increase of output power and efficiency,
an elimination o f mode competition, and immediate start up of magnetron oscillations were
observed [14]. Extensive experimental testing of the shaped cathode embedded in the AFRL
A63 relativistic magnetron is scheduled to begin soon [14].
The transparent cathode design (Fig. 2(c, d)) was introduced as a way to increase the syn­
chronous electromagnetic field within the rotating electron cloud, thereby providing improved
conditions for fast conversion of the electrons' potential energy into electromagnetic energy
[10], [16].
The transparent cathode consists of a number of longitudinally oriented emitters peri­
odically arranged around an imaginary cylindrical surface (cathode plane). This cathode is trans­
parent to TE modes, which are the operating modes in magnetrons (that is why it is called a
“transparent” cathode). The penetration of the electromagnetic field within the transparent
cathode provides stronger azimuthal electric field, Ee^O, near the cathode surface compared
with the solid cylindrical cathode where Eq=0 at the cathode surface. PIC simulations of the
A6 magnetron operation with the transparent cathode showed significant improvement of the
magnetron operation in terms o f faster startup time of magnetron oscillations and higher effi­
ciency o f the microwave generation in comparison with the traditional smooth-cylindrical cath­
ode [16]. Other benefits are summarized in [16] as well.
1.2. Nonrelativistic Magnetrons with Microwave Pulse Compression
Various experimental schemes of active HPM pulse compression have been studied
during the last 25 years or so [18]-[21]. All these efforts are inspired by searching for ways to in­
crease radiated microwave power by squeezing an initial long-duration, low-power or even CW
5
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microwave signal into a short-duration, high-power microwave pulse while keeping the total
radiated microwave energy constant. The technique involves the slow excitation o f a resonant
cavity with a rather low-power microwave pulse under conditions when coupling between
stored microwave energy and the cavity output is negligible (high Q cavity), and then firing a
fast waveguide switch to destroy the cavity resonance and, in this manner, sharply increase the
coupling between the stored microwave energy and the cavity output (low Q cavity). The
stored microwave energy is then released during the time X that is sufficiently less than the time
t required for storing the microwave energy inside the resonant cavity; the time t scales with the
quality factor of a high Q cavity as ~ Q / CO. Due to the fact that the stored microwave energy is
released much more rapidly than it is stored in the resonant cavity,
T « t,
the output micro­
wave power is greater than the input power by a factor t/T , approximately.
There are basically two designs of the single-mode resonant cavity microwave pulse
compressor utilizing either a single-arm waveguide Tee (Fig. 3(a)) or a double-arm waveguide
(Magic) Tee (Fig. 3(b)). Each design of the resonant cavity has input and output waveguides
connected, respectively, to the input and output arm of a Tee and a short-circuited arm con­
nected to the side arm of a Tee. The short-circuited arm has a switch located at the position
one-quarter (or, in the worst case, some odd numbers of one-quarters) of the waveguide wave­
length away.
L
Input
2L
Output
Cavity
Cavity
_
Cavity
— N
Switch
1
Switch
Output
b) Double-arm (Magic) Tee.
a) H-plane single-aim Tee.
Fig. 3. Two designs o f the microwave pulse compressor [21].
6
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At the storage mode of the microwave pulse compressor operation, the field distribu­
tion inside the resonant cavity has a minimum (where one-half of the waveguide wavelength is
positioned) at the output of a Tee and a maximum (where one-quarter of the waveguide wave­
length is positioned) at the switch position. When the switch is fired, it changes the microwave
pulse compressor from the storage to the extraction mode, at which point the field distribution
inside the waveguide suddenly changes to have a null at the switch position and maximum at
the output of a Tee. In other words, when the switch is closed, the electrical length of the
short-circuited arm is changed by one quarter of the waveguide wavelength that results in the
extraction of stored microwave energy from the resonant cavity [11].
The most important element in the HPM pulse compression setup is the waveguide
switch; it must support the resonant field distribution inside the cavity with low loss during the
storage time, but switch very quickly when closed at the desired release time. Several switching
mechanisms have been studied thus far: spontaneous breakdown of a gas or vacuum arc in the
hollow waveguide, high-voltage plasma discharge in the gas discharge tube (GDT) triggered by
an external source, and even an injected electron or laser beam. Parameters of any switch op­
eration (rise time o f the switch conductivity, duration of the switch operation, location of the
switch relative to the geometry of the stored cavity mode and output waveguide) greatly deter­
mine the duration Xand rise time dx/dt of the output microwave pulse.
1.3. Contributions and Organization of the Research
The main goal of the research presented in this dissertation is to understand basic
physical processes that determine: i) fast start of desired type of magnetron oscillation in rela­
tivistic magnetrons with the transparent cathode (Fig. 2(d)), and ii) parameters of compressed
microwave pulse at the output of the microwave pulse compressor built around the Magic Tee
(Kg- 3(b)).
To implement the first part of the research, a prototype of the relativistic magnetron
with a transparent cathode driven by the SINUS-6 accelerator [22], [23], [24], [25] was built and a
series of preliminary experiments were performed showing the possibility to obtain fast start of
desired type of magnetron oscillations. The SINUS-6 accelerator used in these experiments is
7
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located in the Pulsed Power, Beams, and Microwave Laboratory o f Electrical and Computer
Engineering Department o f the University of New Mexico [26]-[32]; it is similar to that one, that
drives the NAGIRA radar system (Fig. 1(a)). Photographs of the main parts of the SINUS-6 ac­
celerator are shown in Fig. 4 where the following components are shown: Tesla transformer
with pulse-forming line inside the oil tank (Fig. 4(a)), tapered transmission line (Fig. 4(b)), vacuum
chamber with radiation shielding (Fig. 4(c)), and output antenna (Fig. 4(d)).
c)
d)
Fig. 4. SINUS-6 accelerator located at ECE Department University of New Mexico: a) Tesla transforming with
pulse-forming line inside the oil tank, b) tapered transmission line, c) radiation shielding with vacuum chamber
inside, vacuum pump inside the Faraday cage and vacuum measuring system, d) output antenna.
To implement the second part of die research, a prototype of a single-mode cavity mi­
crowave pulse compressor with the waveguide switch made of homemade GDT's driven by a
high-voltage (30 kV) pulse generator was built and a series of preliminary experiments were
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
performed showing the possibility to obtain measurable gain in microwave power with a short
rise time of the pulse. The microwave pulse compressor used in these experiments was assem­
bled from off-the-shelf waveguide components available in the Pulsed Power, Beams, and Mi­
crowave Laboratory. Photographs of the main parts of the microwave pulse compression setup
are shown in Fig. 5 where the following components are shown: waveguide assembly with dou­
ble-arm (Magic) Tee (Fig. 5(a)), and waveguide switch consisting of the GDT placed in center of
a short waveguide section (Fig. 5(b)).
a)
b)
Fig. 5. The microwave pulse compressor: a) waveguide assembly/resonant cavity with the double-arm (Magic) Tee,
b) gas discharge tube (GDT) switch inside the sort section of X-band waveguide.
The reminder o f this dissertation is organized as follows. Chapter 2 presents computer
simulations and experimental measurements of the prototype of the relativistic magnetron with
a transparent cathode, accompanied by an analysis of the obtained results. Chapter 3 presents
computer simulations and experimental measurements of the prototype of the microwave
pulse compressor, and an analysis of the obtained results. Overall conclusions from this work
are presented in Chapter 4. Appendix is a publication showing the possibility o f output magne­
tron mode transformation within the antenna of a diffraction output scheme.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2. RELATIYISTIC MAGNETRON WITH TRANSPARENT CATHODE
The benefits of replacing a smooth-cylindrical cathode with one of the enhanced ge­
ometry cathodes (Fig. 2) are already very well known. It has been demonstrated in many com­
puter simulations that when it is used in relativistic magnetrons [10], [12]-[16], the startup time of
the desired type of microwave oscillations decreases, the efficiency of the microwave genera­
tion increases, and the desired type of microwave oscillations tends to be locked during the
pulse duration, which means less mode competition or even the complete elimination of mode
competition.
However, while the advantages of the enhanced geometry cathodes over its smoothcylindrical counterparts are dear, the reasons why it is so are not completely understood. There
could be three different mechanisms responsible for the manifestation o f these advantages:
i)
the formation of azimuthally varying electron emission, when the emission occurs not
from the entire surface o f a cold cathode but from selected regions only (emission
priming). This effect takes place when any of the enhanced geometry cathodes are used
—the encrusted (Fig. 2(a)), the shaped (Fig. 2(b)), or the transparent (Fig. 2(c)) one;
ii)
the formation of an azimuthally varying quasi-static electric field in addition to the azi­
muthally periodic electric field formed by the anode block of a magnetron (electric
priming). This effect takes place when either the shaped (Fig. 2(b)) or the transparent
cathodes (Fig. 2(c)) are used.
iii)
the formation of an azimuthally varying quasi-static magnetic field in addition to axial
magnetic field provided by magnetic system of a magnetron (magnetic priming). This
effect takes place only when the transparent cathode (Fig. 2(c)) is used or when external
permanent magnets are added [33]-[35].
Therefore, what form of magnetron priming or combination o f some particular prim­
ings is more effective for making a relativistic magnetron operate better? Can one form of
priming suppress another form o f priming and/or vice-versia - can one form of priming en­
hance another form of priming? Answers to these questions can be found by intensive com­
puter simulations of a relativistic magnetron with an enhanced cathode under conditions when
10
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different kinds of primings are simulated separately from one other and/or in combination
with each other. This research lies, unfortunately, beyond of scope of this dissertation.
Nevertheless, among the three different designs of the enhanced geometry cathodes
(Fig. 2), the transparent one is distinguished by its unique properties combining all three of the
above-mentioned forms of magnetron priming. One can see that, while the encrusted cathode
(Fig. 2(a)) provides only emission priming, and the shaped cathode (Fig. 2(b)) provides both
cathode and electric priming, the transparent cathode (Fig. 2(c)) provides the unique combina­
tion of all three —emission, electric, and magnetic priming. This is why the transparent cathode
is studied in this research as the electron source in the prototype of the relativistic magnetron
with enhanced geometry cathode driven by the SINUS-6 accelerator (Fig. 6).
Fig. 6. The view on the SINUS-6 high-current electron-beam accelerator located in the Pulsed Power, Plasma
and Microwave Laboratory, ECE Department, the University of New Mexico.
SINUS-6 (Fig. 4, Fig. 6, Fig. 7) —the pulsed-power nanosecond-duration electron-beam
accelerator —consists again of a Tesla transformer combined with a pulse-forming line, highvoltage gas switch, transmission line, vacuum chamber with vacuum diode, a set o f magnetic
11
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coils with magnetic system power supply, vacuum system, control system operated using a PC,
and different auxiliary systems/units.
energy j
Capocuivs
Higli
TrnntRtjtrcion
Vnl!ii£e
•Switch
Line
High Vehafe
Swt'ch (5paft Oitp>
.Filled wiiti Nitrogen gja.
Tesla Tn«Mtomw£ t :30COj
Fig. 7. The basic configuration o f the SINUS-6 accelerator [31], [32].
The accelerator operates as follows. When it is activated, two capacitor banks are
charged up to some predetermined voltage: the first capacitor bank supplying the Tesla trans­
former is charged up to a voltage of 300 V, and the second capacitor bank supplying the mag­
netic coil system is charged up to the voltage, which is set up before the operation (0.5-1.5 kV
depending on the magnetic field required). After complete charging of these two capacitor
banks, two trigger signals are sent by the control system that initiate discharge of these capaci­
tor banks, i.e. initiate magnetic field and high-voltage pulses. The two instances when these two
capacitor banks get discharged are synchronized relative to each other in such a way that the
capacitor bank of the magnetic system discharges first, and only when the maximum discharge
current in the magnetic coils is achieved (after ~2-5 milliseconds), the second capacitor bank
discharges on the primary winding of the Tesla transformer.
As it happens, the voltage at the second winding of the Tesla transformer and the volt­
age at the output o f the pulse-forming line, which is mounted just inside the Tesla transformer
and electrically connected to its second winding, increase in time very rapidly (a couple of hun­
dreds kV per couple of microseconds). Then the high-voltage gas switch closes due to a self­
breakdown process connecting the output of the pulse-forming line with the transmission line
input. The gas pressure inside the high-voltage gas switch is set up before the operation (1GO-
12
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400 psi depending on the accelerating voltage required), so it determines the breakdown volt­
age at which the gas switch closes. This means that, by changing the gas pressure inside the gas
switch, one can regulate its self-breakdown voltage, which roughly determines the maximum
accelerating voltage applied to the vacuum diode.
After the closing o f the gas switch, the high-voltage pulse travels from the pulseforming line through the transmission line, which is about 3 meter long, and is applied to the
cathode-anode gap of a vacuum diode. The main purpose of the transmission line is to match
the impedance of the pulse-forming line, ~20 Q, with the intrinsic impedance o f the vacuum
diode, >100 Q. The input impedance of the transmission line is ~20 Q, the output impedance
of the transmission line is ~100 Q, and the vacuum diode impedance is determined by the ge­
ometry of the cold cathode in relation to the geometry o f the anode tube ( ~ 0 2") or whatever
other anode structure sits inside the anode tube. In the ideal case, these two impedances (out­
put impedance o f the transmission line and impedance of the vacuum diode) are the same.
When the high-voltage pulse from the output of the transmission line is applied to the
vacuum diode, explosive emission appears at the cold cathode and emitting electrons get accel­
erated within the anode-cathode gap of the vacuum diode drifting at the same time in the
crossed EXB fields resulting finally in the electron beam formation that travels then down­
stream from the cathode inside the anode tube. The electron beam is used to generate highpower microwaves by whatever anode block/structure of some specific HPM device (BWO,
magnetron, coaxial vircator, etc.) sits inside the anode tube and forms the geome­
try/ configuration of the vacuum diode.
For the purpose of this dissertation, the following configurations of the vacuum diode
were studied:
i)
smooth-cylindrical cathode inside the smooth anode tube immersed in a very large
(maximum achievable) magnetic field. This —ever-simplest configuration of the vac­
uum diode - produces a coaxially insulated tubular electron beam traveling in the axial
direction. Experiments with this particular configuration of the vacuum diode were
performed to calibrate basic diagnostics used to monitor accelerating voltage and elec-
13
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tron-beam current, as well as to measure the current-voltage characteristics o f the ac­
celerator. A photograph of the cold cathodes of different radii is shown in Fig. 8. All
these cathodes were made from the semiconductor grade POCO graphite [36];
Fig. 8. Photograph o f graphite cathodes used to generate thin tubular electron beams to measure I-V
characteristics, cathode radii are 0.9 cm, 1.1 cm, and 1.5 cm.
ii)
smooth-cylindrical and 8-emitter transparent cathode inside the smooth anode tube at
"resonant" magnetic fields. This configuration corresponds to the so-called "smooth­
bore" relativistic magnetron [38]. Experiments with this prototype of the "smooth­
bore" magnetron were performed to tune microwave diagnostics monitoring the time
evolution and radial distribution of radiated microwave power as well as the radiated
microwave frequency. Photographs o f the smooth-cylindrical and transparent cold
cathodes used in this experiment are shown in Fig. 9. All these cathodes were also made
from the semiconductor grade POCO graphite [36];
Fig. 9. Photograph o f smooth-cylindrical and transparent cathode with radius 9.1 mm
used in experiment with smooth-bore magnetron.
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
iii)
smooth-cylindrical and either a 3- or 6-emitter transparent cathode inside the 6-vane
magnetron structure at "resonant" magnetic fields. This configuration corresponds to
the relativistic magnetron itself. Experiments with this prototype of the relativistic
magnetron were performed to study the effect of the transparent cathode on the char­
acteristics o f the radiated microwave power as compared with its smooth-cylindrical
counterpart. Photographs of the smooth-cylindrical and the 6-emitter transparent cath­
odes ( 0 0.9 cm) used in this experiment are shown in Fig. 2(d), and photographs of the
anode block of the 6-vane relativistic magnetron are shown in Fig. 10. Both the cathode
and anode block were made from the semiconductor grade POCO graphite [36].
Fig. 10. Photographs o f the 6-vane anode block used in experiment with relativistic magnetron.
The reminder of Chapter 2 is organized as follows. Section 2.1 presents results of the
current-voltage characteristics measurements and a short discussion concerning these results.
Section 2.2 presents results o f the prototype of the "smooth-bore" magnetron simula­
tions/measurements and Section 2.3 presents results o f the prototype of the 6-vane relativistic
magnetron simulations/measurements. Analysis of the results obtained is presented in Section
2.4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.1. Current-Voltage Characteristics of the SINUS-6 Accelerator
One o f the very important operational features o f any accelerator is its current-voltage
(I-V) characteristic determining how much of the emitted electron current one can obtain at a
given accelerating voltage at any given moment o f time. Generally speaking, the I-V character­
istic depends on the impedance of the vacuum diode alone. However, given the fact that the
Tesla transformer of the SINUS-6 accelerator is the current source (or source of an electrical
current) and that the total amount of electron current emitted from the cold explosiveemission (with unlimited emission capability) cathode driven by the Tesla transformer is de­
termined by the impedance of the vacuum diode and by accelerating voltage (which the Tesla
transformer is available to provide at any given moment of time because this is the current
source and not a voltage source), the following two scenarios determining the total amount of
electron current emitted from the cold cathode are possible:
In the first very general case, when the total emitted electron power, which is a product
o f accelerating voltage and total emitted electron current, is less then the total electrical power
available from the Tesla transformer, the total emitted electron current and the accelerating
voltage do not affect each other. This means that the accelerating voltage is still determined by
transient processes developed inside the electrical scheme of the Tesla transformer and both
pulse-forming/transmission lines, and the total emitted electron current is determined by this
accelerating voltage and the impedance of the vacuum diode. However, in the worst case,
when the total emitted electron power tries to exceed the total electrical power available from
the Tesla transformer, the total emitted electron current affects the accelerating voltage in such
a way that it reduces the accelerating voltage down to the level at which the total emitted elec­
tron power is equal to the total electrical power available from the Tesla transformer. Thus, the
basic reason of the I-V characteristics measurements is to find out when this limitation occurs
or, in other words, to find out what is the limiting emitted electron-beam current above which
the total emitted electron power begins to affect the accelerating voltage by reducing it.
Measurement of an I-V characteristic means the measurement o f both cathode-anode
voltage drop or accelerating voltage and total emitted electron current or electron-beam current
in one pulse. However, given the current condition of the SINUS-6 accelerator, the only point
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where the high-voltage pulse can be quantitatively measured is at the end o f the transmission
line (K:=2500 at Fig. 11), and the only point where the emitted electron current can be quantita­
tively measured is the collector placed downstream from the cathode inside the anode tube
(Fig. 12).
Additionally, the qualitative measurements o f the total emitted electron-beam current
can be obtained using the Rogovski coil located near the cathode (N=1000 at Fig. 11). This coil
measures current of downstream electron flow which travels from the cathode down to the
collector and current o f that part of the upstream electron flow which is deposited to the an­
ode tube (Fig. 12) and does not monitored by the Rogovski coil as the upstream electron flow.
However, depending on the magnetic field configuration in the vacuum diode, a part o f the
upstream electron flow is not deposited to the anode tube, travels back to the end o f the trans­
mission line through the Rogovski coil, and is monitored by the Rogovski coil as the upstream
electron flow causing at the output of the Rogovski coil a superposition of two different signals
that correspond to, respectively, the downstream and the upstream electron flows.
Capacttattm di-rtder K-2800
\S
CaptcUntlm divider K-5000
Rogowkl coll N-10Q0
Kogonid coll *»1700
✓/
Fig. 11. Diagnostics used on the SINUS-6 accelerator, coefficients K define the voltage ratio provided by the
capacitive dividers, (Ci+C 2)/C i, and coefficients N define number of windings in the Rogovski coils.
These two electron currents determined by downstream and upstream electron flows
are limited by their own space charge accumulated in the appropriate parts of the anode tube
given the fact that the downstream electron flow travels inside the hollow anode tube toward
the output antenna of the accelerator (Fig. 12), and the upstream electron flow travels in the op­
posite direction between the cathode/cathode holder and the anode tube (Fig. 12) toward the
Rogovski coil N^IOOO (Fig. 11).
17
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o , o o o e + oo
O.OOOE+OO
a)
s
-
|
T 0
100
300
200
Z (n]
T ^ ‘
400
(E
"b)
Fig. 12. Calculation o f electron trajectories in a coaxial vacuum diode with smooth-cylindrical cathode and
smooth anode tube showing two opposite flows o f electrons: the downstream electrons flow to the right from
the cathode, while the upstream electrons flow to the left from the cathode:
a) screen-shots o f the graphical output o f the Field Precision code [37],
b) screen-shots o f the graphical output of the MAGIC code [39].
Given all the above-mentioned circumstances, the measured I-V characteristics turn
out to be relations between i) the measured values of the limiting electron-beam current flow­
ing downstream from the cathode (Fig. 12), and ii) the inferred values of voltage at the end of
the transmission line (Fig. 11).
2.1.1. Simplest theory of limiting currents in cylindrical geometry
Traditionally, the total (limiting) electron-beam current achieved at a given accelerating
voltage in cylindrical geometry in an anode tube is supposed to be the Bogdankevich-Rukhadze
limiting current, IBR, determined by electron-beam space charge alone [40]. This limiting current
is determined by the space charge of the electron beam entering the cylindrical anode tube
along the guiding magnetic field lines with some non-zero initial velocity o f beam electrons
(the boundary condition), Vrj£0, expressed in terms of the dimensionless parameter % [40]-[43],
f 2
rl
3
(1)
2 In
where ra and rb are the anode tube and the electron beam radii, yais the dimensionless parame­
ter associated with the voltage drop U between the traveling electron beam and the anode tube,
18
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m, and qe are the electron mass and charge, respectively, c is the speed o f light, I0 is the Alfven
current [44], [45]
and
= V,J c, and V0is the electron velocity.
In some cases, however, when the cathode with radius rk - the source o f the beam
electrons —is immersed in a (uniform) magnetic field, the maximum electron-beam current,
still limited by its own space charge, is governed by another boundary condition, which is zero
electron initial velocity on the cathode surface, Vg~0. This limiting current is called the Fedosov-Belomytsev current, Im, and is determined as follows [46]
2 In
n
r F = -0 .5 + J l y a + 0 .2 5 .
Following this simple explanation of the theory o f limiting currents, the electron-beam
current measured in the SINUS-6 accelerator downstream from the cold explosive emission
cathode immersed in a strong longitudinal magnetic field (Fig. 12) should be the limiting Fedosov-Belomytsev current determined by (4), (5).
2.1.2. Calibration of the diagnostics
Given the circumstances pictured above, measurements of the accelerating voltage
pulses have been performed using a voltage divider mounted at the end of the transmission
line (K=2500 at Fig. 11) at a distance —21 inches upstream from the edge o f the cathode, and
measurements of the electron-beam current pulses have been performed using a graphite col­
lector placed at a distance 4-25 inches downstream from the edge of the cathode inside the an­
ode tube and the current-viewing resistor 0.01 Q (CVR) inserted in the collector circuit. The
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
measured signals have been transferred using 18.3 m (60-feet) long coaxial cables to the
TEK644A oscilloscope located inside a screen room. The monitored pulses have been ac­
quired and stored in the PC.
Typical signals registered by the oscilloscope from the accelerating voltage and the elec­
tron-beam current diagnostics are shown in Fig. 13. The measurements have been performed
using a smooth-cylinder graphite cathode with radius 1.1 cm (Fig. 8), an anode tube with radius
2.5 cm, a cathode collector distance —11.5 cm, and gas pressure in the gas switch of 110 psi.
One can see in Fig. 13 that the FWHM o f both pulses is about 15 ns, and there is a time delay of
about 5 ns between the voltage and the electron-beam current pulses caused mainly by the dis­
tance between the voltage divider and the CVR located outside the vacuum volume close to
the end of the anode tube where the Rogovski coil N=1700 is located (Fig. 11).
20
18
• dectron-1
16
>
if
!>
&
3
o
accelerating voltage 4.
o
10
8
Io 6
O 42
110 psi
0maximum of
accelerating volatge ....
•10
-5
0
-2 .
-4
5
10
15
20
25
30
-10
35
-5
0
5
10
15
20
25
30
35
'lime, ns
Time, ns
a)
b)
Fig. 13. The measured signals registered by the oscilloscope in the screen room: a) the accelerating voltage diag­
nostic (with additional 2 0 db attenuator), and b) the electron-beam current diagnostic. Rk=l .1 cm, R«=2.5 cm,
Lk-C= 1 1 .5
cm, P g = 1 1 0 psi.
However, in order to extract correct values of accelerating voltage and electron-beam
current from measured oscillograms (Fig. 13), all diagnostics have to be calibrated. Below is the
description of measurements/calculations that have been performed to calibrate these two di­
agnostics.
1)
Coaxial cables: The 18.3 m long coaxial cables PE3087-720 have been calibrated to
measure the attenuation coefficients corresponding to the actual time variation o f the volt-
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
age/current pulses (Fig. 13). Calibration o f coaxial cables was performed using a HP 8720D
Network Analyzer, which allows one to measure r-parameters of any two-port device, which in
our case are the coaxial cables. The measured .^-parameters of all coaxial cables used in this
research are presented in Fig. 14, and since one of the cables that connects the voltage divider
with an oscilloscope uses a 20-db HP 8491A attenuator (Fig. 13(a)), j-parameter measurements
of one of the 18.3 m long cable with this attenuator have been made as well (Fig. 15).
One can see in
Fig.
u that in the frequency range 25-50 MHz, which approximately cor­
responds to the measured voltage/current variation in time (Fig. 13), the %-parameter or the
attenuation coefficient of the coaxial cable is about 0.8. One can also see in
Fig.
is that in the
same frequency range 25-50 MHz, the r?_,-parameter or the attenuation coefficient of the coax­
ial cable with 20 dB attenuator is about 0.08.
0.9
cable#l
•cable#2 ■cable#3
cable#4'
■cable#5
0.12
1
Liner magnitude
with attenuator 20 dB
4/ 14/2005 13:53:53
S
21
&
Ia
PE3087-720 (60 feet)
4/14/2005 08:41:43
0 .0
0.1
0 .2
0.3
0 .4
0.5
0.6
0.7
0.8
0.9
1.0
Frequency, GHz
Fig. 14. si^-parameter o f the 18.3 m coaxial cables.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Frequency, GHz
Fig. 15. T-parameters o f the 18.3 m coaxial cable with
20 db attenuator H P 8491A.
2)
Voltage divider. The capacitive voltage divider K=2500 (Fig. 11) has been calibrated to
obtain the coefficient that relates the voltage at the output of the divider, V Mv, to the actual
voltage measured by the divider, V„. Calibration o f the voltage divider was performed using a
high-voltage pulse generator, FPG-30-2 o f FID Technology GmbH, that produces —25-30 kV
voltage pulses of —50 ns FWHM duration on a matched load, —50 Q (Fig. 16). This pulse gen­
erator was utilized also in the experiments with the microwave pulse compressor to fire the gas
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
discharge tube (Fig. 5(b)) that opens the resonant cavity and releases in such a way the stored
microwave energy outside of the cavity (see Chapter 3).
ch2
I
£
4)
-40
-20
0
20
40
60
80
100
120
140
•100
160
-50
0
50
Time,ns
100
150
200
250
300
Time,ns
a)
b)
Fig. 16. Single pulse of the FPG-30-2 pulse generator on a 50 Q load: a) the load is floating;
b) the load is grounded to the SINUS-6 accelerator body.
The pulses produced by the high-voltage generator FPG-30-2 (Fig. 16) were measured
by the 0.01 Q current-viewing resistor inserted in the load circuit under conditions: i) when the
load was connected only to the grounded body o f the FPG-30-2 pulser (Fig. 16(a)), and ii) when
the load was connected to the grounded body of the SINUS-6 accelerator (Fig. 16(b)) in such a
manner that both the FPG-30-2 pulser and the accelerator were grounded at one point.
Next, the central electrode of the transmission line was additionally connected to the
high-voltage side o f the load and two signals were measured simultaneously (Fig. 17): one from
the same current-viewing resistor, 0.01 Q, monitoring the total discharge current flowing
through the load (Fig. 17(a)), and another one (Fig. 17(b)) from the output of the voltage divider
K=2500 (Fig. 11) monitoring voltage at the central electrode of the transmission line near its
end, which is the only point where, given the current condition of the SINUS-6 accelerator
(Fig. 6, Fig. 7),
the accelerating voltage generated by the Tesla transformer (Fig. 13(a)) can be
measured quantitatively.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ch2
£
2
■
>o
>
§>
iS
o
>
ch3
100
250
Time, ns
b)
a)
Fig. 17. Measured voltage pulses used to calibrate the voltage divider: a) the voltage calculated from the signal
measured by the current-viewing resistor, b) the voltage measured at the output o f the voltage divider K=2500.
The calculated relation between the two measured voltage pulses, which is proportional
to the dividing coefficient of the voltage divider, is ~0.37. Taking into account that the signal
measured by the current-viewing resistor corresponds to the voltage, V 0 (Fig. 17(a)), the coeffi­
cient is calculated as
1 0.01Q
Vdiv
0.37 6 0 0
3)
: 0.45 10“
(6)
Calibration coefficients: The total calibration coefficient of the accelerating voltage diag­
nostic that shows the relation of the voltage registered by the oscilloscope, V m in V, to the ac­
tual voltage measured by the voltage divider, V 0 in kV, with additional account of signal at­
tenuation caused by the measuring cable with a 20 dB attenuator (Fig. 15) is
V
103
= 0.08 •0.45— v = 0.0361.
VJkV)
103
—
(7)
The total calibration coefficient of the electron-beam current diagnostic that shows the
relation of the voltage registered by the oscilloscope, V m. in V, to the actual electron-beam cur­
rent measured by the low-inductance shunt, 0.01 Q, I0 in kA, with additional account o f signal
attenuation caused by the measuring cable (Fig. 14) is
V
1
—**■ =0.01Q-0.8—- - = 8.
/„ (M )
IQ"3
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(8)
w
2.1.3. Voltage, current, and total electric power measurements
The same measurements (Fig. 13) were performed across a broad range of gas pressure
in the gas switch - from 20 psi to 200 psi with a step o f 10 psi. At each gas pressure, 10 pulses
were measured and recalculated using the calibration coefficients
(7)
and
(8)
and stored in the
PC. A set of 20 oscillograms, consisting of one pulse taken from 10 measured ones at each gas
pressure, is shown in Fig. 18, and 3D oscillograms incorporating all 200 pulses arranged as a
function of maximum voltage achieved in the pulse are shown in Fig. 19.
4.5 ->
5 0 -|
-50
s
uI
-250
63
-300
o
>
-4 5 0 '
-500
-550.
0
2
4
6
8
10
12
14
16
18
0
20
Time, ns
2
4
6
8
10
12
14
16
18
20
Time, ns
Fig. 18. Measured oscillograms o f accelerating voltage and electron-beam current in the gas pressure range from 20
psi to 200 psi with the step o f 10 psi. Rk=l.l cm, Ra=2.5 cm, Lk.c=11.5 cm.
Fig. 19. Measured 3D oscillograms o f accelerating voltage and electron-beam current in the gas pressure range
from 20 psi to 200 psi with the step o f 10 psi. Ri=l-1 cm, Ra=2.5 cm, Lk-c=11.5 cm.
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The maximum values o f the accelerating voltage and the electron-beam current pulses
are extracted then from the measured oscillograms (Fig. 18, Fig. 19) and plotted as function of
the gas pressure in the gas switch (Fig. 20)1.
550
3
400.
3
§ 350
2.50-
2.25'
2.0 0 '
—
Present measurements
-* • — Vatche Soualian, 1998 —
P-71
0
20
40
60
80
100
120
140
160
180
200
0
220
Pressure, psi
20
40
60
80
100
120
140
160
180
200
220
Pressure, psi
a)
b)
Fig. 20. The maximal values obtained in the accelerating voltage pulses (a) and in the pulses of electron-beam
current (b), measured at different gas pressures (Fig. 18).
The obtained results (Fig. 20) show that the lowest accelerating voltage which is achiev­
able at 20 psi is about 200 kV at an electron-beam current o f ~1.5 kA; the highest accelerating
voltage which is achievable at 200 psi is about 600 kV at an electron-beam current of —4.25
kA. Note that there is a big spread at each given gas pressure. The results show also that the
dependence of the maximum accelerating voltage on the gas pressure (Fig. 20(a)) is linear while
the voltage is below —500 kV and is less linear at voltages above —500 kV. The measurements
were compared with data taken from [31]. One can see good coincidence between the two
measurements at voltages —500 kV, and very poor one at voltages >500 kV (Fig. 20(a)). The
possible explanation of this disagreement is below.
The analysis of measured oscillograms (Fig. 18) shown in Fig. 20 is very important for es­
timation of the maximum electric power available from the Tesla transformer o f the SINUS-6
accelerator for a single shot. The point is that the disagreement between the present measure­
ments (Fig. 18) and results presented in [31] on the voltage vs. gas pressure plot (Fig. 20(a)) at high
1 The maximum accelerating voltage is but one metric o f many possible that one can use to compare I-V char­
acteristics. Unfortunately, it is not possible to direcdy measure the cathode voltage.
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
voltages (above —500 kV) does not indicate on any error made either in this research or in [31].
It just shows that during the measurements made in [31] the emitted electron current was not
big enough to affect the accelerating voltage by reducing it. Furthermore, it does show that the
measurements made in this research were performed under conditions when the emitted elec­
tron current (at voltages greater then 500 kV) gets to be so high, 4.0-4.5 kA (Fig. 20(b)), that the
total emitted electron power gets to be comparable to the total electrical power available from
the Tesla transformer. This effect allows one to calculate the limiting electrical power available
to operate the SINUS-6 accelerator.
Estimations of the total electron-beam power in the downstream electron flow made
using results shown in Fig. 20 give a value of 2.5-3.0 GW in the maximum of a pulse. Taking
into account upstream electron flow as well (Fig. 12), the total estimated electric power available
from the Tesla transformer of the SINUS-6 accelerator turns out to be at the level o f —4-5
GW, which is a very reasonable value.
2.1.4. I-V characteristic and impedance of vacuum diode
Results presented in Fig. 20 can be used also to plot: i) the I-V characteristic o f the vac­
uum diode by relating the electron-beam current to the accelerator voltage (with the care at
that this is inferred) at any given value o f gas pressure, and ii) the impedance of the vacuum
diode by dividing the accelerator voltage by the electron-beam current at any given value of gas
pressure.
The I-V characteristic obtained in this manner is shown in Fig. 21 and the impedance is
shown in Fig. 22 (for cathode radius 1.1. cm and cathode-collector distance 11.5 cm). The ob­
tained I-V characteristic (Fig. 21) is compared with results of measurements (at —610 kV) taken
from [30]. The I-V characteristics measured for other radii of the cold cathode (Fig. 8) and a
comparison of these measurements with theoretical predictions (l)-(5) are shown in Fig. 23.
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
200
4.5
250
300
350
400
5/2/2005 3.8:39:14
■
4 .0 .
45 0
500
550
600
650
4.5
j
Larald Moreland, 1995
p.67, A-K gap is 15 mm
120
3 .0 .
CJ
%
2.5
Q
.
a
3.5
5/7/2005 36:35:21
2 .0 .
impedance, -140 £2
the
1.5-
3.0-
150
150
200
250
300
350
400
450
500
550
600
650
200
250
300
350
400
450
500
550
600
650
Maximum Voltage, kV
Maximum Voltage, kV
Fig. 21. I-V characteristic obtained from the measured
Fig. 22. Impedance o f the electron beam obtained from
maxima of voltage and current (Fig. 20) and the meas­
the measured maxima o f voltage and current (Fig. 20).
ured data taken from [30].
3.5
r£=0.9 cm
<' 3.0
&
C 2.5
83 2.0
u
1.1 cm
r*=l. 5
1.5
o
cc
a 1.0
8 0.5
&
w o.o
e
B
M 05
03 0 . 0 .
100 150 200 250 300 350 400 450 500 550 600
100
Accelerating Voltage (kV)
limiting current
limiting current
150 200 250 300 350 400 450 500 550 600
Accelerating Voltage (kV)
b)
a)
4.5-.
♦*
4.0.
3.5
O
2.5'
2.0
a l.o-
—
L_ limiting current
limiting current
IBRlimiting current
I limiting current
S,
0.5
0.0
100 150 200 250 300 350 400 450 500 550 600
100 150 200 250 300 350 400 450 500 550 600
Accelerating Voltage (kV)
Accelerating Voltage (kV)
c)
d)
Fig. 23. I-V characteristics measured at different radii of the solid cathode: a) all three together, b) Rit=0.9 cm, c)
Rk=l.l cm (please compare with Fig. 21) and d) Rk^l.5 cm. The measured results are compared with theoretical
dependence o f the Fedosov-Belomytsev current Ifb (4), (5) and the Bogdankevich-Rukhadze current Jbr (l)-(3).
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A brief analysis of the obtained results (Fig. 23) shows that:
•
at accelerating voltages below —250 kV, the measured electron-beam current coincides to
some extent with the Bogdankevich-Rukhadze current (l)-(3), which is the limiting current
determined by a non-zero initial electron velocity condition, i.e. when the electron beam
enters the region of uniform magnetic field with a constant velocity. In this case, electrons
are supposed to be already accelerated before entering the magnetic field region;
•
at accelerating voltages above —450 kV, the measured electron-beam current coincides
very well with the Fedosov-Belomytsev current (4), (5), which is the limiting current deter­
mined by a zero initial electron velocity condition, i.e. when the electron beam is formed
inside the region o f uniform magnetic field with zero initial velocity. In this case, the elec­
trons are supposed to be produced inside the magnetic field region;
•
at accelerating voltages from —250 kV to —450 kV, the measured electron-beam current
smoothly changes (as the accelerating voltage increase) from the Bogdankevich-Rukhadze
to the Fedosov-Belomytsev current limits.
It is not clear right now why the behavior of the I-V characteristics is like this. One of
the explanations of this effect is that, for the relatively short pulses o f the electron-beam the
time required to fill the cathode-collector space (Fig. 12) by the electron-beam space charge is
going to be comparable with the electron-beam pulse duration. In this situation, part of the
downstream electron flow travels from the cathode down to the collector (Fig. 12) in free space
not compensated or only partly compensated by the electron-beam space charge that causes
the electron-beam current to increase above the Fedosov-Belomytsev limit (4), (5). The analo­
gous effect of the measured electron-beam current increase above the appropriate limit was
detected and studied experimentally during measurements of the Child-Langmuir limiting cur­
rent in the planar vacuum diode [47], [48]. In order to show that the results obtained in this re­
search (Fig. 23) is the cylindrical geometry analog of the plane geometry cathode measurements
where the above-limiting electron-beam currents were observed [47], intensive computer simu­
lations of the temporal dynamics of a thin tubular electron beam formed in strong longitudinal
magnetic field and traveling in an axial direction inside the smooth anode tube should be per­
formed. This research lies, unfortunately, beyond o f the scope of this dissertation.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.1.5. Summary of diagnostics calibration and I-V characteristics measurements
The research activity described in Section 2.1 was performed mainly to calibrate basic
diagnostics monitoring voltage and electron-beam current from the SINUS-6 accelerator. The
calibration coefficients presented in (7) and (8) were obtained. Along with this, the very impor­
tant information showing maximum electrical power available from the Tesla transformer of
the accelerator was obtained (Fig. 20). It turns out that the maximum electrical power available
from the Tesla transformer is about 5 GW in the maximum of a pulse.
Another result obtained during these measurements is the unusual behavior o f the I-V
characteristics (Fig. 23) plotted as the relation of maxima of the electron-beam currents obtained
in a pulse to the maxima of accelerating voltages obtained at the same pulse. These characteris­
tics show that at low accelerating voltages the measured dependences coincide with the Bog­
dankevich-Rukhadze limiting current (l)-(3), but at high accelerating voltages they coincide with
the Fedosov-Belomytsev limiting current (4), (5).
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.2. Smooth-Bore Magnetron with a Transparent Cathode
The smooth-bore magnetron is essentially a magnetically insulated coaxial diode, where
electrons are emitted from a cathode and form an electron flow or Brillouin hub rotating
around the emitter in an external crossed longitudinal magnetic Ho and radial electric Eo fields
with a2imuthal velocity Ve# determined as [49]
2r„
(10)
where H 0z is the longitudinal magnetic field and H 0o is the azimuthal magnetic field produced
by the cathode current I flowing along the emitter [50], U is the accelerating voltage applied
between the cathode and anode with radii rk and r# respectively, (rz- rg) / 2 ra is the effective
cathode-anode gap width [51], and rbis the radius of the electron flow rotating inside the anode
tube
The criterion of magnetic insulation preventing deposition of the rotating electron flow
on the anode surface is [38]
(11)
where ya is the relativistic factor (2), H cis the critical magnetic field below which the magnetic
insulation is violated, and mt and qt are the electron mass and charge, respectively.
The key feature of the magnetron is that due to some fluctuations in the azimuthal
electron charge density distribution inside the Brillouin hub, caused, probably, by different
kinds of electron flow instabilities, the magnetic insulation gets violated below the critical mag­
netic field H c (11) and the magnetron structure of the electron flow with a number of rotating
electron spokes is formed within the cathode-anode accelerating gap. As it happens, the azi­
muthally oscillating electron current begins to synchronously interact with some specific azi­
muthal eigenmodes of the coaxial waveguide, characterized by its inner rk and outer ra radii,
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
producing microwave oscillations. After this, the magnetron operates as an oscillator due to the
internal feedback of the interacting system “azimuthally oscillating electron currents - excited
electromagnetic oscillations” and radiates either in many frequencies as synchronism can simul­
taneously occur with many possible eigenmodes of the coaxial waveguide, or in a single fre­
quency that emerges from mode competition.
It should be noted at this point that the exact theory of the origin of the rotating elec­
tron spokes in a smooth-bore magnetron is not yet developed [52]. There are a number o f sug­
gestions explaining the violation of magnetic insulation (11) and the formation of rotating elec­
tron spokes inside the smooth coaxial waveguide below the critical magnetic field H 0, among
those are back-bombardment instability of secondary-emission cathodes [53], [54], instability of
the Brillouin hub during its rotation in crossed E-H fields [55], [56], electron charge diffusion
across the cathode-anode gap as a consequence of energy exchange within the Brillouin hub
[57], etc. Therefore, what is the origin of the magnetron-like instability when a number o f rotat­
ing electron spokes appear in the smooth-bore magnetron? Answers to this question can be
found by intensive computer simulations of a smooth-bore magnetron at different magnetic
field that are the "resonant" magnetic fields for different types of the rotating electron spoke
structure. This research lies, unfortunately, beyond the scope of this dissertation.
A study of the smooth-bore magnetron operation was performed in this dissertation to
develop the technology of transparent cathode manufacturing (Fig. 2(d)) and the practice of its
use with the SINUS-6 accelerator (Fig. 6), as well as to tune and calibrate microwave diagnostics
monitoring output microwave power radial distribution and its variation during the pulse, and
the frequency of the output.
2.2.1. Computer experiments with smooth-bore magnetron
For the purpose o f this research, a smooth bore magnetron with an 8-emitter transpar­
ent cathode (Fig. 9) was simulated using the 2-dimensional version of the Magic code [39]. The
geometrical parameters o f the simulation model are: anode radius is 25.4 mm; outer cathode
radius is 9.1 mm ( 0 18.2 mm); inner cathode radius is 6 mm; azimuthal dimension of one sin­
gle emitter is 30°; azimuthal distance between two adjacent emitters is 15°. The simulations
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
were performed at accelerating voltages 400 kV, 500 kV, and 600 kV and at different external
magnetic fields Hoz in order to find the "resonant" magnetic field at which the magnetron oscil­
lations at the frequency of interest are most intense. The accelerating voltage U increases from
zero to some constant voltage, 600 kV for example, with a rise time of ~1 ns, while the exter­
nal magnetic field Hoz is a constant during the simulation time.
The simulations showed that at a given accelerating voltage there are different electron
flow structures that are formed at different external magnetic fields (Fig. 24).
Fig. 24. The electron flow structures obtained at accelerating voltage 600 kV and external magnetic fields:
a) 0.3 T; b) 0.33 T; c) 0.36 T; and d) 0.38 T.
At accelerating voltage 600 kV and below a magnetic field of 0.3 T, the electron flow
rotates as a solid disk (Fig. 24(a)). As the external magnetic field Hoz increases, the rotating elec­
tron flow is transformed into the 2-spoke structure (Fig. 24(b)) at 0.31-0.33 T, into the 3-spoke
structure (Fig. 24(c)) at 0.34-0.37 T, into the 4-spoke structure (Fig. 24(d)) at 0.38-0.40 T, and into
the higher order structures at external magnetic field above 0.4 T.
Each specific electron flow structure (Fig. 24) corresponds to some specific set of fre­
quencies of microwave oscillation that can be recognized as unique spectral lines on a calcu-
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
lated spectrogram of microwave oscillations (Fig. 25). The first three most intense spectral lines
are produced by the electron flow structure characterized by two rotating spokes (Fig. 24(b)) ra­
diating at frequency ~2 GHz (Fig. 25(a)), three spokes (Fig. 24(c)) radiating at frequency ~3 GHz
(Fig. 25(b)),
and four spokes (Fig. 24(d)) radiating at frequency ~4 GHz. The calculated depend­
ences of the frequency of microwave oscillations on the external magnetic field Hqz obtained
by analyzing calculated spectrograms (Fig. 25) are shown in Fig. 26.
o
o
o
LT>
0
10
20
F requency
20
10
30
(GHz)
30
F requency
a)
(GHz)
b)
Fig. 25. Calculated spectrograms o f microwave oscillations obtained at:
a) 600 kV and 0.33 T; b) 600 kV and 0.36 T.
10
One can see in Fig. 26 that the given
9
geometry of smooth-bore magnetron with 8-
8
2 spcikes
emitter transparent cathode (Fig. 24) produces
4 spokes
5 spokes
7
at least 4 different spectral lines, the frequen­
cies of which slightly decrease as the external
magnetic field increases. It should be noted
also that the intensities of the spectral lines,
which are expressed in terms of Volts/GHz
3
2
3
2
1
O'
0 .3 0
0.32
0 .3 4
0 .3 6
0.38
0.40
0.42
0 .4 4
0.46
Magnetic Field (Tesla)
in the 2D calculational geometry (Fig. 24), are
Fig. 26. Calculated frequencies o f microwave
also different at different external magnetic
fields (Fig. 25).
oscillations at accelerating voltage 600 kV and different
external magnetic fields.
The calculated dependences of the intensities of the first four most intense spectral
lines corresponding to different frequencies of microwave oscillations on the external magnetic
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
field H 0z obtained by analyzing calculated spectrograms of microwave oscillations (Fig. 25) are
shown in Fig. 27.
One can see in Fig. 27 that the most
intense spectral line corresponds to the three-
200'
spoke electron flow structure (Fig. 24(c)) radiat­
3 spokes
5 spokes
N
|
ing at frequency ~3 GHz (Fig. 25(b)) at mag­
MO-
S. 120'
.§• 100-
netic field 0.34-0.37 T, which turns out to be
c
the "resonant" magnetic field for the given
geometry of the smooth-bore magnetron.
1-- 1 I
0 .3 2
Two other less intense spectral lines occur at
0 .3 4
0.36
Magnetic Field (Tesla)
fiequencies ~2 GHz (Fig. 25(a)), which corre-
R g 27 Calculated mtensities ofmicrowave escalations
sponds to the two-spoke electron flow Struc-
at accelerating voltage 600 kV and different external
ture (Fig. 24(b)) at magnetic field 0.31-0.33 T,
magnetic fields.
and ~4 GHz, which corresponds to the four-spoke electron flow structure formed at magnetic
field 0.38-0.42 T (Fig. 24(d)). At higher magnetic fields when more than four electron spokes are
formed, the intensities of spectral lines are an order of magnitude lower.
Simulations at lower accelerating volt­
■ transition from 2- to 3-spoke
• ■transition from 3- to 4-spoke
1A transition from 4- to multi-spoke
ages, 500 kV and 400 kV, show that the appro­
0 .4 0 -
4/12/2006 16:32:36
4-spoke
priate 2-, 3-, and 4-spoke electron flow structures
radiating at the same frequencies (~2 GHz, ~3
3-spoke
k
0.34
GHz, and ~4 GHz, correspondently) are formed
2-spoke
at lower magnetic fields relative to the 600 kV
0.28
accelerating voltage (Fig. 26). For example, the
three rotating electron spokes are formed at the
400
450
500
550
600
Accelerating Voltage (kV)
external magnetic fields 0.30-0.33 T at 500 kV
Fig. 28. Dependence o f the number o f rotating
and at the external magnetic fields of 0.27-0.29 T
at 400 kV (Fig. 28).
electron spokes on accelerating voltage and external
magnetic field.
The final result obtained from the simulations o f the 8-emitter smooth-bore magnetron
operation (Fig. 24) shows that the maximum calculated intensity o f microwave oscillations is
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
produced by the three-spoke electron flow structure (Fig. 24(c)) radiating at frequency 3 GHz at
all accelerating voltages used in these calculations - 600 kV, 500 kV, and 400 kV (Fig. 28).
Additional simulations were performed to study operation of a smooth-bore magne­
tron with a 6-emitter transparent cathode to find out how the angular dimension of single emit­
ters affects the formation o f electron spokes and, hence, microwave generation. Results of
these simulations are shown in Fig. 29.
Tiroe 5,031 ns:
PHASBSPACE f o r a l l p a r t ic l e s
Dime 5.053 ns:
X (m)
PHASBSPACE f o r a l l p a r t ic l e s
i
X iiri)
Magn, FFT of FIELD_INTEGRAL E.DL at SL0T1
Magn, FFT of FIELD_INTEGFAL E.DL at SL0T1
o
>o
20
0
30
Frequency
10
l i n e : |l.9fll>cm, 0 .6 b4 rad > To (1.905cm , 1 .4 4 6 rad )
Peaks (GHz): 2 .9 8 9 , 3 .2 5 3 , 5 .9 2 1 , 3 .8 7 3 , 1 .1 0 3 , Df=100.001 MHz
M a g n etic F ie ld 4 .0 0 E -0 1 t e s l a
Anode Cathode V e lta c e 6.00E+05 v o l t s
MAGIC2D.Sir.ale V e r s io n : 7 .4 3 . Apr 19, 2005
1 D ate: Apr 1 2 .2006
20
30
Frequency
(GHz)
A u th o r: Andxey D A ndreev
U n iv e r s i ty o f Mew Mexico
D ev ice : SINUS-4 U b itro n
F i l e : 6RodsMaanetron.M2D
Time: 16:58
1 Pace:
L in e : (1.905cm , 0 .9 1 6 ra d ) Tc (1.905cm , 1 .1 7 8 rad )
Peaks (GHz): 2 .9 2 8 , 6 .9 9 3 , 2 .7 0 9 , 5 .9 2 2 , 8 .4 8 6 , D f=100.001 MHz
M agnetic F i e ld 4.0QE-01 t e s l a
Anode Cathode V o lta a e 6.00E+05 v o l t s
MAGIC2D,Sinale V e r s io n : 7 .4 3 , Apr 19. 2005 1 D ate: Apr 12.2006
a)
40
(GHz)
A u th o r: A ndrey D A ndre
U n iv e r s i ty o f New Mexi
D ev ice : SINUS-6 U b itr o
F i l e : DHodsMaanetron.H
lim e : 09:44
1 Paq>
b)
Fig. 29. The electron flow structures obtained at accelerating voltage 600 kV and external magnetic field 0.4 Tesla
at different angular dimensions o f single emitters o f the 6-emitter transparent cathode:
a) 10 degrees, and b) 50 degrees.
One can see in Fig. 29 that the angular dimension of single emitters does affect the for­
mation o f rotating spokes and spectra o f microwave oscillations. It turns out that the use of
more narrow emitters of the transparent cathode results in better selection of one preferrable
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
type of magnetron oscillations, which in this case radiates at the same frequency 3 GHz
(Fig. 25(a))
and corresponds to a three-electron spoke structure, which means better mode selec­
tion. It is very interesting also to note that the number of single emitters (8 emitters at Fig. 24(c)
and 6 emitters at Fig. 29) does not affect the number of rotating electron spokes, three spokes,
and frequency of microwave oscillations, 3 GHz. What is really important is the proper combi­
nation of accelerating voltage and "resonant" magnetic field. It follows from these results that
it is probably not very important to have the same number of single emitters or emitting re­
gions at the surface of a smooth cylindrical cathode (Fig. 2(a, b)) as the expected number of ro­
tating electron spokes in the smooth-bore magnetron.
2.2.2. Microwave measurements with smooth-bore magnetron
During the experiments with a smooth-bore magnetron equipped with an 8-emitter
transparent cathode (Fig. 9) and driven by the SINUS-6 accelerator (Fig. 6, Fig. 7) the following
operational parameters were measured: accelerating voltage monitored by a capacitive voltage
divider K=2500 mounted at the end of transmission line o f the accelerator (Fig. 11), emitted
electron current monitored by Rogovski coil N=1000 mounted at the input o f anode tube of
the accelerator (Fig. 11), and microwave power monitored by an S-band near-field probe (with
an S-band 40 dB directional coupler, a 10/20 dB coaxial attenuator, and the HP8437B crystal
detector) placed at a distance ~60 cm from the output antenna (Fig. 4(d)). A diagram of the ex­
periments is shown in Fig. 30, a photograph of the near-field probe positioned in front of out­
put antenna of the accelerator is shown in Fig. 31, and measured s-parameters o f the 40 dB di­
rectional coupler are shown in Fig. 32.
detector
electron sheath
emitters
Fig. 30. Diagram o f microwave measurements by a near-field probe.
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
%
<D-40
-70------
0.0
S-Band Directional Coupler
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Frequency (GHz)
Fig. 31. Photograph o f the 3-band near-field probe with
Fig. 32. Calculated r-parameters o f the 40 dB direc­
40 dB directional coupler, high-power load, HP8492A-
tional couples used to measure microwave power.
10 dB coaxial attenuator and HP8437B crystal detector.
It should be noted at this point that the radiated microwave power is measured by the
near-field probe only at one specific point in front of the output antenna o f the accelerator
(Fig. 31);
there is no way right now to measure the total radiated microwave power in one pulse.
Below is a description of how the microwave power and microwave frequency are measured
by the near-field probe (Fig. 31).
2.2.2.1. Measurements of microwave power distribution
The radiated microwave power is sampled by an 3-band near-field probe, length of
which is 35 cm, attenuated by a 40 dB directional coupler, transformed by a waveguide-tocoaxial adapter into high-frequency voltage oscillations (microwave signal) carrying information
about both frequency and power o f microwave radiation, and attenuated one more time by an
HP8492A-10dB coaxial attenuator (Fig. 31). The attenuated microwave signal is monitored by
an HP8437B crystal detector outputting the amplitude (envelope) of the microwave signal (de­
tector signal). The detector signal travels through the 18.3 m long RG-223/U coaxial cable
(Fig. 14)
into the screen room, where it is recorded using a TDS644A oscilloscope together with
pulses of accelerating voltage (Fig. 13(a)) and emitted electron current; the last one is monitored
by the Rogovski coil N=1000 (Fig. 11). A diagram of the experiment to measure pulses o f the
radiated microwave power is shown in Fig. 33.
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Screen Room
Fig. 33. Diagram o f the experimental measurements of radiated microwave power: 1 —near-field probe, 2 —90° Eband, 3 - 40 dB directional coupler, 4 - high-power load, 5 - waveguide to coaxial cable adapter, 6 - 10 dB coaxial
attenuator, 7 - crystal detector, 8 - coaxial cable, 9 - oscilloscope TDS644A.
Such a simple microwave measurement set-up (Fig. 33) allows one to sample pulses of
the radiated microwave power and to record the envelope of its amplitude at some specific
point located in front of SINUS-6 accelerator. One can see, for example in Fig. 31, how the
near-field probe is located at a position 45° relative to the axis of the accelerator. The distance
between the antenna and the imaginary line determining the near-field probe position is 60 cm
along the axis of the accelerator that allows one to avoid sampling reactive energy from the
output antenna of the accelerator.
Thus, there are three signals observed by the oscilloscope in the screen room: accelerat­
ing voltage monitored by the capacitative voltage divider K=2500 at the end o f the transmis­
sion line (Fig. 11), emitted electron current monitored by the Rogovski coil N=1000 (Fig. 11),
and the microwave power monitored by the HP8437B crystal detector in front o f the output
antenna of the SINUS-6 accelerator (Fig. 30). First of all, in order to be sure that the near-field
probe detects the actual microwave signal radiated by the output antenna of the accelerator,
but does not detect some other signals not relating to the actual microwave signal, the input
waveguide port of the near-field probe was wrapped by the copper mesh, so it was closed, and
all three pulses were measured. Then, the input waveguide port of the near-field probe was
open (without the copper mesh) and the same three signals were measured again. Oscillograms
showing the detector response obtained in this experiment are shown in Fig. 34.
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
—■— Accelerating Voltage
— — Accelerating Voltage —— Rogovskii Coil Current
tii Coil Current
-30 g
>
i
-2 0 0 -
> " -2 0 0 -
-40 op
8
fe
8(U
-3 0 0 -
8
-3 0 0 -
-50 3
—*— Detector Sij
-6 0 °
—*— Detector Signal
TDS644A, 50 A */
3/8/2006 14:08:50
TDS644A, 50 fc
3/8/2006 14:23:05
-20
•10
0
t?0-J
10
20
Time (ns)
30
40
50
60
70
80
Time (ns)
a)
b)
Fig. 34. Measured pulses o f accelerating voltage, total emitted electron current and microwave signal (50 dB attenua­
tion) at ~500 kV, -0.75 Tesla, H-plane orientation and 0° position o f the near-field probe: a) near-field probe is
closed by cupper mesh, b) near-field probe is open.
One can see in Fig. 34(a) that when the near-field probe is closed (wrapped by the cop­
per mesh) the detector registers only a base signal of ~8 mV. However, when the near-field
probe is open (Fig. 34(b)) the pulsed signal is registered that is caused by the microwave power
sampled by the near-field probe. Additional measurements have been performed to find out
what is the cause of the base signal registered by the crystal detector in both cases —when the
near-field probe is closed and when it is open (Fig. 34). It turns out that this base signal is caused
by the pulsed magnetic field produced by the magnetic coils o f the accelerator. The oscil­
lograms of the detector output measured by two different oscilloscopes with different input
impedance when the detector was not connected with the near-field probe are shown in Fig. 35.
2.0
Crystal Detector
3/8/2006 13:01:39
3/8/2006 13:37:22
TDS644A, input 50 Cl
150
TDS320, input 1 M£2
$
'
-0.5
1
Magnetic System
Crystal Detector
-150
-200
Time (ms)
Time (ms)
Fig. 35. Measured pulses o f discharge current of magnetic coils and detector signal.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The measurements of the detector response with the closed/open near-field probe
(Fig. 34)
and without any connected near-field probe (Fig. 35) experimentally proved the fact that
the microwave measurement set-up (Fig. 33) allows one to sample pulses of the radiated micro­
wave power produced by the SINUS-6 accelerator and radiated through its output antenna.
The three pulses measured at a magnetic field 0.75 Tesla, at H-plane orientation and
45° position of the near-field probe relative to the axis of the accelerator are shown in Fig. 36.
Note that the time lag of ~15 ns between pulses of the accelerating voltage and the detector
signal is determined by the time required for microwaves to travel from the magnetron to the
crystal detector through the output radiating antenna of the accelerator, about 60 cm of open
air distance between the antenna and the near-field probe, and through the whole microwave
measuring circuit (Fig. 33).
lOO-i —
Accelerating Voltage —
lOO-i —
Rogovsku Coil Current
Accelerating Voltage
Rogovskii Coil Current
- 10 0 -
-100-
-2 0 0 -
>
■a
-2 0 0 -
-4 0 §>
-300-
-60
— ■— Detector Signal
b
-300-
Q
-400-
3/8/2006 16:03:40
3/8/2006 14:23:05 TDS644A, 50 a
-600-20
-10
0
10
20
30
Detector Signal
-500- TDS644A, 50 Q
-70
40
50
60
70
-600.
-20
80
Time (ns)
-10
0
10
20
30
40
50
60
70
80
Time (ns)
a)
b)
Fig. 36. Measured pulses o f accelerating voltage, total emitted electron current and microwave signal (50 dB attenua­
tion) at ~500 kV (a) and ~450 kV (b), ~0.75 Tesla, H-plane orientation and 45° position of the near-field probe.
The proper combination o f accelerating voltage and magnetic field at which the detec­
tor signal is maximum is found by varying both accelerating voltage and magnetic field. It turns
out that the maximum detector signal is detected at "resonant" magnetic fields of 0.31-0.32 T
and accelerating voltages of 500-550 kV. The 3D oscillograms of the accelerating voltage and
the crystal detector signal (with 60 dB attenuation) obtained at this "resonant" magnetic field
are shown in Fig. 37.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a)
b)
Fig. 37. Measured pulses o f a) accelerating voltage and b) detector signal (60 dB attenuation)
at magnetic field 0.315 T, H-plane orientation and 0° position o f the near-field probe.
Analysis of the oscillograms (Fig. 36) shows that maximum of the detector signal corre­
sponds to that combination of accelerating voltage and magnetic field at which the maximum
calculated intensity of microwave oscillations is produced by the three-spoke electron flow
structure, as it was found during simulation of the smooth-bore magnetron operation (Fig. 28):
•
the measurements show that "resonant" magnetic field ~0.315 T and accelerating voltage
~550 kV correspond to the maximum measured amplitude of the detector signal (Fig. 37);
•
the calculations show that magnetic field 0.31-0.33 T and accelerating voltage 550 kV cor­
respond to maximum calculated intensity of the microwave oscillation (Fig. 28), when three
rotating electron spokes are formed (Fig. 24(c)).
22.2.2. Measurements of microwave frequency
Measurements o f microwave frequency were performed using a TDS7404 oscillo­
scope, which allows one to record microwave signals with frequency up to ~ 5 GHz. The radi­
ated microwave power was sampled by the 3-band near-field probe (Fig. 31), attenuated by a 40
dB directional coupler, transformed by a waveguide-to-coaxial adapter into high-frequency
voltage oscillations (microwave signal) carrying information about both frequency and power
o f microwave oscillation sampled by the 3-band near-field probe, and attenuated one more
time using a HP8492A-20dB coaxial attenuator. The attenuated microwave signal is applied to
a HP11667B power splitter, the first output of which is connected to the HP8437B crystal de-
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tector and the second output is connected to microwave cable. The microwave signal moni­
tored by the HP8437B crystal detector travels through the 60 feet-long RG-223/U coaxial ca­
ble into the screen room where it is recorded using a TDS644A oscilloscope together with
pulses of accelerating voltage and total electron-beam current (Fig. 36). The microwave signal
from the second output o f the power splitter travels through the 25 feet-long microwave cable
into the Faraday cage, where it is applied to another HP11667B power splitter. The microwave
signal from the first output o f this power splitter is monitored by another HP8437B crystal de­
tector and used for triggering the TDS7404 oscilloscope. The microwave signal from the sec­
ond output of the power splitter is directly observed by the TDS7404 oscilloscope.
A diagram of the experiment to measure microwave frequency is shown in Fig. 33. A
photograph of the first power splitter located near the near-field probe is shown in Fig. 39, and a
photograph of the second power splitter located in the Faraday cage is shown in Fig. 40. This
more complicated microwave measurement set-up (Fig. 38, Fig. 39, Fig. 40) allows one to sample
the radiated microwave power and record both its frequency using the TDS7404 oscilloscope
in the Faraday cage (Fig. 40) and the amplitude (envelope) using TDS644A oscilloscope in the
screen room.
Faraday Cage
Screen Room
Fig. 38. Diagram o f the experimental measurements of microwave frequency: 1 - near-field probe, 2 - 90° E-band,
3 - 40 dB directional coupler, 4 - high-power load, 5 - waveguide to coaxial cable adapter, 6 - 20 dB coaxial attenu­
ator, 7 - power splitter, 8 - crystal detector, 9 - coaxial cable, 10 oscilloscope TDS644A, 11 - microwave cable, 12 power splitter, 13 —crystal detector, 14 - oscilloscope TDS7404.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 39. Photograph o f first power splitters connected to
Fig. 40. Photograph o f second power splitters located
the output o f HP8492A 20 dB coaxial attenuator.
inside the Faraday cage.
The microwave frequency measure­
0.000
-0.005
ments are performed at a "resonant" magnetic
field 0.315 T and at an accelerating voltage
~550 kV, the combination at which the
maximum detector signal was found during
the
measurements
(Fig. 37).
of microwave
power
The five pulses of the detector signal
with maximum amplitude are shown in Fig. 41.
These pulses are recorded by the TDS644A
3/22/2006 13:30:21
13
_Sb
£
-0.015
—....... pulse #1
— — pulse #2
■------- pulse #3
—
pulse #4
— .....pulse #5
- 0.020
-0.025
§
s
-0.035
-0.040
-0.045 -0.050
-50
-25
0
25
50
75
100
125
150
Time (ns)
oscilloscope in the screen room (Fig. 40), which
Fig. 41. Measured pulses o f detector signals at ~550
kv> H -) 315 T; at H„band orientatlon and 0o posltlon of
detects only the envelope of the monitored
the near-field probe,
microwave power.
The microwave signal recorded inside the Faraday cage using the TDS7404 oscillo­
scope (Fig. 40) is analyzed using a demonstration version of the AutoSignal code [58]. The code
allows one to calculate the time-frequency spectrogram of the recorded microwave signal
showing the dynamics o f all measured frequencies during the pulse. The frequency and timefrequency spectrograms of two of these five pulses obtained using the AutoSignal code [58] are
shown in Fig. 42 and Fig. 43, respectively.
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
oscaiogram .txt
oscillogram .txt
riequencyopecimm
1
rrequencyspectrum
1
•3® |
•300 ®
Frequency
Fig. 42. Frequency spectrograms calculated from measured pulses o f microwave signal at magnetic field 0.315 T,
accelerating voltage ~550 kV, and H-plane orientation and 0° position o f the near-field probe.
Fig. 43. Time-frequency spectrograms calculated from measured pulses of microwave signal at magnetic field
0.315 T, accelerating voltage ~550 kV, and H-plane orientation and 0° position o f the near-field probe.
One can see from the obtained spectrograms (Fig. 42, Fig. 43) that the maximum inten­
sity of the microwave signal corresponds to a frequency of ~3 GHz. This is exacdy the same
frequency at which the maximum calculated intensity of microwave oscillations is produced by
the three-spoke electron flow structure, as was found during the simulation of the smooth-bore
magnetron operation (Fig. 28).
Therefore, the measurements indicate that a magnetic field of 0.315 T and an accelerat­
ing voltage -550 kV correspond to the maximum measured amplitudes of the detector signal
(Fig. 41)
and that at this combination o f accelerating voltage and magnetic field the microwave
frequency is —3 GHz (Fig. 43). The calculations indicate also that a magnetic field o f 0.31-0.33 T
and an accelerating voltage 550 kV correspond to the maximum calculated intensity o f the mi-
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
crowave oscillation (Fig. 28) at frequency 3 GHz, when three rotating electron spokes are
formed inside the smooth-bore magnetron radiating at frequency ~3 GHz (Fig. 24(c), Fig. 27, and
Fig. 28).
2.2.2.3. Measurements of total radiated microwave power
The total radiated microwave power is obtained by integration of the radial distribution
of the radiated microwave power sampled by the same i ’-band near-field probe (Fig. 31). To
measure the radial distribution, the near-field probe is moved in front o f the output radiating
antenna along an imaginary line [59] running perpendicular to the axis of SINUS-6 accelerator.
At each specific point at this imaginary line where the near-field probe is located, the probe is
oriented to the center of the output radiating antenna. A schematic of the experiment to meas­
ure the radial distribution o f the radiated microwave power showing the near-field probe loca­
tion at different positions in front of the accelerator is shown in Fig. 44.
The measurements are performed at a
"resonant" magnetic field 0.315 T and accel­
erating voltage —550 kV, the combination at
which the maximum detector signal was
\
\
found earlier (Fig. 37) at both H - and H-plane
orientations of the near-field probe. A dia­
\i
Vy‘
gram of the experiment to measure the radi­
ated microwave power is shown in Fig. 33. At
each position of the near-field probe, 10
pulses with maximum amplitude of the detec­
tor signal are averaged, and analyzed then.
Fig. 44. Diagram of the experimental measurements of
radial distribution of microwave power: 1 —output an­
tenna of accelerator, 2 - near-field probe.
The resultant radial distributions of the measured detector signals are shown in Fig. 45.
The measured radial distribution o f the detector signal (Fig. 45) cannot be, however, directly
used to obtain total radiated microwave power. In order to do this, the crystal detector is cali­
brated using a HP83752B synthesized sweeper with known microwave power output at a
known frequency of microwave oscillations.
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
It should be noted at this point that the anode tube of the SINUS-6 accelerator ( 0 2")
acts as a waveguide beyond cutoff for lowest TEu waveguide mode at frequency ~ 3.459 GHz
and for the TEoi waveguide mode of interest here at frequency at 7.198 GHz. For this reason,
the measured microwave power belongs to X- and higher bands o f microwave spectrum2. The
calibration curve showing the relation between the microwave power produced by the
HP83752B synthesized sweeper at frequency 7.56 GHz, and the response of HP8437B crystal
detector to this microwave power is shown in Fig. 46. This calibration curve is used to recalcu­
late the amplitude of the detector signal (Fig. 45) to obtain the radiated microwave power.
4500 n
3/28/2006 12:50:20
.
Narda 4503 # 08654.
... - • - N a r d a 4 5 0 3 # 10799
- -- A - N a r d a 4503#11006
60-
H-plane
3000
3/13/2007 12:47:47
402
2000
b
E-plane
500
10-
0
-500
10
20
30
40
50
60
70
80
-15
Radial Distance (cm)
-10
•5
0
5
10
15
20
25
Input Power @ 7.56 GHz (dBm)
Fig. 45. Measured radial distribution o f detector signals
Fig. 46. The calibration curve showing HP8437B crystal
at accelerating voltage ~550 kV and magnetic field
detector response to the input microwave power at
~0.315 Tesla.
frequency 7.56 GHz.
Integration of the measured radial distributions of the detector signal (Fig. 45) with ac­
count o f the calibration curve (Fig. 46) and 60 dB attenuation of the radiated microwave power
sampled by the T-band near-field probe gives the total radiated microwave power from the
output radiating antenna of the SINUS-6 accelerator (Fig. 4(d)). It turns out that the radiated
microwave power is ~100 kW at each orientation of the near-field probe, at both H- (Fig. 31)
and E-planes. The total radiated microwave power from the smooth-bore magnetron with 8emitter transparent cathode (Fig. 9) is then ~200 kW in the maximum of the pulse. This is the
high limit of estimated microwave power produced by the smooth-bore magnetron (Fig. 9).
T h e same measurements were made with the first relativistic smooth-bore magnetron by Bekefi [38] where the
total radiated microwave power were measured to be ~ 4 kW.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.2.3. Summary of smooth-bore magnetron measurements
The research activity described in Section 2.2 was performed to tune and calibrate the
microwave diagnostic (Fig. 33, Fig. 38) used to monitor output radiation parameters of a relativistic magnetron. To perform this work, a prototype smooth-bore magnetron was manufactured
and studied using the SINUS-6 accelerator (Fig. 6, Fig. 7) as a driving source. The experiments
with an 8-emitter transparent cathode (Fig. 9) embedded in the smooth-bore magnetron allowed
one to tune the microwave diagnostic designed to measure microwave power and frequency of
the radiated microwaves. Comparison between simulations (Fig. 26-Fig. 28) and measurement
(Fig. 36)
gives the same microwave frequency ~ 3 GHz (Fig. 42, Fig. 43) and exactly the same
"resonant" magnetic field —0.315 Tesla at an accelerating voltage ~ 550 kV in both cases.
Another result obtained during simulations of the smooth-bore magnetron operation is
that the number of single emitters of a transparent cathode does not affect formation of the
desired number of rotating electron spokes inside the magnetron. The three electron spokes
relating to the most intense spectral lines of the smooth-bore magnetron operation are formed
when either 8 (Fig. 24(c)) or 6 (Fig. 29(a)) single emitters used on the transparent cathode. This fact
probably indicates that, among the three different forms of the cathode primings (emission,
electric, and magnetic) the emission priming that corresponds to the "encrusted" cathode de­
sign (Fig. 2(a)) is less effective in view of the desired type of the magnetron oscillations to sup­
port. The last statement, however, needs more detailed computational studies.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.3. Relativistic Magnetron with a Transparent Cathode
Finally, in order to understand the basic physical processes that determine fast start of
desired type of microwave oscillation in relativistic magnetrons with a transparent cathode, the
prototype of a magnetron with both transparent or solid cylindrical cathode driven by the
SINUS-6 accelerator (Fig. 6 and Fig. 7) was manufactured and studied. A photograph o f the 6emitter transparent cathode with radius 0.45 cm is shown in Fig. 2(d), a photograph o f the 3emitter transparent cathode with same radius is shown in Fig. 47, and a photograph of the solid
cathode that is used in this experiment to compare the results obtained with this cathode and
results obtained with the transparent cathodes is shown in Fig. 48.
Fig. 47. Photograph o f 3-emitter transparent cathode
Fig. 48. Photograph of solid cathode used in experi-
used in experiments with relativistic magnetron.
ments with relativistic magnetron.
The anode block of the magnetron (Fig. 10) has the following dimensions: length of the
block is —72 mm, anode diameter is —25 mm, vane diameter -3 8 mm, angular dimension of a
single vane is 40°, and the number of vanes is 6. Photographs of two components from which
the anode block (Fig. 10) was made of are shown in Fig. 49. This construction of the anode block
provides axial/diffractional output of microwave radiation. The relativistic magnetron with dif­
fraction output has a number of advantages in comparison with the traditional magnetron with
radial output. Among them are: compactness of the magnetic system and output microwave
block (antenna), uniform load of all resonators/vanes of the magnetron, ability to transform
output radiation mode into the desired one just inside the output antenna, among others (see
Appendix).
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 49. Photographs o f two components o f the anode block o f a prototype o f a relativistic magnetron.
Computer simulations (2D Magic code) o f the 6-vane (Fig. 49) relativistic magnetron
with the solid cathode (Fig. 48) shows that the start of Tt-mode of magnetron oscillations occurs
just after nanoseconds of the magnetron operation (Fig. 50(a)) at an external magnetic field 0.7
Tesla and accelerating voltage 650 kV (Fig. 50(b)). The operating frequency of the 71-mode mag­
netron oscillations is ~6 GHz (first harmonic) and the second harmonic of the 71-mode oscil­
lates at frequency of ~12 GHz (Fig. 50(c)).
.059 ns:
FIELD INTEGRAL E.DL a t SL0T1
for a ll particles
94
lin e : h . 60bcm, 6. vkfcrad) To (l.m cm , i.GOSrad)
R elativistic Magnetron v itn a r t i i l d a i emission
Magnetic Field 7. 00E-01 tesla
Anode Cathode Volteaa 6. 50E+OS volts
MAGlC2D.£inole Version: 8. 03. Julv 20 2006 1 Date: Ort 26.2006
a)
Author: Andrey D Andreev
Universitv ol New Mexico. £CE De
Device: A/SINUS-0 MAGNETRON
Pile: 6VaneMacr>etror..H2D
Time: 14:40
f Paae: 1/9
b)
Fig. 50. Computer simulations o f the 6-vane relativistic
Magn, FFT o f FIELD INTEGRAL E.DL a t SL0T1
magnetron (Fig. 49) with solid cathode (Fig. 48):
a)
structure o f the electron flow showing 7t-mode of
the magnetron oscillations;
b)
electric field oscillation inside first resonator o f the
magnetron;
Freq u en cy
(GHz)
Peaks (ffife): 6. 071, 12. 141, 5. 857, 11. 887, 5. 215,"l
Magnetic Field 7. 00E-01 tesla
Anode Cathode Voltane 6. 5fjEtO!> vnlt.s
9. 03, July 20 2006 [ Dale: Pel ?6, 2006~
MAGIC21,3 i imie~Vex ■
c)
Device: A/S1HUS-6 MAGNETRON
I Pane: 480
Qj
spectrum o f the electric field oscillations inside the
first resonator of the magnetron.
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Given the known frequency (Fig. 50(c)) o f the 7t-mode magnetron oscillation (Fig. 50(a)),
one can determine the operational domain of the magnetron, which shows the region on the
accelerating voltage vs. the magnetic field plot where the magnetron can efficiently operate in
the 7t-mode. The operation domain is determined by two dependences: one of them is the cri­
terion o f magnetic insulation (Hull criterion) preventing deposition o f the rotating electron
flow on the anode surface (11), and the other is the Buneman-Hartree condition [55] which
specifies the dependence of accelerating voltage on magnetic field above which the specific
type of magnetron oscillations can exist.
2.3.1. The Buneman-Hartree condition
The Buneman-Hartree condition depends on the number of rotating electron spokes
determining magnetron operating mode n and frequency of magnetron oscillations COn. “Mag­
netron modes are designated by the mode number n, the number of times the i f field pattern
repeats around the anode; that is, fields vary as in f e, 0=-27CjN , where N is the number of
vanes. Two principal modes are the 71-mode, when the pattern repeats in every other resonator
(n=N/2) and the 27t-mode when each resonator has the same pattern (n=N)” [55].
A calculation o f the Buneman-Hartree curve begins with determination of the phase
velocity vpb o f synchronous i f field andt can be written as [61]
vph = Y
r /i
[m/s],
W
where (Oj27C'vs, frequency in Hz of the «th azimuthal mode and the wave number k determines
the spatial period of the t f field inside the resonant system
, In
2n-N r ,, ,
k = ----- = ---------- [rad/m],
2 L 2-2 n-ra
(13)
where L is the spatial length o f the microwave structure and N is the number of resonators
along this length. Substituting (13) into (12) gives the phase velocity o f the t f field inside the mi­
crowave structure [62, P.229]
v
<*„ •2 •r
N
canra
[m/s],
n
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(14)
where n= N /2 is the number of the »A azimuthal mode with a frequency (On.
The exact phase synchronism inside the given microwave structure may be achieved
when the electron rotates in the crossed static radial electric E and axial magnetic B fields with
synchronous azimuthal drift velocity, v$=vph that depends on the average radius of the rotating
electron flow rin the interaction space, and is determined as
v
6
ExH
E
H2
H
= C1
r-^-C
U
(15)
= C ---------- 7— — r .
rH\n{rJrt )
The Buneman-Hartree resonant condition (when the electron drift velocity (15) equals
to phase velocity of the t f wave (14),
for cylindrical geometry (including relativistic ef­
fects) is [55], [63]
me
me
IS l
cn
cn
(16)
Taking into account (14) and (15), the Buneman-Hartree condition (16) can be rewritten
as
(17)
where vph is determined by (12) and for the JZ-mode results in (14). With additional account o f the
magnetic field of the cathode axial current I, and introducing (dp}~vpljc , the Buneman-Hartree
condition (17) is written as [63]
.. eBBHd J
Y=
~~ +
me
\
(18)
me
rt v
In the case of zero axial current, 1=0, (18) reduces to (17). Additional modification of the Bun­
eman-Hartree condition (18) is for the non-zero axial drift of electrons, v^O, [63].
The Buneman-Hartree resonant condition can also be written as [64],
(19)
1 -J l-
y ph
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
It follows from (17) and (19) that the Buneman-Hartree magnetic field is determined as
eBm _
f
c
me2
\2
(20)
1 4-^rl-Jl-
clv„
mc
(21)
eB„.
■I
dB
me 2
In the very special case when the electron drift velocity v q (15) equals the electron veloc­
ity v0 determined by the static electric field E inside the cathode-anode gap, i.e. when ve=vpl.~v0,
the Buneman-Hartree condition (21) can be rewritten as
eBK
me1
eBi)H _
me2
~ ^ ‘
(23)
1
FW.
d ep pl
eBm, _
me2
(22)
1
d,PP„ F M
1
_ rPyk
d j pt
F
(24)
d.
k
The same equation is derived in [62, P.229] from the conservation of canonical angular
momentum
, N eB(r2 - r l )
r v e( r ) =
\
2 me
(25)
l > ,
v ,(r) _ eB{r2 - r 2)
(26)
2me2
c
eB _ r v* 0) 2r
me2
c r2- r2
(27)
When (27) is evaluated for the case when the space charge cloud extends to the anode,
f^=ra, the result is
eB
vs ( r j
me2
c
2r
K - r2’
eB_= %ft
me2
(28)
d.
which is the same as (24) if
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(29)
The calculated, using (11) and (19)- (21), operational domain o f the magnetron with the
solid cathode used in this research (Fig. 47-Fig. 50) and radiating at frequency 6 GHz (7E-mode,
Fig. 50(c))
is shown in Fig. 51(a) and the calculated operational domain of the classical A6 relativis­
tic magnetron radiating at frequency 2.33 GHz (71-mode) is shown in Fig. 51(b).
.
■Hull Cut-of Threshold
‘Buneman-Hartree Condition for 7t-mode
700'
700-
10/24/2007 12:43:33
>
600'
&
& 500.
•>
3
400.
•s
I
Hull Cut-of Threshold
1Buneman-Hartree Condition for 7t-mode
.........Buneman-Hartree C Midi ion for h t-nlode
"
r 1 ! I
; l
600-
Solid Cathode
500-
Solid Cathot e
400300200-
100'
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.30
Magnetic Field (T)
0.35
0.40
0.45
0.50
0.55
0.60
Magnetic Field (T)
a)
b)
Fig. 51. Operational domain for Jt-mode magnetron oscillation calculated for the magnetron with the solid cathode
used in this research (Fig. 47-Fig. 50) (a) and for die classical A6 magnetron (b).
It should be noted at this point that the traditional Buneman-Hartree conditions (19)(21)
determine the operational domain (Fig. 51) of a relativistic magnetron with a solid cathode
only (Fig. 50(a)). There is still no any theory that can be implemented to calculate the operational
domain of a relativistic magnetron with any other type of enhanced cathode geometry (Fig. 3),
including the transparent cathode (Fig. 47). At present, only PIC simulations can reveal those
specific combinations of accelerating voltages and magnetic fields at which a relativistic magne­
tron with transparent cathode can operate at the desired mode of magnetron oscillation
(Fig. 50).
Below is the description of the optimization process that was performed for an A6
magnetron (Fig. 51(b)) using the Magic code [39].
2.3.2. Optimization of a transparent cathode geometry and position
Introduction of a transparent cathode (Fig. 47) as an alternative to a traditional solid cy­
lindrical cathode (Fig. 48) has resulted in a huge variety of possible configurations of a magne-
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
tron's vacuum diode consisting o f the cathode and the anode block. Indeed, while the tradi­
tional design of a solid cylindrical cathode allows one to vary only the diameter of the cathode,
while keeping the same geometry of the anode block (Fig. 52), design of the transparent cathode
allows one to additionally vary a lot of other parameters: number of single emitters (Fig. 53(a, b)),
angular dimension or width of the emitters, shape/geometry of the emitters (Fig. 53(c, d)), and
even the azimuthal position of these emitters relative to the resonant vanes (Fig. 54).
1.074 ns:
fo r a l l p a rtic le s
1.004 ns:
fo r a l l p a rtic le s
Fig. 52. Different radii o f a solid cylindrical cathode in a relativistic magnetron.
1.002 n3:
fo r a l l p a rtic le s
1.002 ns:
for a l l p a rtic le s
Fig. 53. Different geometries o f a transparent cathode in a relativistic magnetron: a) 3 emitters (Fig. 47),
b)
6 emitters (Fig. 10(d)), c) 3 blades, and d) 6 blades.
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
R * c o s (P h i) (rn)
a)
R * c o s (P h i) (m)
b)
Fig. 54. Different azimuthal position o f emitters o f a transparent cathode: a) 6 emitters positioned at 0° relative cen­
ter o f the first resonant vane, b) 6 emitters positioned at 20° relative center of the first resonant vane.
It should also be noted that each unique design of the transparent cathode (Fig. 53,
Fig. 54)
has its own unique combination of some specific properties that can be described in
terms of the cathode primings: emission, electric, or magnetic. Furthermore, as it was noted in
the Introduction, one form of priming can suppress another form of priming and vice-versa —
one form of priming can enhance another form of priming; different combinations of these
three primings can result in different dynamics of electron-flow/microwave radiation in mag­
netrons.
For the purpose o f this dissertation, the following calculations were performed leading
to the optimization of the transparent cathode design: i) optimization of the geometry of the
transparent cathode by comparing the operational parameters of the A6 relativistic magnetron
driven by a solid cathode (Fig. 52(a)), 6-emitter transparent cathode (Fig. 53b)), and 6-blade cath­
ode (Fig. 53(d)); and ii) optimization of the 6-emitter transparent cathode azimuthal position in
relation to the resonant vanes of the A6 relativistic magnetron (Fig. 54).
Calculations were performed using the 2D version of the Magic code [39] and the fol­
lowing operational parameters of the magnetron were analyzed: magnitude of magnetron oscil­
lations within the first resonant vane, frequency spectrum of these oscillations, and intensity of
the spectral lines corresponding to the main frequencies of the magnetron oscillations.
55
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2.3.2.1. Optimization of the cathode geometry
Computer optimization of the cathode geometry was performed using a 2D model of
the A6 relativistic magnetron characterized by anode radius 2.11 cm, cathode radius 1.58 cm,
and resonant vane radius 4.11 cm. Three different designs of the cold cathode were analyzed:
solid cathode (Fig. 52(a)), 6-emitter transparent cathode (Fig. 54(b)), and 6-blade cathode
(Fig. 54(d)).
Calculations were performed with constant azimuthal magnetic field 0.45 Tesla and
accelerating voltage 260 kV (Fig. 51(b)), which was increased from zero to its stationary value in
-7.5 ns (the pulse rise time). The calculated electron flow configurations inside the magnetron
at 3 ns, 6 ns, and 9 ns o f the pulse are shown in Fig. 55.
for a ll p a rticles
3.017 ns:
for a l l particles
for a ll particles
□
(.042 na:
for a ll particles
(.012 as:
for a ll particles
for a ll particles
9.003 ns:
for a l l particles
(.004 as:
for a l l p a n icle s
for a ll particles
Fig. 55. Electron flow configurations in the A6 relativistic magnetron at different time moments and three different
geometries o f the cold cathode.
Analysis of the calculation (Fig. 55) shows that only the 6-emitter transparent cathode
(Fig. 55(b))
provides the conditions when three rotating spokes are formed that corresponds to
56
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7t-mode magnetron oscillation in a 6-vane magnetron. Neither the solid cathode (Fig. 55(a)) nor
the 6-blade one (Fig. 55(c)) can provide these three rotating spokes. The frequency spectrograms
obtained during the simulations are shown in Fig. 56. These spectrograms were obtained by cal­
culations of the same magnetron (Fig. 55) at different magnetic fields, ranging from 0.3 Tesla up
to 0.65 Tesla with a step of 0.1 Tesla.
AQ.
H
£
I
pfeque
prequen
•2.Field310 #,8e*t«2-K
lSpctu2,Field210 ,Seaoc2*l<
b)
a)
-n
CL
33
<T)'
£
CL
H
Frequency (GHz)
C)
Frequency (GHz)
Frequency (GHz)
\SpeOr2, fields l(f 4 .Secccrt- l<f
i2,fieldS]0~3,Seetof2'10*6)
lSr«clr2,Fiel4210 .SectorMI
Fig. 56. Frequency spectrograms obtained during calculations o f the A6 relativistic magnetron operation with dif­
ferent cathodes (Fig. 55) in the broad range o f magnetic field, 0.3-0.65 Tesla.
The obtained spectrograms show (Fig. 56) that in the broad range of magnetic fields
only the 6-emitter transparent cathode (Fig. 55(b)) supports 7t-mode magnetron oscillations,
which is the most intense one, ~30 M V/GHz (Fig. 56(b)). The solid cathode supports Tt-mode
magnetron oscillations only at very high magnetic field when the intensity of these oscillations
is very low, ~3 M V/GHz (Fig. 56(a)), and the 6-blade cathode gives a mixture of 7t-mode mag­
netron oscillations with other modes, which means poor mode selection (Fig. 56(c)). This result
supports the conclusion made after analysis of the electron flow structure dynamic (Fig. 55) that
the most effective geometry o f the cathode is the 6-emitter transparent one (Fig. 55(b)).
57
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2 . 3 . 2 2 . Optimization of 6-emitter transparent cathode azimuthal position
There is still one more degree of variation of the 6-emitter transparent cathode design
that allows one to change the operation of the cathode in the relativistic magnetron. This de­
gree of variation is the azimuthal position of a single emitter relative to the resonant vanes of
the anode block. The calculations were performed to find the optimal position of the cathode:
the azimuthal position was varied from 0° to 55° with a step of 5°, and the magnetic field was
varied as in the previous case (Fig. 56) from 0.3 Tesla up to 0.65 Tesla with a step of 0.1 Tesla.
The calculated electric field oscillations inside the first resonant vane of the magnetron as well
as the spectrum of these oscillations obtained at three different azimuthal positions of the
transparent cathode, 0°, 25°, and 50°, are shown in Fig. 57 and Fig. 58, respectively.
.31««
Fig. 57. Calculated electric field oscillations inside the first resonator o f anode block.
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Frequency (GHz)
Frequency (GHz)
Frequency (GHz)
Fig. 58. Calculated frequency spectrograms o f electric field oscillations inside the first resonator o f anode block.
The calculations (Fig. 57, Fig. 58) show that, despite the fact that electric field oscillations
inside the resonant vanes start practically at the same time at all different positions of the 6emitter transparent cathode inside the anode block (Fig. 57), the spectrum of the electric field
oscillations is different (Fig. 58). The obtained result (Fig. 58) indicates that the most intensive 7tmode magnetron oscillations without competition from other modes at all magnetic fields used
in the calculations occur at that position of the transparent cathode where the emitters of the
cathode stay near the edge of the resonant vanes of the anode block (Fig. 58(c)). This position is
the most optimal one to generate pure TC-mode of magnetron oscillations in the A6 relativistic
magnetron and agrees with the result of Bosman et al [16].
59
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2.3.3. Experimental measurements of microwave radiation from the relativistic
magnetron with transparent cathode
Thus, the prototype of the 6-vane relativistic magnetron (Fig. 49) radiating at frequency
~6 GHz (Fig. 50(c)) which corresponds to 71-mode of magnetron oscillations (Fig. 50(a)) is
mounted inside the anode tube o f the SINUS-6 accelerator (Fig. 6) and either the solid cathode
(Fig. 48)
or the transparent one (Fig. 47) is used as a source of electrons whose rotating flow in­
side the magnetron structure (Fig. 50(a)) results in microwave generation. To measure the output
microwave pulse parameters, the homemade C-band, X-band (Fig. 59), and Ku-band near-field
probes were used.
Fig. 59. Photographs o f the C-band (left) and X-band (right) near-field probes, H-plane orientation of the probes.
A diagram of the microwave measurements with the near-field probes is shown in
Fig. 30
and Fig. 33, and, following the practice developed during the measurements of the
smooth-bore magnetron operation (Fig. 36) three pulsed signals are monitored in the screen
room: accelerating voltage monitored by the voltage divider K=2500 (Fig. 11), emitted electron
current measured by the Rogovski coil N=1000 (Fig. 11), and microwave power measured by
the crystal detector (Fig. 33, Fig. 59).
All the measurements have been performed at maximum achievable accelerator volt­
age, which is ~ 700 kV, in order to obtain maximum microwave power output. However, since
the magnetron is a resonant device that efficiently works only at optimal combinations o f the
applied voltage and the magnetic field determined by the operational domain of the magnetron
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(Fig. 51),
the "resonant" magnetic field should be additionally specified in order to obtain maxi­
mum microwave output from the magnetron. As follows from the calculated operational do­
main of the magnetron (Fig. 51(a)), which is determined by the Hull cutoff threshold and the
Buneman-Hartree condition, the "resonant" magnetic field corresponding to an accelerating
voltage of —700 kV is about 0.7-0.8 Tesla, and the preferable value is —0.7 Tesla because this is
closer to the "resonant" magnetic field for the Hull threshold, leading to better conditions for
the desired mode of a magnetron operation to exist.
In order to find the "resonant" magnetic field experimentally, a series of measurements
were made at different magnetic fields varying from 0.3 Tesla to 1.2 Tesla in a step o f 0.1 Tesla
when the magnetron is driven by the solid cathode. During these measurements, all three
pulsed signals (accelerating voltage, total emitted current, and detector signal) are monitored
and then the maxima of these signals are plotted as a function of the magnetic field (Fig. 60).
10
1 0/25/200621:15:16
V oltage
9
■—■-
8
7
61
51
Current
4
5
3
£
45 c m + 0 0 cm
E-plane
solid cathode
as
2
D etector
1
0
0 .2
0 .3
0 .4
0 .4
0 .5
0 ,6
0 .7
0 .7
0 .8
0 .9
1 .0
1 .0
1.1
1 .2
1.3
M agnetic Field (Tesla)
Fig. 60. The measured dependences o f accelerating voltage, total emitted current, and detector signal on the mag­
netic field. These dependences were obtained using the magnetron with solid cathode (Fig. 48).
One can see from the measured dependences (Fig. 60) how it surprisingly turns out that
the experimentally determined "resonant" magnetic field at which the radiation output of the
magnetron is maximum, 0.7 Tesla (Fig. 60), coincidence very well with the "resonant" magnetic
field determined from the calculated operational domain of the magnetron, which is also 0.7
Tesla (Fig. 51(a)). This fact clearly indicates that all calibrations performed during measurements
of I-V characteristics of the electron beam (Section 2.1) and microwave parameters of the
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
smooth-bore magnetron (Section 2.2) are performed correctly and that these calibrations and
tuning o f the microwave diagnostics can be used without any doubt during measurements of
microwave parameters of the 6-vane relativistic magnetron (Fig. 49) used in this research. One
can see also in Fig. 60 that at very high emission currents (which occurs at lower magnetic fields)
the accelerating voltage decreases a little bit. This effect, experimentally revealed also during the
I-V characteristics measurements (Fig. 20(a)), indicates that in this case the total emitted electron
power is comparable with the total electric power available from the Tesla transformer; this
results in the decrease in the accelerating voltage.
During these measurements, the near-field probes (Fig. 59) are oriented to sample the
microwave power in two planes: when the broad wall of a probe is oriented horizontally (bi­
plane, Fig. 59) and when it is oriented vertically (E-plane). At each probe position and orienta­
tion, the radial distribution of the radiated microwave power is measured (Fig. 44). Examples of
the measured pulses of accelerating voltage, total emitted electron current, and detector signal
obtained at different radial positions of the C-band probe at both E-plane and H-plane of its
orientation are shown in Fig. 61-Fig. 64.
1 0 /2 5 /2 0 0 6 1 1 :1 1 :4 1
4 5 c m +0 0 cm
H -p lan e
10/25/200611:16:41
4 5 c m +05 cir
H -plane
solid cathode
0.2 5
11106 (ns)
T im e (ns)
1 0 /2 5 /2 0 0 6 1 1 :2 0 :3 1
45 c m + 1 0 '
H -plane
45 c m +15 cm
10/25/200 6 1 1 :2 5 :2 9
H -plane
solid cathode
>
too
200'
!|
°|
-2i
2a15
o -100
•30
-20
-10
0
10
20
30
40
50
60
70
80
90
T im e (ns)
Fig. 61. Oscillograms obtained with the solid cathode (Fig. 48), H-plane orientated C-band near-field probe.
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 0 /2 5/2006 19:50:22
4 5 c m + 0 0 cm
E -plane
10/25/2006 20:06:17
E -plane
100
?!
o|
100
■0.2 g
■30
-20
-10
0
10
20
30
40
60
70
80
90
-20
•30
•10
0
10
20
30
40
1 0 /2 5 /2 0 0 6 2 0 :0 2 :2 7
4 5 c m + 1 0 cm
E- plane
solid cathode
>
50
-0.2 g
SO
60
70
80
90
10/25/2006 20:05:45
200
I75
>
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
T im e (ns)
Fig. 62. Oscillograms obtained with the solid cathode (Fig. 48), E-plane orientated C-band near-field probe.
4 5 cm + 0 0 cm
4 5 c m +05 cm
E -p lan e
3 -ro d cathode
3-ro d cathode
200
£
I
?!
5 -100
-30
-20
-10
0
10
20
30
40
50
60
70
80
?a
90
•30
-20
-10
0
10
20
30
40
50
60
70
80
90
T im e (ns)
^ 100
5
10/27/2006 12:07:00
4 5 c m + 1 5 cm
E -plane
45 c m +10 cm
E -plane
3-ro d catho de
^
100
-100
-30
-20
-10
0
10
20
30
40
50
60
70
•30
-20
-10
0
10
20
30
40
50
60
70
80
90
Fig. 63. Oscillograms obtained with the transparent cathode (Fig. 47), E-plane orientated C-band near-field probe.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4 5 c m +0 0 cm
H -plane
1 0 /2 7 /2 0 0 6 1 2 :1 5 :0 9
45 c m +05 cm
H -plane
10/27/2006 12:18:43
3 -ro d cathode
100'
-10
•273
’fime(ns)
T im e (ns)
1 0 /2 7 /2 0 0 6 1 2 :2 0 :5 8 '
4 5 c m + 1 0 cm
4 5 c m +15 c m
10/27/2006 12:23:17
£
s
>
■
>o
•‘S
0.33
:2, i
0.4 O
T im e (ns)
T im e (ns)
Fig. 64. Oscillograms obtained with the transparent cathode (Fig. 47), H-plane orientated C-band near-field probe.
The same kinds o f oscillograms (Fig. 61-Fig. 64) were also obtained using X-band and
Ku-band near-field probes, stored in the PC, and then analyzed. The total number of measured
pulses is enormous because at each radial probe position (Fig. 44) and probe orientation (Fig. 59)
there are 10 pulses that are taken to obtain a statistically averaged value of the signal at its
maximum. The measured pulses were analyzed using the MathCAD code [65] allowing one to
treat all these oscillograme at once.
A lot of interesting information can be obtained from the measured oscillograms
(Fig. 61-Fig. 64) and, by the way, this is the only way to obtain any information about the magne­
tron operation —to analyze the measured oscillograms (Fig. 61-Fig. 64).
Some very interesting features obtained after analyzing the obtained oscillograms
(Fig. 61-Fig. 64) include the difference in the total emitted electron currents produced by these
cathodes (Fig. 65), which shows a difference between the solid and the transparent cathode op­
eration in the relativistic magnetron and the dependence of the total emitted current on the
magnetic field, one of which is the "resonant" magnetic field (Fig. 60).
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7n
10/27/2006 12:54:17
10/31/200611:32:33
600-
3-rod cathode, E-plame
3-rod cathode, H-plame
solid cathode, E-plame
solid cathode, H-plame
<
500-
3
300-
200-
—■— 3-rod cathode, C-band
—• — 3-rod cathode, X-band
—A— 3-rod cathode, Ku-band
O
3 73
45 cm
H-plane
100 -
0
5
10
15
20
0
25
5
10
15
20
25
Radial Distance (cm)
Radial Distance (cm)
Fig. 65. Total emitted current measured as a function o f the radial position of the near-field probe (Fig. 44).
One can see in Fig. 65 that the total emitted current from the transparent cathode
(Fig. 47)
is definitely less then the total emitted current from the solid cathode (Fig. 48), by about
30-40%. This result can easily be explained by the fact that the total emission area o f the solid
cathode is greater than the total emission area of the transparent cathode. However, in spite of
the fact that the measured difference (Fig. 65) can be very easily explained, this result is probably
the first experimental evidence of the difference between the solid and the transparent cath­
odes operating inside a magnetron. The fact that the total emitted current decreases as the
magnetic field increases (Fig. 60) cannot be completely understood from the given measured
and calculated data; however, it surely indicates some very important feature of, probably, any
relativistic magnetron operation.
Another very interesting feature from the analysis of the measured oscillograms (Fig. 61Fig. 64)
is that the start of the microwave oscillations, given how it is detected by the crystal de­
tector, occurs at the same time for either solid or transparent cathode3. This result does not
indicate, however, that there are no positive effects from the transparent cathode on the rise
time of the desired type of microwave oscillation in the magnetron. The point is that the crystal
detector can register a very broad spectrum of microwave signals, from 1 GHz to 12.5 GHz;
due to this fact the signal registered by the detector at the front of the microwave pulse can
3 It could be also that the TDS 644A oscilloscope (2 G s/s) used in these measurements does not have the tem­
poral sensibility to resolve subtle changes in the rise time o f microwave power monitored by the crystal detec­
tor.
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
actually be microwave radiation with any other frequency or a mixture of frequencies, not nec­
essarily the desired type of microwave oscillation. In order to extract the real rise time of the
desired frequency of microwave oscillations radiated by the magnetron, the time-frequency
spectrograms of the microwave signals sampled by the near-field probe should be calculated
(Fig. 43),
or some kinds of waveguide/coaxial filters that allows one to selected the desired fre­
quency of the microwave signal should be used together with the near-field probes. This re­
search work lies, unfortunately, beyond the scope of this dissertation.
Nevertheless, the radial distribution of the radiated microwave power measured by the
crystal detector has also been extracted from the measured oscillograms (Fig. 61-Fig. 64) as the
averaged maxima o f the detector signals measured at different radial positions o f the near-field
probes (Fig. 44). The radial distributions measured by the C-band probe are shown in Fig. 66.
3.0
3-rod Cathode
solid cathode
10/27/2006 12:43:55
-i
■
—
0 .9 -
3-rod Cathode
solid cathode
45 cm
H-plane
0 .7 '
>
%
c
I
g - 0.5
fe
0 .4 .
Z
0-3
0.0
10/27/2006 12:39:51
45 cm
E-plane
0 .5
Z
O
0
5
10
15
20
0 .3
0
25
Radial Distance (cm)
5
10
15
20
25
Radial Distance (cm)
Fig. 66. Measured radial distribution o f microwave power delivered by magnetron with solid and transparent cath­
odes at FI-plane and E-plane orientations o f the C-band near-field probe.
One can see from the results (Fig. 66) that the microwave power radial distribution pro­
vided by the transparent cathode has a clear minimum in the center of the distribution or on
the axis of the accelerator. The radial distribution obtained from the solid cathode has two
maxima - one is at the center of the distribution and another one is at a radial distance of ~ 10
cm from the center. The measured results can be interpreted as follows. It looks like the trans­
parent cathode radiates mostly at that radiation mode that corresponds to the Tt-mode o f mag­
netron oscillations and provides minimum in the center of the radiation pattern. In contrast,
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the solid cathode radiates a mixture of two or a number of radiation modes, one of which cor­
responds to the 7t-mode of magnetron oscillation and the other has a maximum o f the radiated
power in the center of the radial distribution. The two different radiation patterns correspond­
ing to these two different radiation modes mentioned above are shown in Fig. 67.
(a)
(b)
Fig. 67. The radiation pattern produced by Jt-mode o f magnetron oscillations (ITbi) mode (a) and the radiation
pattern produced by some other radiation mode (TEn, for example) (b).
Thus, the radiation pattern shown in
Fig. 67(a)
results in a radial distribution o f the
microwave power that is similar to the one
^
«
measured
(Fig. 66),
from
the
transparent cathode
and the mixture of two radiation pat­
3-rod cathode, C-band
3-rod cathode, X-band
3-rod cathode, Ku-band
0.9 ■
10/31/2006 11:25:37
45 cm
H-plane
°-7'
0 .6 '
& 0.5
U 0.4.
tern shown in Fig. 67(a, b) results in that radial
distribution o f microwave power that is simi­
0.0
lar to the one measured from the solid cath­
0
5
10
15
20
25
Radial Distance (cm)
ode (Fig. 66). The radial distribution of the mi­
Fig. 68. Measured radial distribution o f microwave
crowave power measured using X-band and
Ku-band probes are shown in Fig. 68.
power for the magnetron with transparent cathode at
H-plane o f three different near-field probes.
The above-introduced explanation of the measured radial distribution o f the radiated
microwave power suggests that the transparent cathode radiates only one desired radiation
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
mode, which corresponds to the 7t-mode of magnetron oscillation, while the solid cathode ra­
diates a mixture o f two different radiation modes. This statement allows one to assume that the
transparent cathode provides better mode selection in comparison with its solid counterpart
and, therefore, allows one to obtain the pure desired radiation mode in front of output antenna
of the magnetron.
2.3.4. Summary of the relativistic magnetron measurements
The research activity described in Section 2.3 was performed to study the basic opera­
tional parameters of a relativistic magnetron with a transparent cathode that determines the fast
start of the desired type of magnetron oscillations. To perform this research, a prototype of a
6-vane relativistic magnetron with axial output of microwave radiation was manufactured
(Fig. 49)
and studied using the SINUS-6 accelerator (Fig. 6, Fig. 7). The measurements of output
radiation parameters of the magnetron (Fig. 61-Fig. 64) showed that the transparent cathode
(Fig. 47)
provides better mode selection by eliminating competition from other possible operat­
ing modes o f the magnetron (Fig. 66, Fig. 68). Along with this, the rise time of the microwave
oscillation is the same for both cathodes used in these measurements (Fig. 61-Fig. 64) —the trans­
parent (Fig. 47) and the solid one (Fig. 48).
68
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2.4. Conclusion
In the course of the research described in Chapter 2, a prototype o f the relativistic
magnetron (Fig. 10) with diffraction output (Fig. 30) and transparent cathode (Fig. 2(d)) was built
(Fig. 49)
and tested (Fig. 61-Fig. 64). As the source of high-voltage pulses driving this magnetron,
the nanosecond electron-beam accelerator SINUS-6 (Fig. 4) was used. The SINUS-6 accelera­
tor, whose main part is the Tesla transformer (Fig. 7), is capable of producing up to ~700 kV
voltage pulses of about 10-15 ns duration (Fig. 18) with a maximum discharge current o f ~7 kA.
The maximum discharge current of the SINUS-6 accelerator is limited by the total electric
power available from the Tesla transformer in a single pulse, which is about 5 GW (Fig. 20(a)).
In order to study the basic operational characteristic of the relativistic magnetron and
to compare parameters of the output microwave pulse produced by the traditional solid cath­
ode (Fig. 48) and the transparent one (Fig. 49), a thorough calibration of the basic diagnostics
allowing one to monitor accelerating voltage (Fig. 14-Fig. 17) and radially distributed output mi­
crowave power (Fig. 31-Fig. 37) and frequency (Fig. 38-Fig. 43) was performed. During these meas­
urements, the current-voltage characteristics of a thin tubular electron beam formed and trans­
ported in a smooth-cylindrical waveguide were measured (Fig. 23), and the prototype of a
smooth-bore magnetron with transparent cathode (Fig. 9) was tested (Fig. 45).
The experiments performed with the prototype o f a relativistic smooth-bore magne­
tron allowed for the gaining of experience for manufacturing different geometry transparent
cathodes (Fig. 2(d), Fig. 9, Fig. 47) and their use with the SINUS-6 accelerator. These experiments
showed also the great potential of the smooth-bore magnetron use as the simplest source of
high power microwaves to study transparent cathode operation in laboratory experiments.
The computer model of the 6-vane relativistic magnetron with the transparent cathode
was studied using the Magic code. Computer simulations showed that the transparent cathode
allows selection of the desired operating mode of a relativistic magnetron among all other pos­
sible modes of operation (Fig. 55, Fig. 56). It was shown also that the optimal position of single
emitters of the transparent cathode is when the emitters are positioned near the edges of the
resonant vanes o f the anode block (Fig. 57, Fig. 58), in agreement with Bosman et al [16].
69
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The experiments performed with the prototype of a relativistic magnetron with trans­
parent and solid cathodes (Fig. 61-Fig. 64) showed the possibility to select the desired operational
mode of the magnetron when it works with the transparent cathode in comparison with the
case when it works with the solid cathode (Fig. 66).
70
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3. MICROWAVE PULSE COMPRESSOR
The theory o f active microwave pulse compression is already very well developed [68]
and experiments have demonstrated the possibility of microwave pulse compression [18]-[21]
resulting in microwave power gain o f 10-20 dB achieved in single-mode resonant cavities, 2030 dB or more achieved in multimode cavities, and 50-70 dB projected for superconducting
cavities [11]. However, while the idea of microwave pulse compression has been demonstrated
experimentally a long time ago [11], it seems as though nobody has paid attention yet to the rise
time of the compressed microwave pulse and factors affecting this parameter. Therefore, the
practical questions about what needs to be done to decrease the rise time of the compressed
microwave pulse still remain and the present research was performed to partially address this
question.
For the purpose of this research, the double-arm (Magic) Tee configuration o f the
resonant cavity (Fig. 3(b)) was chosen as the microwave pulse compression setup, which can be
built from standard WR-90 waveguide components in the laboratory. A detailed diagram o f the
microwave power compression setup incorporating the microwave source, the resonant cavity,
the gas switch with high-voltage pulser, and the microwave diagnostics is shown in Fig. 69. A
photograph of the waveguide assembly forming the resonant cavity with input and output
ports is shown in Fig. 70.
Sliding S hort
Microlab/FXR,
X630C
C urrent Monitor
P e a rs o n 4 1 0
►To O scillo sco p e
W R -90 WG,
3 .8 gm
Amplifier,
V arian
VZM 6991K3
Ferrite
Isolator,
N arda 1210
Flexible
W R-90
W avegu id e,
30 cm
P u lser, 3 0 kV
FID F PG 302
Two WG T ransitions
W R -90 to W R-62
9.5 cm e a c h
Sw itch
' W R -90 W G,
3 0 cm
D irectional
C oupler, - 2 0 dB
Microline 235
A n te n n a .
-L
W R-90
Magic
T ee
Directional
C oupler, - 2 0 dB
M icroline 2 3 5
S ynthesized
Sw eeper
HP 83752B
T
C rystal
D etecto rs
HP 8473B
Sliding
Short
W aveline
661
O scilloscope,
Tektronix
TD S644A
5 0 0 MHz BW
Fig. 69. Scheme of the microwave power compressor.
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 70. Photograph o f the microwave pulse compressor.
The reminder of Chapter 3 is organi2 ed as follows. Section 3.1 presents a brief theory
of the pulse compression experiment based on a simplified example of a resonant cavity con­
nected with input waveguide through a simple diaphragm. Section 3.2 describes prototype of
the microwave pulse compressor assembled in the laboratory and shown in Fig. 70, as well as
the principle of its operation. Section 3.3 presents the results of computer simulations of the
microwave power compressor. Section 3.4 presents results of experimental measurements of
the microwave power gain obtained from the prototype microwave pulse compressor (Fig. 70).
Analysis o f the results is presented in Section 3.5.
3.1. Theory of the microwave pulse compressor
The following theory allows one to estimate the gain of microwave power G that is
possible to achieve inside a simplified microwave pulse compressor (Fig. 71) consisting of: 1)
input waveguide, 2) diaphragm, and 3) resonant cavity.
72
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2
1
Fig. 71. Simplified diagram o f the microwave pulse compressor: 1 - input waveguide, 2 - diaphragm,
3 - resonant cavity. Ai, A 2, Bi, B2 - electric field components of electromagnetic waves traveling in opposite direc­
tion relative diaphragm at both sides o f the diaphragm.
The electric field amplitudes of four microwave signals traveling toward (Ai and A2)
and away from (Bi and B2) the diaphragm, either inside (A2 and B2) or outside (Ai and Bi) the
resonant cavity (Fig. 71), relate to each other through the following matrix representation [68]
ikt
A]
B2
\
(30)
ik,
where ki is the coupling coefficient between the input waveguide (1) and the resonant cavity
(3) determined by the geometry of the diaphragm (2) (see Fig. 71). This coefficient can be low
when kj—>0, critical, when ki=0, or high, when ki—>1.
The relation between the electromagnetic wave traveling within the resonant cavity
from the diaphragm, B2 , and electromagnetic wave traveling within the resonant cavity toward
the diaphragm, A 2 , can be written using the attenuation constant a as
A = - B 2exp(~oz) ■
(31)
Substituting (31) into (30) gives the following two equations [68]
(32)
and
73
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In the storage mode of the microwave pulse compressor, the electrical length o f the
resonant cavity L equals an odd number n of the waveguide half-wavelengths, Xg/ 2
2n ,
— L =n n ,
K
(34)
where n = l, 2, 3, . . . . In this case the electric field amplitude B2 (33) is maximum, which means
that
V 1-
K
~ ex p (-o z )
^ = Q
(35)
(l - -Jl - /c,2 exp(-o z )j yjl - k?
It follows from (35) that at optimal conditions of the microwave pulse compressor operation in
the storage mode, the optimal coupling coefficient kij0pt is
=exp (-oz)
and
K r, = ± V
l - e x p ( - 2oe. ) .
(37)
Assuming that OCz«l, one can reduce (37) to the following expression
kupl=±2O Z .
(38)
Substituting (37) into (32) and (33) gives the electric field amplitudes at optimal conditions of the
microwave pulse compressor operation in the storage mode,
B,= 0,
(39)
and
B2 = ± .
^
= ± i- ^ ~ .
^1 - e x p ( - 2orz)
klopl
^
The maximum gain M o f the electric field amplitude inside the resonator is determined
from (40) as follows
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M = — = [l - exp(-2<az)]"I/2
A
(41)
Assuming that CC«1, one can reduce (41) to the following expression
1
4 2az
M
(42)
The microwave power P of an electromagnetic wave traveling in one direction can be
written then using (41) as
P = \M2\A?,
(43)
or
(44)
1- exp(-2ocz)
where Po=(Ai)2 is the input microwave power. Assuming that OCz«l, one can reduce (44) to
the following expression
1
0 2a
(45)
P = P0— .
K J
The microwave energy W stored inside the resonant cavity can be written using mi­
crowave power (44) and group velocity Dg as
w
2PL
W = -------,
(46)
where
(47)
v.
2nk„
The microwave energy Wi dissipated inside the resonant cavity during one period of micro­
wave oscillations can be written as
<«>
V.
OX,
75
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Equation (48) can be used to write the quality factor of the resonant cavity Q and at­
tenuation coefficient <Xthrough the geometrical factor o f the resonant cavity D
(49)
(50)
Substituting (50) into (38) gives a relation between the attenuation coefficient OC, quality
factor Q, and geometrical factor D of the resonant cavity at optimal conditions of the microwave pulse compressor operation in the storage mode
Substituting (50) into (42) gives a relation between the maximum gain G of the micro­
wave power, the quality factor Q, and the geometrical factor D o f the resonant cavity at opti­
mal conditions of the microwave pulse compressor operation in the storage mode [68]
The microwave power gain G (52) is what can actually be measured in the experiment
by comparing input Po and output Pi microwave power.
3.2. Design of the microwave pulse compression experiment
The microwave pulse compression setup was designed around an X-band (WR-90)
double-arm (Magic) Tee (Fig. 3(b)) using standard waveguide components available. A Varian
TWT microwave amplifier was used as the source o f input microwave power, and a gas dis­
charge tube mounted inside the straight section of WR-90 waveguide (Fig. 5(b)) was used as the
switch. A photograph o f the gas discharge tube used in this experiment is shown in Fig. 72(a); a
photograph of the high-voltage pulse generator, FPG-30-2 of FID Technology GmbH, that
produces —25-30 kV voltage pulses o f —50 ns FWHM duration on a matched load, —50 G,
and ignites the switch is shown in Fig. 72(b).
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a)
Fig. 72. Photographs o f the gas discharge tube (a) and high-voltage pulser igniting the gas discharge inside that
tube (b).
The microwave pulse compressor operates as follows. When both the HP 83752B
Sweeper and Varian VZM6991K3 Amplifier are turned on, the CW or long pulse microwave
signal goes through a Narda 1210 ferrite isolator toward the tapered waveguide section con­
nected to the input waveguide arm o f the Magic Tee (Fig. 69). The tapered waveguide section,
which is a pair of WR-90—WR-62 transitions connected by WR-62 ports, partially closes the
input of the Magic Tee in such a manner that only part of the applied microwave power goes
into the resonant cavity and the reminder of the power is reflected back to the source. This is
why the ferrite isolator is inserted between the source of microwave power and the tapered
waveguide section —it prevents the reflected microwave power from going back to the source
and affect its operation. The measured sn parameter of the tapered section showing what part
of the input microwave signal is reflected back from the tapered waveguide section is shown in
Fig. 73;
the measurements were performed using an HP8720D Network Analyzer. The input
microwave power is measured before the tapered waveguide section using an HP 8473B detec­
tor to compare it later with output microwave power measured at the output of the Magic Tee.
The detailed diagram of the input microwave power measurement is shown in Fig. 74(a),
a photograph of the waveguide assembly used to measure the input microwave power is shown
in Fig. 74(b), and the measured oscillograms of input microwave power (both CW and 500 |ls
pulse) are shown in Fig. 74(c).
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.2 -1
pair of WR90-WR62 and 6MWR62
pair of WR90-WR62
pair o f WR90-WR62 and 3" WR62
1 .0 -
7/28/2006 10:23:41
0 .8 -
(HP)
>
7/28/2006 10:24!!
0 .6 -
-3 0 -
pair o f WR90-WR62 and 6 " WR62
pair of WR90-WR62
pair of WR90-WR62 and 3MW R62
-4 0 -
0 .4 -
0.2 -
-5 0
9 .0
9 .2
9 .4
9 .6
9 .8
0.0
10.0
9 .0
9.2
Frequency (GHz)
9 .4
9 .6
10.0
Frequency (GHz)
Fig. 73. Measured r/rparameter of the tapered waveguide section.
A m p lifie r,
V arlan
VZM 6991K3
Ferrite
Isolator,
N arda 1210
Flexible
W R-90
W aveguide,
3 0 cm
W R-90 WG,
3 0 cm
Directional
C oupler, - 2 0 dB
Microline 235
A n ten n a
Crystal
D etecto rs
HP 8473B
S y n th esiz ed
Sw eeper
H P 83752B
O scilloscope,
Tektronix
TD S644A
5 0 0 MHz BW
6/13/2006 11:05:49
After 20 dB Attenuation
0 .0 0 -
o
Pulsed mode
&
CW mode
-0 .0 5 -
Time (ms)
C)
Fig. 74. Diagram (a), and photograph (b) o f the waveguide assembly designed to the input microwave power meas­
urements, and measured pulses (oscillograms) o f the input microwave power (c).
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Thus, the main purpose of the tapered waveguide section is to close the input arm o f the
Magic Tee and, in this manner, to provide the condition when most of the output microwave
power stored inside the resonant cavity during the storage mode of the cavity operation is ex­
tracted only through the output arm of the Magic Tee when the resonant cavity turns into the
extraction mode of the cavity operation after firing the gas switch.
Following the tapered waveguide section, either CW or long pulse microwave power
Fig. 74(c)
goes into the resonant cavity formed by: 1) side arms of the Magic Tee, 2) two
waveguide sections, one of which has the gas discharge tube (Fig. 72(a)) right in the center of the
waveguide (Fig. 5(b)) and another one which can be either a directional coupler measuring mi­
crowave power inside the resonant cavity (Fig. 70) or just a straight waveguide section (or is not
used at all here), and 3) sliding shorts connected to the open waveguide ports from both sides
of the resonant cavity (Fig. 69). The main purpose of the sliding shorts is to fix/establish a
standing wave electromagnetic field distribution within the resonant cavity in the storage mode
of the microwave pulse compressor (with the open switch) and move/adjust the standing wave
distribution in such a manner that it has a minimum (where one-half of the waveguide wave­
length is positioned) at the output of the Magic Tee and a maximum (where one-quarter of the
waveguide wavelength is positioned) at the switch position. Under these conditions, the reso­
nant cavity is filled by the input microwave power until the moment when the gas switch is
closed.
The gas switch itself consists of a glass tube with two sharp electrodes inserted into it
from both its open sides (Fig. 72(a)). Inside the glass tube is air under atmospheric pressure and
both sides of the tube are sealed to provide the condition for a gas discharge to form within the
closed volume. The gas tube is mounted in the center of a waveguide section and is fixed in
such a manner that the two electrodes inserted inside the tube are positioned outside the inner
volume of the waveguide (Fig. 5(b)). When a high-voltage pulse of about 30 kV is applied across
these two electrodes, a gas discharge occurs and the discharge plasma fills the glass tube,
changing the resistance of the inter-electrode gap from infinity to nearly zero. The measured
oscillograms of the discharge current and a photograph of the gas discharge developed inside
the glass tube are shown in Fig. 75.
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
400-i
•600-
4/27/2006 15:19:11
•800
-1000
-40
-20
20
40
60
80
100
120
140
160
180
Time (ns)
Fig. 75. Measured oscillograms o f discharge current (a) and photograph of an actual gas discharge
in the gas discharge tube (b).
As was mentioned in the Introduction, the operational parameters of the gas discharge
(with the rise time of the discharge current pulse to the most extent) greatly determine the pa­
rameters of the output compressed microwave pulse. From this point of view, there are a
number of constructive/geometrical characteristics o f the gas discharge tube whose variation
can result in a much faster discharge current rise time. Among these parameters are: 1) gas mix­
ture composition inside the tube (Ne, Ar, or some other gas or mixture of different gases in­
stead of air), 2) gas pressure inside the gas tube (Paschen pressure [69] instead of atmospheric),
3) distance between the two electrodes, 4) diameter of the gas tube, etc. The research leading to
the optimization of the gas discharge tube operation lies, unfortunately, beyond of scope of
this dissertation.
Nevertheless, upon closing the gas switch (Fig. 75(b)) situated right at the center of a
short waveguide section (Fig. 5(b)), the standing wave distribution inside the resonant cavity
changes to have a null at the switch position and a maximum at the output of the Magic Tee.
The stored microwave power then travels through the output of the Magic Tee and is moni­
tored by the HP 8473B crystal detector connected through the waveguide-to-coaxial adapter
on either side output of a directional coupler (Fig. 70) or an attenuator placed right at the output
o f the Magic Tee. If the directional coupler is used to monitor output microwave power, a
waveguide antenna or dummy load is connected to the output port of the coupler (Fig. 70). The
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
crystal detector response is monitored by an oscilloscope, and then acquired and stored in a
PC. The measured output microwave power is compared with the input microwave power
(Fig. 74(c))
and the gain of microwave power G (52) is detected.
3.3. Computer simulation of the microwave pulse compression experiment
Computer simulations of the microwave pulse compressor (Fig. 70) were performed us­
ing the HFSS code [70J, which is the industry-standard software for S-parameter, Full-Wave
SPICE extraction, and 3D electromagnetic field simulation of high-frequency and high-speed
components. The HFSS model with arm lengths 121.5 mm and 33.5 mm was created (Fig. 76)
that corresponds to the open switch configuration of the prototype of the microwave pulse
compressor shown in Fig. 70.
Fig. 76. HFSS model o f the microwave pulse compressor shown in Fig. 70.
The importance of this particular configuration of the resonant cavity (Fig. 76) with
these specific lengths of the side arms of the Magic Tee, 121.5 mm and 33.5 mm, is that this is
the one o f a few configurations of the prototype of the microwave pulse compressor for which
the microwave power gain G was observed at frequency —8.26 GHz. The measured oscil­
lograms of both input and output pulses of microwave power obtained using this setup and
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
demonstrating microwave power gain obtained in this experiment at frequency —8.26 GHz are
shown in Fig. 77.
0 .0 0 -t
9/5/2007 15:16:14
f0=8.258 GHz
P =-6 dBm
-0.05
9/11/2007 14:32:09
f=8.262 GHz
P0=-6 dBm
-0.10
Att=40 dB
Input Pulse
Output Pulse
Output Pulse
Output Pulse
Output Pulse
O utput Pulse
-0.15
- 0.20
,v¥nv*VM
*1ri*
“1
—
-10
-0.25
0
—
—
—
—
—
Input signal
O utput signal
O utput signal
O utput signal
O utput signal
O utput signal
20
“i30—
-0.30
-0.35
-0.40
5
10
Time (us)
Time (us)
a)
b)
Fig. 77. The oscillograms showing the microwave power gain obtained at frequency 8.26 GHz.
The HFSS model of the prototype of the microwave pulse compressor (Fig. 76), that
was developed in accordance with the design of its actual counterpart (Fig. 70) has input port 1
located at the top o f the Magic Tee orthogonal to the z-axis and output port 2 located in front
of the Magic Tee orthogonal to the x-axis (Fig. 76). There is, however, one sufficient difference
between the HFSS model (Fig. 76) and the actual setup (Fig. 70) - the HFSS model does not in­
clude the gas switch located in the long arm, 121.5 mm, of the resonant cavity. This is, of
course, not a very accurate representation of the actual configuration of the setup (Fig. 70); how­
ever, development o f an HFSS model of the gas switch is ongoing right now and will be incor­
porated into the existing model of the microwave pulse compressor (Fig. 76) in the near future.
The frequency-domain simulations performed using the HFSS m odel (Fig. 76) allows
one to plot S2i-parameter vs. the input frequency o f the microwave signal which shows how
m uch o f the stored microwave energy goes from the resonant cavity through the output port
o f the Magic Tee relative to the input microwave energy in the storage m ode o f the microwave
pulse compressor. The calculated s-parameters are shown in Fig. 78 in comparison with the
measured S2i-parameter o f the resonant system i) when the gas switch is inside the short sec­
tion o f a waveguide (Fig. 70), and ii) when just a sm ooth waveguide is used instead o f the same
length waveguide with the gas switch.
82
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-10
-1 0
-20
-20
-40
-40
m
33
o
££a>
(0
Q.
CO
-30'
<r>
aE>
-50'
CO
C
O
CL
-70
70
_90^
9/13/2007 11:40:35
’ “ . Smooth Waveguide
.100-4—4 7.0
7.5
8.5
8.0
9.0
9.5
10.0
8.0
Frequency (GHz)
8.5
9.0
9.5
10.0
Frequency (GHz)
a)
b)
Fig. 78. Calculated j--parameters of the smooth-waveguide resonant cavity (Fig. 76) and measured .^/-parameter of
(a) the resonant cavity with the smooth waveguide and (b) the resonant cavity with the same length waveguide and
the gas switch at the center (Fig. 5(b)).
One can see from Fig. 78(a) that results of HFSS calculations and the results of meas­
urements agree very well with each other when the measurements are performed under the
condition when there is just a smooth section of a waveguide instead of the waveguide section
with a gas switch placed in the center (Fig. 5(b)). However, when measurements are performed
with the gas switch, there is a difference between the calculated s-parameters and the measured
ones (Fig. 78(a)); the second resonant minimum, for example, moves from ~8.5 GHz, which
corresponds to the smooth waveguide measurements and calculations (Fig. 78(a)), to a lower
frequency o f ~8.26 GHz. This means that, in order to precisely calculate the physical processes
occurring inside the microwave pulse compressor, the additional model of a gas switch in its
open as well as in its closed states should be incorporated into the existing HFSS model
(Fig. 76).
Nevertheless, even from the calculations (Fig. 78), one can see that there are some spe­
cific frequencies at which the output microwave power traveling through port 2 o f the Magic
Tee outside the resonant cavity is extremely low. These frequencies are the resonant frequen­
cies and they are optimal for the microwave pulse compressor to operate. At these specific fre­
quencies the standing wave distribution inside the resonant cavity has a minimum (where onehalf of the waveguide wavelength is positioned) at the output of the Magic Tee, but unfortu-
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
nately does not necessarily have a maximum (where one-quarter of the waveguide wavelength
is positioned) at the switch position if the switch were designed and made before obtaining the
calculation results. The electric field distribution was also calculated by HFSS for these three
particular frequencies, 7.5 GHz, 8.54 GHz, and 9.82 GHz (Fig. 79), where the minimum mi­
crowave power output was calculated earlier (Fig. 78).
E F ie ld C V /n ]
7.6401e*003
7.1626e+003
6. 6851e*003
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4.2976e*003
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a)
E F 1 e ld [V /(l]
8.292le*003
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3.6278e*003
3.1095e*003
2.59136*003
2.07306*003
I.5548e*003
1.0365e*003
5.18256*002
■
b)
84
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E F 1 e ld [V /n 3
I 5,0885e+003
4.77056+008
4.4525e+B03
! 4.1344e+003
3.8l64e+003
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1.9082e+003
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1.2721e+003
9.541@e+002
6.3607e+002
3,1803e+002
c)
Fig. 79. Electric field distribution inside the HFSS model o f the microwave pulse compressor (Fig. 70) at frequen­
cies a) 7.5 GHz, b) 8.54 GHz, and c) 9.82 GHz. The orthogonal plane shows the gas switch position.
The calculations of the electric field distribution within the resonant cavity (Fig. 79)
show an exact coincidence of the gas switch position and one of the maxima of the standing
wave distribution inside the resonant cavity at frequency 8.54 GHz (Fig. 79(b)). It should be
noted that all the calculations that are presented in Fig. 78 and Fig. 79 are performed without the
gas switch placed in the long arm of the resonant cavity. The actual resonant frequency (in the
prototype of the microwave pulse compressor with a gas switch (Fig. 70))) that corresponds to
the electric field distribution shown in (Fig. 79(b)) was measured to be ~8.26 GHz (Fig. 78(b)) and
this turns out to be exactly the same frequency at which microwave power gain was detected in
the experiment (Fig. 77(b)).
The answer to the question as to why microwave power gain was detected only at that
one specific frequency 8.26 GHz while not at the other two resonant frequencies ~7.24 GHz
and ~9.7 GHz (Fig. 78(b)) comes from the measurements of the same S2 1 -parameter of the
resonant cavity with a closed gas switch that is shown in Fig. 80(a). The closed gas switch was
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
simulated by a piece of copper tube inserted into the glass tube during the measurement of sparameters using the Network analyzer (Fig. 80(b)).
fig:**'go' Ki."":'
K E f J S ®l
9/13/200712:00:18
-
Mode! of closed Gas switch
F r e q u e n c y (G H z)
a)
b)
Fig. 80. Measured r-parameters of the resonant cavity with closed gas switch and 40 dB attenuator at output of the
Magic Tee (Fig. 77(a)) (a) and Network Analyzer HP 8720D used in these measurements (b).
Measurements o f the S2 i-parameter with the closed gas switch showed that there is only
one frequency, ~8.26 GHz, at which the output of the Magic Tee is completely open when the
switch is closed. At the other two frequencies, ~7.24 GHz and ~9.7 GHz, not all the stored
energy is released, which means that the standing wave distribution inside the resonant cavity at
these two frequencies does not have a maximum at the output o f the Magic Tee when the
switch is closed. The frequency 8.26 GHz is the same frequency at which a minimum of the
standing wave distribution at the output of the Magic Tee was measured when the switch was
open (Fig. 78(b)).
It follows from the HFSS simulations that in the very broad frequency range 7-10 GHz
there could be only one single frequency that corresponds to the following two very important
conditions at which the microwave power amplification would be possible:
1) when the switch is open, the standing wave distribution inside the resonant cavity
should have a minimum at the output of the Magic Tee;
2) when the switch is closed, the standing wave distribution inside the resonant cavity
should have a maximum at the output of the Magic Tee.
86
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Only when both of these conditions are satisfied, which occurs only at frequency ~8.26 GHz
at this given configuration o f the resonant cavity with the lengths of side arms o f the Magic
Tee, 121.5 mm and 33.5 mm (Fig. 77(a)), microwave power amplification is possible.
An HFSS model of the gas switch should be developed and incorporated in the exist­
ing model of the resonant cavity (Fig. 76) in order to find other operating frequencies. Only
then the different configurations of the resonant cavity with different lengths of the side arms
o f the Magic Tee will be calculated in the frequency domain to find at what single frequency
the S2 i-parameter is minimum when the switch is open and is maximum when the switch is
closed. It should be the same frequency at two different modes of the microwave pulse com­
pressor operation: both storage mode and extraction mode. This work lies, unfortunately, be­
yond the scope of this dissertation.
3.4. The microwave pulse compression experiment
Despite the fact that the present computer model (Fig. 76) does not allow one to find
the operating frequencies of the microwave pulse compressor because it does not have an ap­
propriate model of the gas switch, the measurements using the prototype microwave pulse
compressor (Fig. 5(a), Fig. 70) are still possible to perform and the microwave power gain can be
found experimentally.
This work is still ongoing and microwave power amplification already has been ob­
served at a number of other frequencies within the X-band using the gas discharge switch
(Fig. 75(b)) and, in some cases, a manually operated waveguide switch HP X930A (Fig. 83). The
manually operated switch was used to compare the compressed output microwave power pulse
obtained using this switch (Fig. 83) with pulses of output microwave power obtained using the
much faster gas switch (Fig. 5(b)). The difference in the rise time of the conductivity o f the gasdischarge switch can show how it affects the rise time of the output compressed microwave
pulse. Below are oscillograms showing microwave power gain obtained during the course of
this research.
87
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0.5-i
-1.0
8/9/2006 13:5734
8/9/2006 14:05:17
0. 0 ’
8
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I
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Input Signal
Output Signal
Output Signal
-4 .0
0
-1
1
2
3
0.0
-0 .5
4
1.0
0.5
Time (jos)
1.5
2.0
Time (ps)
Fig. 81. Microwave power gain at frequency —7.56 GHz obtained using the gas switch.
4/10/2007 16:21:56
Manual Switch
HP X930X
f= 6.6l6G H z
output
input signal
(after isolator)
Time (ms)
Fig. 82. Microwave power gain at frequency ~6.2 GHz
obtained using manual switch (Fig. 83).
Fig. 83. The manually operated switch H P X930A.
6 /5 /2 0 0 7 15:4 7 :0 6
6 /5 /2 0 0 7 1 5 :4 2 :2 9
f= 9 .7 9 8 8 G H z
1
f= 9 .7 9 8 8 G H z
\
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--------input sig n al
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--------o u tp u t s ig n al
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--------o u tp u t s ig n al
--------o u tp u t s ig n al
--------input s ig n a l
--------o u tp u t sig n a l
--------o u tp u t s ig n al
--------o u tp u t sig n a l
--------o u tp u t sig n a l
--------o u tp u t sig n a l
M anual S w itch H P X 9 3 0 A
c lo s e d -to -o p e n sw itching
M anual S w itch H P X 930A
o p e n -to -c lo s e d sw itching
20
40
T im e (m s)
T im e (m s)
a)
Fig. 84. Microwave power gain at frequency ~9.85 GHz obtained using the same manual switch (Fig. 83).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
b)
The comparison between the compressed microwave pulses obtained using the gasdischarged switch (Fig. 77(a)) and the manually operated switch (Fig. 84(b)) is shown in Fig. 85.
.
0 0-1
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100
200
300
400
Time (as)
Fig. 85. Oscillograms o f the compressed microwave pulse obtained using the gas-discharge switch (Fig. 5(b)) and
the manually waveguide operated switch (Fig. 83).
The result shown in Fig. 85 clearly indicates that the rise time of the compressed output
microwave pulse produced by the microwave pulse compressor depends on how fast the
switch operates. With the fast gas-discharge switch (Fig. 5(b)), where the switching time is de­
termined by the time of the gas discharge formation inside the glass tube (Fig. 75), the rise time
of the microwave pulse is about 300-400 ns (Fig. 77). The rise time of the compressed micro­
wave pulse, when it is obtained with the manual switch (Fig. 83), is about 200-300 |ds (Fig. 84).
89
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3.5. Conclusion
In the course o f the research described in Chapter 3, a prototype o f the microwave
pulse compressor was built (Fig. 69, Fig. 70) and tested (Fig. 77, Fig. 81, Fig. 82, Fig. 84). A simple gas
discharge tube (Fig. 72(a)) placed in the center of a short straight waveguide section (Fig. 5(b)) was
used as a switch changing the electrical length of the resonant cavity and in this way opening
the resonant cavity filled with microwave energy stored during the time when the switch was
open. A Varian TWT VZM6991K3 was used as a source of input microwave power and an
FID FPG 302 30 kV pulse generator (Fig. 72(b)) was used as a driving source for closing the
switch (Fig. 75(b)).
The HFSS computer model of the resonant cavity was built (Fig. 76) and calculations
have been performed showing that, for proper operation of the microwave pulse compressor
not only a resonance should be established inside the resonant cavity when the gas switch is
open (Fig. 78, Fig. 79), but —at the same position of the gas switch —the maximum o f the electric
field distribution inside the resonant cavity should stay exactly at the output of the resonant
cavity when the gas switch is closed (Fig. 80(a)). The HFSS model o f the microwave pulse com­
pressor (Fig. 76) needs to be upgraded to include a model o f the gas switch in order to correctly
calculate the electric field distribution inside the resonant cavity (Fig. 79) when the gas switch is
open and when it is closed (Fig. 78(b)).
The experiments performed with the prototype of the microwave pulse compressor
showed the possibility o f obtaining microwave power gain up to 10 dB using both a gas dis­
charge switch (Fig. 5(b)) and a manually operated switch (Fig. 83). It was shown by comparing
these results (Fig. 85) that the faster the switch, the shorter is the rise time of the compressed
output microwave pulse.
90
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4. SUMMARY AND POSSIBLE FUTURE WORK
The importance o f short pulse HPM for enhanced radar systems is determined by a
number of very important factors, among which the decrease of the signal-to-noise ratio is,
probably, most sufficient when the transmitted microwave power reaches levels of 1 GW and
higher. Using shorter microwave pulses in enhanced radar systems also minimizes the dead
time, which is the time when the receiver is turned off while the transmitter operates, and al­
lows one to detect smaller-cross-section targets.
The main goal of the research presented in this dissertation is to experimentally study
and explore two different methods that can be used to produce short-pulse, high-power mi­
crowaves. The first method is to use a transparent cathode in a relativistic magnetron and the
second method is to use a fast waveguide switch and a microwave pulse compressor pumped
by a low-power microwave source, such as a non-relativistic magnetron. It was already experi­
mentally demonstrated in many previous studies that both methods can produce 1 GW and
greater microwave power with high pulse repetition rate and frequency stability from one pulse
to the next. However, the main factor that really determines the ability to obtain short pulses of
high-power microwaves —the rise time of the microwave pulse —did not receive much atten­
tion until recently.
The general idea to increase the rise time of output microwave pulse produced by a
relativistic magnetron is to use novel cathode designs, among which the transparent cathode
has such a unique combination o f properties that distinguishes it from all other types of en­
hanced geometry cathodes. It was shown in many calculations that the transparent cathode
provides faster start of microwave oscillations at the desired operational mode of a relativistic
magnetron in comparison with its solid cylindrical counterpart.
In order to experimentally validate these calculations, the prototype of a smooth-bore
relativistic magnetron and a prototype of a 6-vane relativistic magnetron both equipped with a
transparent cathode and driven by the nanosecond high-current SINUS-6 accelerator were de­
signed, build and tested. The measurements of output microwave radiation produced by the 6vane relativistic magnetron with the 3-emitter transparent cathode and a comparison of these
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
measurements with analogous ones obtained from the same magnetron operated with the solid
cylindrical cathode showed that the transparent cathode allows one to select the desired operat­
ing mode of the magnetron among all others. This conclusion was reached by analyzing the
measured radial distribution of the output microwave power obtained using both types o f cath­
odes - the transparent cathode and the solid cathode. The measurements also showed that the
start of microwave oscillations, as it was detected by the broad-band crystal detector, occurs at
about the same time when both cathodes were used to operate with the relativistic magnetron.
This fact can probably be explained by an assumption that, in addition to the desired opera­
tional mode of the magnetron, some other types of magnetron oscillations producing different
frequencies of output microwaves are detected as well.
The general idea to produce short-pulse microwave output from the microwave pulse
compressor is to use a very fast waveguide switch that opens a resonant cavity and releases the
stored microwave energy. In order to experimentally demonstrate this assumption, the proto­
type of a microwave pulse compressor was built and tested. The measurements were per­
formed using two different switches: i) a fast one, which was made using a gas discharge tube
driven by a nanosecond high-voltage pulser, and ii) a relatively slow manual waveguide switch.
Measurements of the compressed microwave pulse obtained using both these methods showed
that when the fast gas discharge switch was used in the experiment the rise time of the output
compressed microwave pulse was much faster, even given the fact that the same resonant stor­
age cavity was used in the experiment.
The overall conclusions that can be reached as a result of the experimental research
presented is this dissertation are: i) the transparent cathode can be used as a factor allowing to
reduce the start-up time of the desired type of microwave oscillations in relativistic magnetrons,
ii) the smooth-bore magnetron can be used to experimentally study basic peculiarities of the
transparent cathode operation in relativistic magnetrons, and ii) as fast a closing switch as pos­
sible should be used in a waveguide to obtain fast rise time of the output microwave pulse
from microwave pulse compressors.
The possible future work that can be performed on the basis of the research presented
in this dissertation should concentrate on a more detailed study of the output microwave radia-
92
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tion produced from both sources - both smooth-bore and 6-vane relativistic magnetrons with
transparent cathode and microwave pulse compressor with fast gas discharge switch. The ex­
perimental work with the relativistic magnetron should definitely be connected with measure­
ments of the time-frequency spectrograms of the output microwave radiation. The analysis of
these spectrograms should be performed to compare the rise time of the specific microwave
oscillations that correspond to the frequency of interest. Experimental work with the micro­
wave pulse compressor should be connected with developing and utilizing discharge tubes that
provide as fast a closing time as possible in the tube by having the most optimal mixture and
pressure of gas.
The computational studies should be performed as well to reveal that type of cathode
priming (or combination of different primings) that provides the most favorable conditions for
a fast start of the desired type o f microwave oscillation in a relativistic magnetron. The simula­
tions of a smooth-bore relativistic/nonrelativistic magnetron, as the simplest microwave
source, and a 6-vane relativistic/nonrelativistic magnetron, as a more complicated microwave
source with additional anode priming, will help to design the most optimal geometry of the
enhanced geometry cathode and to choose the most optimal azimuthal position of the cathode
within the anode block of a relativistic magnetron. The calculations o f the microwave pulse
compressor should incorporate the geometry o f the gas discharge switch positioned inside the
resonant cavity. These calculations will help to build and optimize the pulse compressor when
it needs to be designed to operate at some given frequency of interest.
Very interesting work can also be performed that is connected with the study o f the
current-voltage characteristics of a thin tubular electron beam produced by the SINUS-6 accel­
erator. This work should include both experimental measurements and computer simulations
of the electron beam dynamics. The basic idea of this work is to show that the current-voltage
characteristic of a short-pulse electron beam dynamically changes in time and along the trans­
port channel electron beam. For this reason the current-voltage characteristic can not be com­
pletely described using steady-state theories o f the space-charge limited electron beam trans­
port.
93
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5. APPENDIX
© 2006 IEEE.
Reprinted, with permission, from IEEE Transactions on Plasma Science,
June 2006, Volume 34, Number 3, Part I of three parts, pp. 620-626.
94
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620
IEEE TRANSACTIONS ON PLASM A SCIENCE, VOL. 34, NO. 3, JUNE 2006
Mode Conversion in a Magnetron With Axial
Extraction of Radiation
Mikhail I. Fuks, Nikolay F. Kovalev, Andrey D. Andreev, Student Member, IEEE, and Edl Schamiloglu, Fellow, IEEE
Abstract—We demonstrate the ability to form simple radiation
patterns from a relativistic magnetron with axial extraction. This
is achieved by tapering onto a conical antenna only those cavities
of the anode block that correspond to the symmetry of the radiated
modes. The efficiency of mode conversion of the operating 7r-mode
into a radiated mode using this method is demonstrated using com­
puter simulations of a six-cavity magnetron.
Index Terms—Diffraction output, mode conversion, radiation
pattern, relativistic magnetron, 7r-mode of magnetron.
I.
In t r o d u c t i o n
HE RELATIVISTIC magnetron with axial extraction,
also known as the magnetron with diffraction output
(MDO) [1]—[9], is the most compact narrowband high-power
microwave (HPM) source. In an earlier series of experiments
with an X-band MDO, a radiated power of about 0.5 GW [1]
was achieved for an applied voltage of 0.5 MV [1] and 4.0 GW
for an applied voltage of 1.0 MV [2]. The radiation pulse dura­
tion in each case was about 1 0 ns, with a beam-to-microwave
conversion efficiency of about 1 2 %.
The MDO concept (Fig. 1) is based on a conventional mag­
netron resonant system (2 in Fig. 1) comprising N cavities
where the cavities are smoothly tapered in the axial direction
onto a conical hom antenna (3 in Fig. 1) up to a radius that
exceeds the radius corresponding to the cutoff frequency of the
radiated wave in a regular cylindrical waveguide. Such a design
has some advantages compared to a conventional magnetron
with radial extraction of electromagnetic energy (Fig. 2).
Since radiation is extracted radially from one of the cavities
(sometimes from several cavities) in relativistic magnetrons
of the conventional design, a pair of Helmholtz coils (5 in
Fig. 2) is used, as a rule, to provide the necessary uniform
magnetic field in the small interaction space, that is, in the
gap between the resonant system (2 in Fig. 2) and the cathode
(1 in Fig. 2). In essence, the use of such a large magnet
system (5 in Fig. 2) diminishes one of the most attractive
properties of the magnetron—its compactness in terms of its
T
Manuscript received September 21,2005; revised March 24,2006. Research
at the University of New Mexico was supported in part by an Air Force Of­
fice ofd Scientific Research/Department of Defense (AFOSR/DoD) Multidis­
ciplinary University Research Initiative (MURI) Grant on Compact Portable
Pulsed Power, and in part by an AFOSR Microwave Power Research Initiative
(MiPRI) Grant on High Power Microwave Sources.
M. I. Fuks, A. D. Andreev, and E. Schamiloglu are with the Department of
Electrical and Computer Engineering, University of New Mexico, Albuquerque,
NM 87131-0001 USA (e-mail: fuks@ece.unm.edu; edl@eece.unm.edu).
N. F. Kovalev is with the Institute of Applied Physics of Russian Academy of
Sciences, Nizhny Novgorod 603600, Russia (e-mail: kovalev@appl.sci-nnov.
ru).
Digital Object Identifier 10.U09/TPS.2006.875770
Fig. 1. Top: Simplified design of the MDO (1— cathode, 2— resonant system,
3— diffraction output of radiation, 4— coaxial line for magnetron feeding,
5— solenoid). Bottom: Photograph showing the diffraction output of an X -band
MDO [1],
small resonant system with volume V < A3 (where A is the
wavelength of the radiation).
The symmetric design of the MDO with axial extraction al­
lows the use of a truly compact magnetic field-producing system
in the form of a single short solenoid (5 in Fig. 1) whose diam­
eter is determined by the outer diameter of the resonant system
(2 in Fig. 1).
The resistance of the MDO to microwave breakdown is far
better (at least one order of magnitude) than that of the conven­
tional magnetron, in which the output waveguide (3 in Fig. 2) is
coupled with the cavity through a narrow slot (9 in Fig. 2) that
is very sensitive to reflections. Therefore, the diffraction output
can be used in relativistic magnetrons with very high radiated
powers.
In conventional magnetrons, the axial length L of the cavities
is typically about half of the operating wavelength A in order
to avoid competition between longitudinal modes. In the MDO,
however, the limitation on the axial length is less restrictive. The
quality factor Q of the MDO is close to the minimum diffraction
quality factor Q d i f r [ 1 ]
Q « Qdifi = ^ ( j ) •
0093-3813/S20.00 © 2006 IEEE
95
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(1)
FUKS e t a lx M ODE CONVERSION IN A M AGNETRON W ITH AXIAL EXTRACTION OF RADIATION
E unloaded
E loaded
Fig. 2. Design of a conventional magnetron: 1—cathode, 2—resonant system,
3— output waveguide, 4— feeding coaxial line, 5— pair of Helmholtz coils,
6— side cavities, 7— drift space for spent electrons, 8—electron dump, 9—cou­
pling slot. Bottom: Cross section of the magnetron.
Here, n is the number o f axial variations o f the microwave elec­
tric field. A s is clear from (1), the Q factor is largest for the
lowest longitudinal mode (with n = 1) for any length L o f the
cavities. Therefore, the selection o f longitudinal modes is auto­
matically achieved, giving the possibility o f increasing the radi­
ated power P not by increasing the applied voltage U, but rather
by increasing the anode current Ia, which is proportional to L
[10].
The limitation o f the axial length L in the MDO is associ­
ated with decreasing the axial current I z along the cathode as
electrons are deposited onto the anode. This changes the mag­
netic field H 0 = \J H qz + Hfifj (that is tangent to the cathode
surface), which can disrupt the synchronism condition for single
mode generation, that is, the proximity o f the average azimuthal
electron velocity ve = cE0(Hoz /Hfi) to the phase velocity vph
o f the operating wave
Ve ~ f p h -
(2 )
Here, E0 is the radial electric field that is determined by the
applied voltage U in the A - K gap d = R a — R c between the
electrodes (where R a and R c are the anode and cathode radii,
respectively), H (iz is the applied axial magnetic field, H of) =
2 I z / c r for r > R c, and c is the speed o f light. A s a rule, the
azimuthal field Hog is small compared with the applied axial
field H0z, that is x = ( Hoe/Hoz ) 2 < 1- Single-mode regime
operation occurs when the difference between phase velocities
o f neighboring modes exceeds the parameter x , that is,
Auph/uph > x-
(3)
621
Since the leakage current is much less than the anode current, the
axial cathode current Iz ~ Ia is proportional the length L of the
interaction space, and, therefore, x ~ L 2. Thus, the inequality
(3) is, in essence, the condition that limits the length L in the
MDO. (Otherwise, it is possible that synchronous interaction
with different modes in different parts of the MDO can occur.)
Therefore, in principle, the length can be considerably longer
than in conventional magnetrons.
Increasing the radiated power of magnetrons requires in­
creasing the number of cavities N , which in turn increases the
probability of hopping from the operating mode to a neigh­
boring one.
As a rule, the 7r-mode and the 27r-mode are used in magnetrons
as the operating modes, and only these modes are nondegenerate,
whereas all other modes are azimuthally degenerate. The
asymmetric output of the conventional magnetron removes the
degenerate nature of the modes, fixing the nodes and antinodes
of electric fields of the degenerate modes, that is, splitting
each such mode into two submodes, one with a sinusoidal and
the other with a cosinusoidal azimuthal variation with respect
to the output waveguide (Fig. 2, bottom). The submode with
the fixed antinode near the cavity, coupled with the output
waveguide (E loaded), is radiated, unlike the submode with
the node near this cavity (E unloaded). Therefore, the first
submode has a lower Q than the unloaded submode. In the
case of mode hopping from the 7r or 2ir operating mode to
a neighboring degenerate mode, the submode with the larger
Q, that is, the nonradiated submode, is the most probable
new operating mode because of its lower start conditions.
Thus, the magnetron will operate in a manner scattering its
microwave energy onto the electrodes, which can lead to
serious disruption, particularly if the magnetron operates at
a high repetition rate.
The diffraction output of the magnetron does not remove the
degeneracy because all of the cavities are identically loaded.
Therefore, in the MDO any mode can be selected as the oper­
ating mode, and the possibility of mode hopping is not an issue.
It should be noted that, in parallel with the above-enumer­
ated advantages of the MDO, its radiation pattern is more com­
plicated than that of the conventional magnetron, in which the
lowest TEio mode of the output rectangular waveguide is radi­
ated.
In this paper, we demonstrate the ability to effectively convert
the operating zr-mode to simpler radiation patterns, including
a narrow Gaussian wave beam, directly within the diffraction
output of the axial extraction without any additional elements.
This technique was originally proposed in [6],
In Section II, we suggest the design of a mode converter
placed directly within the horn antenna and explain its opera­
tion. In Section III, we demonstrate the efficiency of such con­
version of the operating 7r-mode to radiated modes with more
simple patterns. Section IV discusses the influence of reflections
from the mode converter on magnetron operation. Concluding
remarks are given in Section V.
II. C o n c e p t o f M o d e C o n v e r t e r s
To illustrate the concept of a mode converter within the MDO,
we use the example of a magnetron with a resonant system com-
96
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622
IEEE TRANSACTIONS ON PLASM A SCIENCE, VOL. 34, NO. 3, JUNE 2006
1
- Z & m St*
*■•- >- radii
Fig. 3. Configurations of cavities and their continuation onto the horn antenna
for conversion of the operating x-mode of the magnetron to the radiated T E 3i
mode (left), T E 01 mode (center), and T E n mode (right), respectively.
prising N = 6 identical cavities joined with a conical horn an­
tenna. In the converter the symmetry of the electric fields in the
resonant system of a magnetron operating in the 7r-mode is ex­
ploited, when phases of electric fields in neighboring cavities
are opposite (red lines in Fig. 3).
When all cavities are tapered onto the horn antenna (grey sec­
tors in Fig. 3, left) with gradually decreasing thickness up to
the diameter of the antenna, which exceeds the cutoff condition
for a radiating mode, the radiation pattern corresponds to the
TEn/2,i mode, that is, the TE 31 mode.
When only every other cavity is tapered onto the horn antenna
(grey sectors in Fig. 3, center) in the same manner, the antenna
is excited by electric fields with identical phases, and for this
symmetry of electric fields, the radiation pattern corresponds to
the TEoi mode.
In this case, the other cavities must not be coupled with the
antenna, which can be achieved, for example, by continuation
of these cavities at their maximum radii onto the horn antenna
as shown by the dotted line (4) in Fig. 4. The maximum radius
of these noncoupled cavities in the antenna is still less than the
cutoff radius for the radiating TE0i mode.
Note that the configuration of cavities and their continuation
onto a horn antenna can be different from the sectors indicated
in Fig. 3. For example, in experiments [1] and [2] an MDO with
rectangular cavities and rectangular continuation onto a horn
antenna (Fig. 1, bottom) was used.
When only two diametrically opposite cavities are tapered
onto the horn antenna (Fig. 3, right), the structure of electric
fields exciting the antenna corresponds to radiation of the T E n
mode. The horn antenna radiates this lowest mode of a cylin­
drical waveguide in the form of a narrow wave beam close to
a Gaussian pattern, which is very attractive for many applica­
tions. Obviously, the Gaussian wave beam can be formed by
this method in the MDO when phases of the wave fields in di­
ametrically opposite cavities are opposite, which occurs when
the number of cavities N = (2s + 1) * 2, where s is any integer
including s = 0 , whereas the symmetric radiation pattern can
be formed in the MDO for any even number of cavities.
These mode conversions are not only achieved without in­
creasing the dimensions of the conical horn antenna, but may
even allow for a decrease in the aperture when the azimuthal
index of the radiating wave is less than N/2.
These mode converters can operate across a wide band of
frequencies because they are free of elements that are sensitive
to the frequency of the wave.
Fig. 4. Side view of the MDO. Top: 1— cathode, 2—block of cavities, 3—con­
tinuation of radiating cavity to the horn antenna, 4— possible continuation of
cavity which is not coupled with the antenna. Middle: 3-D isometric view of
the converter to the T E 0, mode. Bottom: Configurations of a resonant system
with mode converters of the operating x-mode to the radiated T E 3i mode (left),
TEoi mode, (center), and T E n mode (right).
TABLE I
D im e n s io n s o f H o r n A n t e n n a s f o r C o n v e r s io n t o D if f e r e n t M o d e s
mode
m
K uwjp c m
R, cm
TE n
6
8.221
9.0
48.4
3
7.498
7.6
41.6
2
3.603
6.2
34.4
TEoi
TEn
ia-----
Fig. 5. Schematic drawing of the conical horn antenna.
III.
E f f ic ie n c y o f t h e m o d e C o n v e r t e r s
To demonstrate the efficiency of this method of mode con­
version, we use computer simulations of an MDO with cathode
radius Rc = 1.58 cm, anode block with axial length 7.2 cm
97
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FUKS e t a l : M ODE CONVERSION IN A M AGNETRON W ITH AXIAL EXTRACTION O F RADIATION
Fig. 6. Far-field distribution when all six resonators are tapered onto the horn antenna: a) |JS|; b) |JEe | ; c) |J5V|. Pattern corresponds to the T E 31 mode.
consisting of six sector cavities, each of them with radial depth
2 cm and a 2 0 ° angular opening to the interaction space as in
the well-known A6 magnetron [11], In order to exclude com­
petition between the 2tt- and 7r-modes, we separate their phase
velocities, which are practically coincident in the A6 magnetron
with the anode radius R0_ = 2.11 cm, by increasing the ra­
dius up to i?a = 2.71 cm. Such an increase is acceptable in
order to provide synchronous interaction of the electrons with
the operating wave in the entire space between the electrodes
(the space charge of the electrons promotes the condition in ( 1 )
in the narrow A -K gap when R,JRc < 2 ~ 2.5 [12]). For the
operating tr-mode with wavelength A = 12.295 cm (which was
found for our magnetron resonant system using the three-dimen­
sional (3-D) fully electromagnetic particle-in-cell code MAGIC
[13]), the radii R of the horn antennas with different number
m of tapered cavity continuations corresponding to the radiated
TE 3 !(m = 6 ), TE 0 i(m = 3), and T E n(m = 2) modes,
are shown in Table I. In addition, the cutoff radii Rmto« corre­
sponding to cutoff cross sections for these modes and flare an­
gles a (Fig. 5) are listed. The length of the conical hom antenna
for all mode converters was chosen to be identical at L = 20 cm.
The choice of parameters for the antennas in Table I is, in
many ways, arbitrary. We are guided by the objective of mini­
mizing the dimensions (to maintain compactness). Because of
this, we find that incomplete conversion of the operating tr-mode
to other modes is possible to a certain extent, and some distor­
tions of the calculated radiation patterns, in comparison with the
ideal (theoretical [14]) field distributions corresponding to radi­
ation of “pure” waves, are expected. In order to decrease these
distortions, the flare angle a should be decreased (thereby in­
creasing the lengths of the converters), and the ratio R /RCutoS
increased.
To estimate the efficiency of the mode converters with pa­
rameters indicated in Table I, we used the HFSS code [15],
which is an interactive software that computes S parameters and
full-wave fields for arbitrarily shaped 3-D passive structures.
Field patterns for the far-field distributions \E(6, <p)|, as well
as its polar \E(6,tp)\$ and azimuthal \E(6,ip)\v components,
which are related to the maximum value of |E(9, tp) |, were cal­
culated and are plotted in Figs. 6 - 8 . In each figure, the colors
show the distribution of field amplitudes with respect to its max­
imum value (in red). In order to interpret Figs. 6 - 8 , it should be
noted that the color scale in Fig. 9(c) is the valid scale to com­
pare the maximum and minimum fields within each picture. You
cannot use the color scale to compare one picture to an adjacent
picture. In comparing columns a) to b) to c) for each of these fig­
ures, the size or magnitude of the lobes are in proper proportion,
so that in Fig. 7, as an example, |E(0, tp)\g is negligible com­
pared with \E{6,<p)\v .) In the far-field region, where the dis­
tance I from the antenna aperture D is large, I
2D 2 /A, the
longitudinal component of the electric field vanishes. Angular
distributions of radiated fields (Figs. 6 - 8 ) show that impurity
due to parasitic modes is insignificant in spite of our nonoptimal
choice of antenna dimensions.
Clearly, the purest radiation pattern corresponding to the ra­
diated TE 31 mode is observed when all cavities are tapered onto
the hom antenna (Fig. 6 ), that is, when all the cavities are iden­
tically loaded.
For the “7r-mode—TEoi ” converter, Fig. 7(b) shows the pres­
ence of the polar Eg component in the radiated TEoi mode in
the far-field region, which can be caused by partial field leakage
from the closed cavities into the hom antenna. Comparing the
polar [Fig. 7(b)] and azimuthal [Fig. 7(c)] electric-field compo­
nents, we estimate that the contribution of the polar component
to the radiated power is about 2 %.
Also, the contribution of the polar component [Fig. 8 (b)] of
the radiation pattern [Fig. 8 (a)] due to a small penetration of the
tr-mode into the antenna in the ‘V-mode—T E n ” converter is
small as well.
Thus, noticeable distortions in the observed radiation patterns
do not necessarily indicate poor conversion. It is known (see,
for example, [14]) that small impurities of parasitic modes may
lead to significant redistribution of radiation power flow. How­
ever, these distortions do not play a crucial role in most applica-
98
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624
IEEE TRANSACTIONS ON PLASM A SCIENCE, VOL. 34, NO. 3, JUNE 2006
.
\
r
—'-“ix.
.
b)
Fig. 7. Far-field distribution when only three alternate resonators are tapered onto the hom antenna: a) \E \; b) \E S |; c) \E V\. Pattern corresponds to the TEoi
mode.
Fig.
8.
c)
b)
a)
Far-field distribution when only two opposite resonators are tapered onto the hom antenna: a) | f i |; b) | E e |; c) |E v \. Pattern corresponds to the T E ii mode.
tions since most of the contribution of the impurities goes onto
forming sidelobes, the divergence of which is larger than that of
the main lobe.
Moreover, we can demonstrate the efficiency of this method
of mode conversion by observing the structure of the electric
fields in the cylindrical output waveguide adjoining the hom
antenna. As shown in Fig. 9, the field structures stand out
conspicuously at wavelength A = 12.295 cm in the output
waveguides after the hom antenna, both when all the cavities
are open [radiating the TE 31 mode, Fig. 9(a)] and when only
two cavities are open [radiating the T E n mode, Fig. 9(b)], For
the ‘V-mode—TEn ” converter, the cross section of the output
waveguide for the radiated mode is chosen to be less than that
of the higher order modes that provide excitation of pure modes
in the output waveguide. Such an output waveguide, after the
diffraction output, would, therefore, be useful as a filter to
remove parasitic mode impurities.
IV.
In f l u e n c e o f M o d e C o n v e r s i o n o n
M a g n e t r o n O p e r a t io n
Significant reflections of the operating tr-mode of the mag­
netron from the interface with the antenna can occur when the
OMWo.OOl
b)
C)
Fig. 9. Distributions of the electric field of converted waves in the output wave­
guide when: a) all six cavities are continued into the hom antenna (T E 3i ), and
b) two opposite cavities are open (T E n ); c) graphical scale representing am­
plitude of the electric field, V/m, corresponding to the input power of 1.0 W
(also applicable to Figs. 6-8).
99
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FUKS e t al. : M ODE CONVERSION IN A MAGNETRON W ITH AXIAL EXTRACTION OF RADIATION
625
well, 2.18 GHz, although the presence of the electron beam sub­
stantially reduces the frequency / = 2.44 GHz of the 7r-mode
of the “cold” system.
V.
0
200
100
400 z. mm
300
Fig. 10. Top: Particle plot of the electron flow inside the interaction space when
all six cavities are open radiating the T E 31 mode (left); three alternate cavities
are open radiating the T E 0i mode (center); two opposite cavities are open radi­
ating the T E n mode (right). Applied voltage is 700 kV and the magnetic field
is 0.6 T. Bottom: View in the r - z plane for the T E 31 mode case, although this
view will be the same for the other two modes as well.
0 9
•6 open
•3 open
•2 open
0.9
o.t
|
im a n n i i.
i, « *
w
n p
t '
’-■w . n .
<
o
CL
0>>
■
Ifi
* 11
i
Ii
’ilirtrtll f a i m«iM i ' a itorttttfriHryAdlfti
I If
O.i
u
0.2
0.0
0
5
10
IS
20
00 35
15 90
T im e.n s
Fig. 11. Output microwave power versus time for the magnetron operating in
the jr-mode with different mode converters when the applied voltage is 700 kV
with rise time 1 ns and magnetic field is 0.6 T. Frequency is 2.18 GHz for all
three cases.
antenna aperture dimension is close to the cutoff cross section
for the radiated wave and/or the flare angle of the conical hom
antenna is large. Furthermore, different combinations of closed
and open cavities in different mode converters lead to azimuthal
inhomogeneities in the reflected fields. It is, therefore, necessary
to assess how these reflections influence MDO operation.
MAGIC simulations found that the MDO operates steadily in
the tr-mode in the region of applied voltage U = 700 kV for
a fixed magnetic field of B = 0.6 T in the interaction space for
each of the mode converters listed in Table I. For example, Fig. 10
(top) shows that electron trajectories in the form of three electron
spokes, which are typical for 7t-mode operation, are almost in­
variant in the magnetrons using different mode converters. Also,
electron trajectories in the r-z plane (Fig. 10 bottom) are iden­
tical for these magnetrons (the trajectories are determined by the
longitudinal distribution of the applied magnetic field).
Fig. 11 shows that differences in the radiated power are sim­
ilarly small. For all these cases, the anode current is practically
the same, about 10 kA. The radiation frequency is the same as
C o n c l u sio n
In this paper, we have demonstrated an effective method to
convert the operating 7r-mode of oscillations in magnetrons with
axial extraction of radiation to simple radiation patterns directly
within their hom antennas without any additional devices. Such
a magnetron, with a unique combination of characteristics such
as high-output microwave power, compact axially symmetric de­
sign (including its magnetic field-producing system), and desired
radiation pattern, should be very attractive for many applications.
References
[1] N. F. Kovalev, B. D. Kol’chugin, V. E. Nechaev, M. M. Ofitserov, E.
I. Soluyanov, and M. I. Fuks, “Relativistic magnetron with diffraction
coupling,” Sov. Tech, Phys. Lett., vol. 3, pp. 430-431,1977.
[2] N. F. Kovalev, A. A. Kolomenski, E. G. Krastelev, M. I. Kuznetsov,
A. M. Maine, E. V. Nechaev, M. M. Ofitserov, V. A. Papdichev, M.
I. Petelin, M. I. Fuks, and L. N. Chekanova, “High-power relativistic
3-cm magnetron,” Sov. Tech, Phys. Lett., vol. 6, pp. 197-198,1980.
[3] J. Benford, “Relativistic magnetrons,” in High-Power Microwave
Sources, V. L. Granatstein and I. Alexeff, Eds. Norwood, MA:
Artech, 1987.
[4] J. Benford and J. Swegle, High-Power Microwaves. Norwood, MA:
Artech, 1992.
[5] A. V. Gaponov-Grekhov and V. L. Granatstein, Eds., Applications o f
High-Power Microwaves. Norwood, MA: Artech, 1994.
[6] M. I. Fuks and N. F. Kovalev, “Magnetron with diffraction output,”
in Program Abstracts 11th Int. Conf. High-Power Electromagnetics:
EUROEM’98, Tel Aviv, Israel, Jun. 14-19,1998, p. 18.
[7] M. Fuks and E. Schamiloglu, “Relativistic magnetron with diffraction
antenna,” in Abstract Book R F 20015th Workshop High Energy Density
High Power RF, Snowbird, UT, Oct. 1-5, 2001.
[8] ------ , “Optimization of the parameters of a relativistic magnetron with
diffraction output,” Proc. SPIE Intense Microwave Pulses IX, vol. 4720,
pp. 18-27, 2002.
[9] E. Schamiloglu, “High power microwave sources: Where do we go
from here?,” in Conf. Record 25th Int. Power Modulator Symp. HighVoltage Workshop, Jul. 2002, pp. 694-698.
[10] V. E. Nechaev, M. I. Petelin, and M. I. Fuks, “Magnetron with rela­
tivistic electron beams,” Sov. Tech. Phys. Lett., vol. 3, pp. 310-311,
1977.
[11] A. Palevsky and G. Bekefi, “Microwave emission from pulsed, rel­
ativistic e-beam diodes, II: The multiresonator magnetron,” Phys.
Fluids, vol. 22, pp. 986-996, 1979.
[12] G. B. Collins, Ed., Microwave Magnetrons. New York: Mc­
Graw-Hill, 1946.
[13] MAGIC ATK Mission Research, Newington, VA [Online]. Available:
http://www.mrcwdc.com/Magic/
[14] Y. T. Lo and S. W. Lee, Eds., Antenna Handbook. New York: Van
Nostrand Reinhold, 1988.
[15] HFSS Ansoft Corp., Pittsburgh,, PA [Online]. Available: http://www.
ansoft.com/products/hf/hfss/overview.cfm
Mikhail I. Fuks received the M.Sc. degree in radio­
physics and electronics from Gorky State University,
Gorky, U.S.S.R., and the Ph.D. degree in physical
electronics from the Institute of Applied Physics
(IAP), Academy of Science of the U.S.S.R., Gorky.
In 1963, he joined the Gorky Radiophysical Re­
search Institute, Gorky, U.S.S.R., and, since 1977,
he has been with AP in the field of high-power mi­
crowave electronics as a Scientist and then as Senior
Scientist and a Head of the Research Group. Since
1999, he has been in the United States in radar tech­
nology sponsored by the Ballistic Missile Defense Organization. In 2000, he
joined the Electrical and Computer Engineering Department, University of New
100
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626
IEEE TRANSACTIONS ON PLASM A SCIENCE, VOL. 34, NO. 3, JUNE 2006
Mexico, Albuquerque, as a Research Professor. His current research interests in­
clude forming and transportation of electron beams, the development and appli­
cation of various types o f high-power microwave sources, and electrodynamic
systems.
Nikolay F. Kovalev was bom on February 27,
1943, in Ivanovo, U.S.S.R. He received the M.S.
degree in design and technology of radio-electronic
devices from the Polytechnical Institute of Nizhny
Novgorod, Nizhny Novgorod, U.S.S.R., in 1966, and
the Ph.D. degree and Sci.D. degree in radiophysics
and microwave electronics from the Institute of
Applied Physics (IAP), Russian Academy of Sci­
ences, Nizhny Novgorod, Russia, in 1983 and 1992,
respectively.
Beginning in 1966, he was with the Gorky Radio­
physical Research Institute, Gorky, as a Senior Engineer. In 1977, he joined
the IAP as Senior Scientist and, since 1984, he has been a Head of Laboratory
with IAP and a Professor at the University of Nizhny Novgorod. In summer
2002, he was a Distinguish Visiting Professor in the Electrical and Computer
Engineering Department, University of New Mexico. His research interests in­
clude high-power microwave electronics, applied electrodynamics, and physics
of electron beams.
Andrey D. Andreev (S’03) received the Diploma
in Physics (an equivalent of M.S. degree in the
U.S.) from the Physics Department, Tomsk State
University, Tomsk, Russia, in 1990. He is currently
working toward the Ph.D. degree in electrical
engineering in the Department of Electrical and
Computer Engineering, University of New Mexico,
Albuquerque.
While living in the U.S.S.R., he served two years
in Soviet Army, studied physics and mathematics
at the Tomsk State University, and worked in
Theoretical Laboratory of the High-Current Electronics Institute, Tomsk,
as a Research Assistant. The main focus of his research was simulation of
degradation processes occurred under the electron beams propagation in gases.
When the Soviet Union became the Russian Federation in December of 1991,
he moved to St. Petersburg, Russia, where he soon joined the Laboratory
o f High-Current Pulsed Accelerators (NIL SIU) of the Efremov Institute of
Electrophysical Apparatus, St. Petersburg. He spent then ten years working
with microsecond-duration high-current electron beam accelerators, multipoint
explosive emission cathodes, high-voltage Marx generators, etc. The ultimate
goal of that Laboratory’s activity was utilization of the microsecond-duration
electron beams to modernization of the surface properties of different metals
and alloys, and he prepared the Candidate of Sciences (analog of a Ph.D.)
thesis devoted to study of the multipoint explosive-emission cathode operation
in high-magnetic fields. In January of 2003, he entered the University of
New Mexico, Albuquerque, where he is now doing his research project in
the Pulse Power, Beams, and Microwaves Laboratory. The research project
utilizes high-current nanosecond-duration electron-beam accelerator SINUS-6
to produce high-power microwaves, which enclosed a lot of experimental,
theoretical, and computational efforts. He is also interested in many aspects of
plasma physics, pulsed-power/high-voltage technique, electromagnetic waves
propagation and antennas, and Galactic cosmic-ray modulation.
Edl Schamiloglu (M’9G-SM’95-F 02) received
the B.S. and M.S. degrees from the School of
Engineering and Applied Science, Columbia Uni­
versity, New York, in 1979 and 1981, respectively,
and the Ph.D. degree in applied physics (minor in
mathematics) from Cornell University, Ithaca, NY,
in 1988.
He became an Assistant Professor of Electrical
and Computer Engineering at the University of
New Mexico (UNM), Albuquerque, in 1988. He
is presently Professor of Electrical and Computer
Engineering and directs the Pulsed Power, Beams, and Microwaves Laboratory.
In the summer of 1990, he was a Lecturer at the U.S. Particle Accelerator
School (USPAS), Harvard University, Cambridge, MA, and in summer 1997,
he lectured at the USPAS, Massachusetts Institute of Technology (MIT),
Cambridge, MA. He has authored or coauthored 60 refereed journal papers,
over 100 reviewed conference papers, and three patents. He coedited Advances
in High-Power Microwave Sources and Technologies (Piscataway, NJ: IEEE
Press, 2001), with R. J. Barker, and he is currently coauthoring High Power
Microwaves, 2nd Ed. (Bristol, U.K.: Institute of Physics Publishing, 2006),
with J. Benford and J. Swegle. His research interests are in the physics and
technology of charged-particle beam generation and propagation, high-power
microwave sources, plasma physics and diagnostics, electromagnetic wave
propagation, pulsed power, and infrastructure surety.
Dr. Schamiloglu received the Sandia National Laboratories Research Excel­
lence Award in 1991, The UNM School of Engineering Research Excellence
Award twice (junior faculty in 1992 and senior faculty in 2001), and the title
of UNM Regents’ Lecturer in 1996. He is a member of the American Phys­
ical Society and a member of the ASEE. He is an Associate Editor of the IEEE
T r a n s a c t i o n s o n P la s m a S c ie n c e .
101
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6. REFERENCES
[1] "High power radar" in High PowerMicrowaves, Second Edition / J. Benford, J. A. Swegle, and E.
Schamiloglu, Taylor & Francis Group, LLC, 2007, pp. 69-71.
[2] M. I. Skolnik, "An introduction to radar" in Radar Handbook, Second Edition / Edited by M. I. Skolnik,
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[3] W. M. Manheimer, G. Mesyats, and M. I. Petelin, "Applications o f high-power microwave sources to en­
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sium, Albuquerque, NM, 30 October - 2 November 2006.
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