close

Вход

Забыли?

вход по аккаунту

?

Microwave emission of large and small orbit rectangular gyrotron devices

код для вставкиСкачать
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. U M I
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may be
from any type o f computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send U M I a complete
manuscript and there are missing pages, these will be noted.
Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand comer and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in reduced
form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6” x 9” black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact U M I directly to
order.
UMI
A Beil & Howell Information Company
300 North Zeeb Road, Ann Arbor MI 48106-1346 USA
313/761-4700 800/321-0600
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M IC R O W A VE EM ISSIO N O F LARGE AND SM ALL O R B IT
RECTANG ULAR G YRO TRON DEVICES
by
Jonathan M ark Hochman
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Nuclear Engineering)
in The University of Michigan
1998
Doctoral Committee:
Professor Ronald M . Giigenbach, Chairman
Associate Professor Mary Brake
Professor Ward D. Getty
Professor Yue Y. Lau
Dr. Thomas A. Spencer, Nuclear Engineer, USAF,
Air Force Research Lab, Phillips
Research Site
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UMI N um ber: 9840557
UMI Microform 9840557
Copyright 1998, by UMI Company. All rights reserved.
This microform edition is protected against unauthorized
copying under Title 17, United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
_ Jonathan Mark Hochman
O ---------------------------------All Rights Reserved
1998
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
This is dedicated to my wife, Dena, whose love is without bound.
ii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ACKNOWLEDGMENTS
There is none more deserving of an accolade than my advisor, Dr. Ronald
Gilgenbach. I wish to acknowledge his superior guidance during my tenure as a graduate
student at the University of Michigan. His commitment and enthusiasm for the
advancement of science and the professional development of his students, and his
inspiration and creativity in research, are unmatched by any I know. Without his
confidence in me and experimental insight in the nature of microwaves and electron
beams I could not have completed my research and this dissertation.
I thank Professor Y. Y. Lau for his many efforts to show me from “first
principles” how coherent radiation is produced. His dedication to teaching and learning
are an inspiration. I wish to express my gratitude to Dr. Thomas Spencer for his plethora
of trips to Michigan to help improve my experimental work. Thanks to Professor Mary
Brake for her unending optimism and enthusiasm, for her efforts always to help me find
employment, and for finding time to read my dissertation. I thank Professor Ward Getty
for teaching me about the uses of plasmas and plasma processing, and answering so many
questions about microwaves.
I would like to thank Dr. Ziya Ackasu who peaked my interest in plasmas,
teaching my first plasma physics class. I learned so much standing at the blackboard in
his office. I thank Dr. Terry Kammash for teaching my first class in fusion and for
keeping me up to date in my favorite sports.
Ron Spears electrical expertise in the lab was invaluable. I wonder how many
students could succeed without his help and advice. I would like to thank the Air Force
Office of Scientific Research for providing my AASERT funding for my research the
iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
past three years. I thank all of the people in our department’s administration, without
whose help I could not have come to Michigan, worked at the university, or completed
my research; thank you Helen Lum, Sue Greenwood, Diana Corey, Ann Bell, Karen
Balson, Pam Derry, and Rhonda Sweet. Thanks for your help and encouragement. I owe
my gratitude to Ed Birdsall, who kept our computers up and running throughout my
duration in the Plasma Bay.
I would like to thank those former students who helped me successfully complete
my work at Michigan, Dr. Mark Walter for getting me started, Dr. John Luginsland for
teaching me the intricate nature of MAGIC, Dr. Shawn Ohler for his advice and always
loaning me equipment from the radiation laboratory, Dr. Sanjay Raman for his assistance
with LIBRA and other microwave components from his lab, Dr. Joe Geddes for his
friendship, Dr. Melisa Buie, Dr. Hong Ching, Dr. Joel Lash, Dr. Joe Schumer, Dr. Peggy
Christenson, and Tony Lujan. Thanks to Kyle Hendricks for all of his questions and
guidance during conference presentations.
I would also like to acknowledge and thank the people currently working with me.
Reggie Jaynes for helping me build and run experiments, and for always sharing his
insights about electromagnetism; Josh Rintamaki for his abundance of energy for getting
things done; Scott Kovaleski for his constant prodding; Bill Cohen, Chris Peters, and
Doyle Vollers. I thank Ricky Ang, August Valfells, and Allen Gamer for getting me
back on the basketball court and off the computer.
I would like to the thank the undergraduates who have worked at the Plasma bay
during the past few years and assisted with the experiments, Antwan Edson, Derick Love,
and Nick Eidietis.
Thanks to David Smithe and Larry Ludeking of Mission Research Corporation for
answering so many questions about M AGIC and assisting me in my computer
simulations.
iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Finally, I have to thank my wife, Dena, who always encouraged me. Without her
love, patience, and support, I don’t know if I could have finished this dissertation. I am
grateful to my parents and family for their love and support for everything I have
undertaken in life.
This work has been supported by the Air Force Office o f Scientific Research,
Multidisciplinary University Research Initiative (M U R I) through a Texas Tech
subcontract, A ir Force Research Lab, Northrop Gurmman Corporation, and the AFOSRsponsored M AG IC Code User’s Group.
v
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE OF CONTENTS
D E D IC A TIO N ...............................................................................................................
II
A C K N O W LED G M EN TS............................................................................................
m
L IS T OF FIG U R E S....................................................................................................... IX
L IS T OF TA B LES.................................................................................................... XXTO
L IS T OF APPENDICES......................................................................................... X X IV
CHAPTER
1. IN TR O D U C TIO N ..........................................................................................
1
1.1 Preamble.............................................................................................
1
1.2 Gyrotrons and other coherent radiation sources................................
2
1.3 Previous work on rectangular cross section devices.........................
6
1.4 Present experi mental w ork................................................................
8
2. RECTANG ULAR CROSS SECTIO N G YRO TR O N
T H E O R Y ......................................................................................................
10
2.1 Introduction......................................................................................
10
2.2 Gyrotron Dispersion Relations and Coupling Constants................
13
2.2.1 Gyrotron dispersion relation, linear theory......................
13
2.2.2 Fundamental mode gyrotron coupling constants ...........
15
2.2.3 Large orbit gyrotron linear growth rates..........................
19
2.2.4 Mode competition in the large orbit gyrotron..................
20
2.3 Active Circulator Applications.......................................................
23
2.4 Quality Factor Determination.........................................................
25
vi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.5 Pulse Shortening...........................................................................
26
3. EX PE R IM E N TA L C O N FIG U R A TIO N AND
DIAG NO STICS............................................................................................
3.1 MELBA Diode................................................................................
28
28
3.2 Diode and e-beam transport magnetic fields................................... 32
3.2.1 Small orbit e-beam magnetic fields.................................
32
3.2.2 Large orbit e-beam magnetic fields.................................
34
3.3 Trigger sequencing..........................................................................
39
3.4 Electron beam extraction and cavity structure................................. 40
3.5 Microwave extraction and cavity cold tests...................................
41
3.6 Electron Beam Voltage and Current Diagnostics..........................
48
3.6.1 MELBA voltage...............................................................
48
3.6.2 Diode current...................................................................
49
3.6.3. Aperture current, cavity entrance current, and exit plate
current.............................................................................
49
3.7 Beam alpha diagnostics....................................................................
50
4. CO M PUTER S IM U L A T IO N S ...................................................................
58
4.1 EGUN simulations for the small orbit gyrotron............................
58
4.2 MAGIC 2D simulations...................................................................
61
4.3 MAGIC 3D simulations...................................................................
69
5. SM ALL O R B IT RECTANG ULAR CROSS SECTION
G YRO TRO N EX PE R IM E N TS................................................................
72
6. LARGE O R B IT RECTANG ULAR CROSS SECTION
GYRO TRON EX P E R IM E N TS ..................................................................
84
6.1 Large Orbit RCS gyrotron results for Cusp LA............................
84
6.2 Large Orbit RCS gyrotron results for Cusp IB .............................
93
6.3 Large Orbit RCS gyrotron results for Cusp I I ..............................
103
vii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6.3.1 Cusp II results utilizing the uniform RCS cavity
104
6.3.2 Diode magnetic field optimization measurements
110
6.3.3. Tapered cavity experiments utilizing cusp I I ............
113
6.3.4 Microwave pulse shortening and spectroscopy results..
117
7. C O N C LU S IO N S .....................................................................................
124
APPENDICES.............................................................................................................
128
B IB LIO G R A P H Y .......................................................................................................
188
viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L IS T OF FIGURES
Figure
1.1.
1.2.
2.1.
2.2.
Cyclotron resonant masers [LAU95]. (a) cylindrical small orbit
gyrotron. (b) cylindrical large orbit gyrotron. (c) peniotron.......................
3
Cyclotron resonant maser interactions. The solid curve represents the
microwave cavity dispersion curve, and the dashed lines represent the
e-beam dispersion relations [SPE91, B A I87].............................................
6
Phase diagram of electron orbits demonstrating the “phase bunching”
mechanism [LAU95, BAI87]....................................................................
11
Negative mass instability effect showing phase bunching of electrons
[LAU95, BAI87]........................................................................................
12
2.3.
Simplified geometry for gyrotron dispersion relation determination
2.4.
Beam and structure mode of dispersion relations....................................
IS
2.5.
Rectangular cross section gyrotron geometry, (a) small orbit
configuration, (b) large orbit configuration...............................................
16
(a) Axial view of the active circulator gyro-TWA. (b) Waveguide
modes and beam mode for a tapered rectangular waveguide with a
tuned beam grazing the vertically polarized TEl0 mode [LAU84]...........
24
2.6.
3.1.
Experimental configuration for small orbit gyrotron experiments
3.2.
Large orbit gyrotron experimental configuration with axial magnetic
14
29
field profile................................................................................................. 30
3.3.
3.4.
MELBA voltage pulse generated by the Marx generator........................
31
(a) Diode magnetic field (G /A) and (b) maser solenoid magnetic field
(G/A) as a function of distance from the anode. The cathode position
is a t-12.2 cm (A -K gap =10.7 cm)............................................................ 33
ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.5. Magnetic field as a function of distance from the anode for a small
orbit gyrotron measurement. This is a superposition of diode and
maser fields. The rectangular cross section cavity region is between
45.5 and 66.5 cm.......................................................................................
34
3.6. Diode magnet field response in G/A as a function of distance from the
anode plate for the large orbit gyrotron measurements. Cusp IA ’s
interaction region started at 45.5 cm, but the cavity was moved
forward to 28.5 cm for cusp IB and I I .......................................................
35
3 .7. Superposition of diode and maser magnetic fields for Cusp IA at
different charging voltages, (a) The solenoid charging voltage was
320 V, and the diode charging voltage was set at 2.76 kV. (b) The
solenoid charging voltage was set at 240 V, and the diode charging
voltage was 1.8 kV..................................................................................... 36
3.8. Maser Solenoidal profile in G/A as a function of distance from the
anode for cusps IB and II. The rectangular interaction region was
placed at a distance of 28.5 cm from the anode......................................... 37
3.9. A typical axial magnetic field profile for cusp IB and II as a function
of distance from the anode. The rectangular interaction region was
placed at a distance of 28.5 cm from the anode......................................... 37
3.10. Radial magnetic field profile for cusp n. Positions indicated on the
right side of the figure indicate distance from the anode. The center of
the cusp is 14 cm from the anode. The axes were converted from
angular positions to X -Y Cartesian coordinates and multiplied by a
factor of 10.................................................................................................
38
3.11. Magnetic field coil currents for a large orbit gyrotron measurement as
a function of time, (a) represents the diode magnetic field current
(5.25 A/div). (b) shows the coil current of the maser solenoidal field
windings (25 A/div). (c) demonstrates the gate pulse used as a
reference for the MELBA Marx trigger and all of the triggers and time
delays.......................................................................................................... 39
3.12. Uniform rectangular cross section interaction cavity...............................
3.13. Cold test frequency spectrum of the RCS cavity (cavity A). Marker 1
appears at a frequency of 2.15 GHz. This corresponds to the TEt0i
mode. Marker 2, which appears at 2.88 GHz, corresponds to the TEou
mode. Marker 4 shows the TEUt mode at 3.50 GHz, and marker 5 is
x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
apparently due to either the TEou mode or possibly the TE 201 mode at
3.97 GHz....................................................................................................
43
3.14. Cold test frequency spectrum of the tapered cavity B. Marker 1
appears at a frequency of 2.18 GHz. This corresponds to the TEt0i
mode. Marker 2, which appears at 3.11 GHz, corresponds to the TE0u
mode. The frequency has shifted due to the taper in the vertical
dimension. Marker 4 at 3.77 GHz shows the TEm mode, and marker
5 at 3.89 GHz appears to be due to either the TEou mode or possibly
the TE| 12 mode...........................................................................................
45
3.15. Cold test frequency spectrum of the tapered cavity C. Marker 1
appears at a frequency of 2.36 GHz. The frequency shift from 2.18
GHz is due to the taper in the horizontal dimension. Marker 2, which
appears at 2.85 GHz, corresponds to the TE0i i mode. Marker 3 shows
the TEm mode at 3.79 GHz.......................................................................
46
3.16. Experimental set-up for transported current measurements for the large
orbit gyrotron............................................................................................
50
3.17. Schematic showing radiation darkening for the large orbit gyrotron.
Each beamlet is given a large kick in the theta direction as it passes
through the cusp.........................................................................................
51
3.18. Radiation darkened glass witness plate for the large orbit gyrotron.
The eight beamlets clearly show coherent o ff centering...........................
52
3.19. Radiation darkened pattern for the small orbit gyrotron...........................
52
3.20. Radiation darkened glass witness plate of the e-beam for the large
orbit gyrotron after passing through cusp I I ............................................... 53
3.21. Comparison of simulation results with experimental results in e-beam
a simulations for the large orbit gyrotron (cusp IA). The crosshatched area is due to the radiation darkened pattern of 1 e-beamlet.
The simulation also demonstrates the coherent off-centering
(simulations from Jaynes [JAY97])...........................................................
54
3.22. Comparison of simulation results [JAY97] with experimental results in
e-beam a simulations for the small orbit gyrotron. The cross-hatched
area represents the radiation darkened pattern of 1 e-beamlet..................
3.23. Electron beam a as a function of cavity magnetic field for the large
orbit gyrotron (cusp II). This shows the range over which a varies.
xi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
The data is based on minimum and maximum radii of the radiation
darkened glass witness plates.....................................................................
56
3.24. Average e-beam a as a function of cavity magnetic field for the large
orbit gyrotron (cusp II) ...............................................................................
4.1
57
EGUN result showing the e-beam trajectory for a uniform 1 kG Bfield. The cathode emits at 2.25 + 0.25 cm with a voltage of -750 kV.
The average a without adiabatic compression is 0.15............................... 60
4.2
EGUN result showing the e-beam trajectory as the B-field is increased
to 2 kG on the interaction region (other parameters are the same as
Figure 4.1). The average a with adiabatic e-beam compression is 0.23... 60
4.3
EGUN result showing the e-beam trajectory as the B-field is increased
to 4.5 kG on the interaction region (other parameters are the same as
Figure 4.1). The average a with adiabatic e-beam compression is 0.32... 61
4.4
Model used for MAGIC 2D code simulations of the RCS gyrotron
oscillator for both the small orbit and large orbit cases.............................
4.5
Trajectory plots from M AGIC 2D code simulations for the large orbit
RCS gyrotron case. While four beamlets were used to initially
populate the simulation space, the beam appeared to demonstrate
bunching and the formation of an annular e-beam similar to the one
depicted from radiation darkening on a glass plate (see Figure 3.20).
Electron beam trajectories are shown at 1 ns (a), 13 ns (b), 20 ns (c),
and 27 ns (d)...............................................................................................
4.6
62
63
Fast Fourier transforms (FFTs) of the electric fields from the small
orbit gyrotron M AGIC 2D code simulations, (a) Ev at a B-field (Bz) of
1.85 kG. The cyclotron frequency occurs at 2.10 GHz and the
fundamental TE10 mode has a resonance at 2.22 GHz. (b) EH at a
magnetic field of 1.85 kG. The cyclotron frequency and the
fundamental mode are present as well as the TEoi mode at 2.82 GHz
and the TEU mode at 3.6 GHz. (c) Ev at a B-field of 2.3 kG shows
only a resonance at 2.12 GHz (TEio). (d) E h at a B-field of 2.3 kG,
where the cyclotron frequency is seen at 2.61 GHz and the TEot mode
is present at 2.82 GHz. Figure 5.6 shows the dispersion relations for
the small orbit gyrotron..............................................................................
4.7
FFTs of the electric fields from the large orbit gyrotron M AG IC 2D
code simulations, (a) Ev at a B-field (Bz) of 1.5 kG. The cyclotron
frequency occurs at 1.63 GHz and the fundamental TEio mode has a
xii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
resonance at 2.34 GHz. (b) E h at a magnetic field of 1.5 kG. The
cyclotron frequency and the fundamental mode are present but the
TEoi does not appear except in the noise, (c) Ev at a B-field of 2.1 kG
shows only a resonance at 2.3 GHz which appears due to both the
cyclotron frequency (2.3 GHz) and the fundamental TEio mode, (d) EH
at a B-field of 2.1 kG, where the TEoi mode is present at 2.82 GHz.
Figure 6.16 shows the large orbit gyrotron dispersion relations...............
4.8
66
Microwave polarization power ratio for the small orbit RCS gyrotron
as a function of B-field from MAGIC code simulations. The model
assumes kz=0, e-beam a = 0.3, and the current = 2 kA............................. 67
4.9
Microwave polarization power ratio for the large orbit RCS gyrotron
as a function of B-field from M AGIC code simulations. The model
assumes kz=0, e-beam a = 1.0, and the current = 200 A ........................... 68
4.10. MAGIC 3D cavity generated for large orbit gyrotron simulations
69
4.11. Polarization power ratio from MAGIC 3D simulations. Below 2.1 kG
the fundamental TEi0 mode is dominant, and above 2.1 kG the
orthogonal TE0i mode becomes dominant................................................
70
5.1. Peak power measured in the vertically and horizontally polarized
waveguide systems for the small orbit gyrotron. (a) without reflecting
strips; (b) with reflecting strips.................................................................
73
5.2. Rectangular cross section gyrotron data signals from shot 4841. (a)
Voltage monitor signal (310 keV/div). (b) Entrance current signal (2
kA/div). (c) Vertically polarized power signal. The peak power
corresponds to approximately 1 MW . (d) Horizontally polarized power
response. The peak power in the horizontally polarized mode was
approximately 15 M W ...............................................................................
74
5.3. Microwave Filter response for MELBA shot 4841. (a) Filter A (2 .0 2.5 GHz), (b) FilterB (2.5 - 3.0 GHz), (c) FilterC (3.0 - 3.5 GHz), (d)
Filter D (3.5 - 4.0 GHz). The filters were placed in the horizontal
polarization................................................................................................. 75
5.4. Microstrip bandpass filter results for the small orbit gyrotron without
reflecting strips, (a) Filters placed in the horizontal polarization, (b)
Filters placed in the vertical polarization................................................... 77
xiii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.5. Microstrip bandpass filter results for the small orbit gyrotron with
reflecting strips, (a) Filters placed in the horizontal polarization, (b)
Filters placed in the vertical polarization..................................................
78
5.6. Dispersion diagram for the small orbit RCS gyrotron. The e-beam is
assumed to have a beam a of 0.3 and a beam energy of 750 keV. (a)
the beam line for the first harmonic at a B-field of 2.25 kG. Observed
frequency interactions are: TE0i (FW ) =2.8 GHz, and TEn (FW) = 3 .7
GHz. (b) frequency interactions for the first harmonic of a 2.9 kG Bfield. Observed interactions include the TE0i (BW) = 2.9 GHz, and
the TEu (FW ) = 3.5 GHz. (c) frequency interactions for the second
harmonic of a 2.25 kG B-field. Observed interactions include the
TE10 (BW) = 3.0 GHz, the TEoi (BW ) = 3.3 GHz, and the TE„ (BW )
= 3.7 GHz. (d) frequency interactions for the second harmonic of a 2.9
kGB-field. Observed interactions include the TEio (BW ) = 3.7 GHz,
and the TE0] (BW ) = 3.9 GHz...................................................................
79
5.7. Polarization Power ratio (V /H ) as a function of B-field. The horizontal
mode was dominant at all field values, and the fundamental TEl0
forward wave was not observed in the vertical polarization.....................
80
5.8. Transported current to the RCS cavity entrance as a function of Bfield...........................................................................................................
81
5.9. Power efficiency for the RCS small orbit gyrotron as a function of Bfield...........................................................................................................
82
5.10. Power versus microwave pulse length for the small orbit gyrotron.
Pulse shortening is clearly visible.............................................................
83
6.1. Transported current to the entrance of the RCS cavity using cusp IA in
axis encircling e-beam measurements. The entrance current appears to
decrease with increasing B-field................................................................ 85
6.2. Peak power measured in vertical and horizontal polarizations for the
large orbit gyrotron (cusp IA; reflecting strips were used in the
horizontal dimension)...............................................................................
6.3. Data from MELBA shot 5183. This data was taken with a cavity Bfield of 1.66 kG. (a) voltage monitor response (400 keV/div). (b) RCS
cavity entrance current (200 A/div). (c) Vertically polarized
microwave output (0.2 MW /div). (d) Horizontally polarized
microwave output (4 MW /div). (e) Filter A response (2 MW/div; 2.0 2.5 GHz), (f) Filter B response (2 MW/div; 2.5 - 3.0 GHz), (g) Filter C
xiv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
response (0.1 MW/div; 3.0 - 3.5 GHz), (h) Filter D response (0.67
MW/div; 3 .5 -4 .0 GHz)............................................................................. 87
6.4. Data from MELBA shot 5191. This data was taken with a cavity Bfield of 1.46 kG. (a) voltage monitor response (400 keV/div). (b) RCS
cavity entrance current (100 A/div). (c) Vertically polarized
microwave output (2 MW/div). (d) Horizontally polarized microwave
output (0.1 MW/div). (e) Filter A response (0 .5 MW /div; 2.0 - 2.5
GHz), (f) Filter B response (0.1 MW/div; 2.5 - 3.0 GHz), (g) Filter C
response (0.1 MW/div; 3.0 - 3.5 GHz), (h) Filter D response (0.1
MW/div; 3 .5 -4 .0 GHz)............................................................................. 87
6.5. Gyrotron microwave power out the bandpass filters with the filters in
the vertical polarization. The filters indicate a clear resonance at 1.47
kG with an emission frequency response between 2.0 and 2.5 GHz.
This corresponds to the forward wave of the fundamental TE10 mode
88
6.6. Gyrotron emission microstrip bandpass filter response as a function of
cavity magnetic field. The filters were placed in the horizontal
polarization. The resonance at 1.67 kG is from the backward wave
(BW ) of the second harmonic o f the second order TE0i mode.................
89
6.7. Dispersion diagram for the large orbit RCS gyrotron using cusp IA.
Marker 1 indicates the dominant interaction of the fundamental mode.
Marker 2 indicates the dominant interaction of the second order TEoi
mode. The e-beam interactions are based on an a (Vpcp/Vparaiiei) of 1.0
as measured experimentally ( see chapter 3). (a) e-beam interaction
using a B-field of 1.47 kG. (b) e-beam interaction using a B-field of
1.67 kG. (c) second harmonic of e-beam using a 1.47 kG B-field. (d)
second harmonic o f e-beam interaction using a 1.67 kG cavity B-field.... 90
6.8. Polarization Power ratio for the large orbit RCS gyrotron (cusp IA ) as
a function of cavity B-field. The shift from one dominant polarization
in the TE10 vertical mode to the TE0i mode in the horizontal
polarization is clearly visible above........................................................... 91
6.9. RCS large orbit gyrotron efficiency as a function of cavity B-field
(cusp IA ). The peak efficiency for this cusp was 5.6 % ..........................
92
6.10. Peak gyrotron microwave power as a function of pulse length for cusp
IA. Pulse shortening is clearly evident...................................................... 93
6.11. Data from MELBA shot 5711. This data was taken with a cavity Bfield of 1.49 kG. (a) voltage monitor response (400 keV/div). (b) RCS
xv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
cavity entrance current (100 A/div). (c) Vertically polarized
microwave output (2 MW/div). (d) Horizontally polarized microwave
output (0.2 M W /div)..................................................................................
94
6.12. (a)Heterodyne mixer signal from shot M 5711 (100 mV/div) (b) FFT of
the mixer signal. The resonance at 160 MHz, which corresponds to a
signal of 2.16 GHz, and the resonance at 8S0 M H z corresponds to a
signal at 2.8S GHz. The mixer signal was taken with the mixer in the
horizontal polarization................................................................................ 94
6.13. Data from MELBA shot S870. This data was taken with a cavity Bfield of 1.88 kG. (a) voltage monitor response (400 keV/div). (b) RCS
cavity entrance current (200 A/div). (c) Vertically polarized
microwave output (0.5 MW/div). (d) Horizontally polarized
microwave output (1 M W /div)................................................................... 95
6.14. (a) Heterodyne mixer signal from shot M5870 (100 mV/div). (b) FFT
of heterodyne mixer signal from shot M5870. The FFT shows two
strong difference frequencies at 60 M Hz and 350 MHz, which
correspond to signals of 2.56 GHz (TE 102) and 2.85 GHz (TEou).
Other modes are clearly visible in this FFT. The heterodyne mixer
was in the horizontal polarization for this MELBA shot........................... 96
6.15. Frequency response of the RCS large orbit gyrotron (cusp IB ) as a
function of magnetic field. These results came from heterodyne mixer
measurements with the RF supplied from either the horizontal or
vertical polarizations. The TEioi, TE 102, TE0n, and TEm cavity modes
were observed. Power levels were not measured with the mixer,
however, below 1.6 kG, the fundamental mode dominated by a
minimum of 1 order of magnitude. Above 1.8 kG, the TE 102 and TEou
modes dominated competing modes..........................................................
97
6.16. Dispersion diagram for the large orbit RCS gyrotron using cusp IB.
The e-beam interactions are based on an a ^ p ^ p /V p ^ i) of 1.0 for the
lower field interactions. These include (a) and (c) which are the ebeam lines for a B-field of 1.47 kG and the second harmonic of this
field interaction. The higher B-field interactions (b) and (d) assume a
beam a of 1.3. The e-beam interaction in (b) is at 1.95 kG and (d) is
the second cyclotron harmonic of (b). The dominant interactions
observed were the forward wave of the fundamental mode(TEio) at
1.47 kG and the forward wave of the oppositely polarized TE0l mode
at 1.95 kG...................................................................................................
xvi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
6.17. Peak power measured in vertical and horizontal polarizations for the
large orbit gyrotron (cusp IB; reflecting strips were used in both
dimensions). The peak power measured in the fundamental mode was
13.8 M W .................................................................................................. 99
6.18. Polarization power ratio for the large orbit RCS gyrotron (cusp IB ) as
a function of cavity B-field. The shift from one dominant polarization
in the vertical mode (TE|0i) to the horizontal polarization is clearly
visible above. The peak ratio achieved was 300. As the B-field was
raised, the ratio dropped to 0.03 (1/30)......................................................
101
6.19. Transported current to the entrance of the RCS cavity using cusp IB in
axis encircling e-beam measurements........................................................
101
6.20. Power efficiency as a function of cavity B-field (cusp IB). The large
orbit gyrotron’s peak efficiency was 6.2 %. The efficiency was
highest at the points where the two dominant resonances occurred
102
6.21. Microwave power as a function of pulse length for the large orbit
gyrotron (cusp IB). As in previous cases, pulse shortening was evident
in cusp IB ..................................................................................................
103
6.22. Transported current measurements for cusp II. The aperture current
shows the current prior to going through the cusp. The average
aperture current was approximately 500 A. The entrance current
which was measured with a Rogowski coil averaged around 220 A for
cusp n. The exit plate current was measured with a graphite paddle at
the exit of the RCS cavity. The average exit current was
approximately 180 A................................................................................
105
6.23. Power out linearly polarized S band waveguide for the RCS large orbit
gyrotron (cusp II). The peak power measured was 9.1 M W in the
vertical polarization and 3.0M W in the horizontal polarization
106
6.24. Frequency response of the large orbit gyrotron (cusp II) as a function
of cavity B-field. As is clearly evident, mode competition was much
worse at higher magnetic fields...............................................................
107
6.25. Polarization power ratio as a function of cavity magnetic field for the
large orbit RCS gyrotron (cusp I I ) ...........................................................
108
6.26. Efficiency for the large orbit gyrotron (cusp I I ) ......................................
108
6.27. Power out of the RCS gyrotron when the horizontal reflecting strips
have been removed...................................................................................
xvii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
109
6.28. Polarization ratio for the large orbit gyrotron (cusp II) with the
horizontal reflecting strips removed.......................................................
110
6.29. Power out linearly polarized waveguides for the large orbit gyrotron
(cusp II) when the diode magnetic field was raised from 1.1 kG to 1.2
kG...............................................................................................
Ill
6.30. Polarization ratio for the large orbit gyrotron (cusp II) with the diode
magnetic field raised from 1.1 kG to 1.2 k G ...........................................
112
6.31. Efficiency of the RCS large orbit gyrotron (cusp II) when the diode
field was raised by 100 Gauss to 1.2 kG.................................................
112
6.32. Power measured in the large orbit gyrotrons when tapered cavities
were used to replace the uniform cavity, (a) Cavity B power
measurements where the vertical dimension is tapered, (b) Cavity C
power measurements; here the horizontal dimension was tapered
114
6.33. Frequency measurements for the tapered large orbit gyrotrons. (a)
Cavity B results; note the frequency shift for the TE0n mode, (b)
Cavity C results; here, the fundamental TEioi mode was supressed
1 IS
6.34. Polarization ratios for the tapered RCS gyrotron experiments...............
116
6.35. Power efficiencies for the tapered cavity experiments...........................
117
6.36. Microwave power as a function of pulse length for the uniform cavity,
large orbit gyrotron (cusp II). While the voltage pulse of MELBA was
on the order of 700 ns, large microwave power signals did not last
more than 200 ns. Higher power microwave pulses were shorter than
ones with low power................................................................................
118
6.37. Microwave power as a function of pulse length for the tapered cavities
(B & C, cusp II). Microwave pulse shortening is apparent....................
119
6.38. Optical emission spectra of aluminum for MELBA shot 6199. The
two aluminum lines are due to the explosive emission cathode, made
of aluminum.............................................................................................
120
6.39. Optical emission spectrum of Hydrogen (H-alpha) for MELBA shot
6236. The H-alpha peak appears stronger with higher microwave
production. The two carbon lines are due to the e-beam hittting the
graphite anode and producing a plasma from scraping...........................
xviii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
6.40. Signal response from MELBA shot 6512 demonstrating the voltage
pulse (a), the vertically polarized microwave signal (b), and a PM tube
response to H-alpha optical emission (c). The vertically polarized
signal here had a peak power of 2.5 M W ................................................
122
6.41. Signal response from MELBA shot 6523 demonstrating the voltage
pulse (a), the vertically polarized microwave signal (b), and a PM tube
response to H-alpha optical emission (c). The vertically polarized
signal here had a peak power of 2.8 M W ................................................
122
A. 1. X -Y plane with gyro-orbit of a single electron about the magnetic field. 129
B. 1. Waveguide geometry.............................................................................
132
E. 1.
Anode aperture for small orbit gyrotron measurements........................
144
E.2.
Slotted anode aperture for large orbit gyrotron measurements..............
145
E.3. Cathode stalk with aluminum cathode tip. Both the cathode stalk and
the tip were coated with Glyptal insulating enamel to prevent emission
except from a bare aluminum ring on the lip with a radius of 2.25 +
0.25 cm............................................................................................ 1 .....
145
E.4. Anode aperture for e-beam a (vperp/Vy) measurements. Eight pinholes
were used to radiation darken a beam pattern on a glass plate...............
146
F. 1. Four filter design using Libra 4.0. The design uses 3 Wilkinson power
dividers to split an input signal four ways. A combination of
microstrip coupled lines create the 500 M Hz filters. The first output at
the top right measures signals from 2.0 to 2.5 GHz. The second signal
measures response from 2.5 to 3.0 GHz. The third signal on the right
measures responses in the frequency range of 3.0 to 3.5 GHz, and the
bottom right signal measures responses from 3.5 to 4.0 G H z................
147
F.2. Theoretical response to the filters designed using Libra 4.0. The
vertical scale is the transmitted power (S21) response in d B .................
148
F.3. Actual response of Filter A (2.0-2.5 GHz) design. The vertical scale, 5
dB/div, is the transmitted power response (S21)....................................
149
F.4. Actual response of Filter B (2.5-3.0 GHz) design. Transmitted power
(S21) is 5 dB/div......................................................................................
150
F.5. Actual response of Filter C (3.0-3.5 GHz) design. The vertical scale is
5 dB/div....................................................................................................
151
xix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F.6. Actual response of Filter D (3.5-4.0 GHz) design. The vertical scale is
5 dB/div....................................................................................................
152
G .l. Uniform cavity response between 1.5 and 2.5 GHz. T h eT E io i mode
appeared at 2.15 GHz. Measurement is of the SI 1 parameter at 3
dB/div........................................................................................................
153
G.2. Uniform cavity response between 2.6 and 3.6 GHz. The T E ou mode
appeared at 2.84 GHz and the TE i 11 had a resonance at 3.34 GHz.
The vertical scale is 5 dB/div...................................................................
154
G.3. Uniform cavity response between 3.5 and 4.5 GHz. The TE 2 0 1 mode
appeared at 4.02 GHz. The vertical scale is 3 dB/div............................
155
G.4. The frequency spectrum for the microwave chamber. The scale is 3
dB/div with a reference line at -35 dB (indicated by the arrow to the
left)............................................................................................................
156
G.5. Frequency spectrum for the 30 dB S-Band directional coupler. Vertical
scale is the transmitted power (S21) at 10 dB/div..................................
157
G.6. Frequency spectrum for a 4 GHz low pass filter. Vertical scale is from
the transmitted power at 10 dB/div.........................................................
158
H. 1. Schematic for pulse and delay generators to set the timing for magnet
banks and MELBA triggering..................................................................
159
H.2. Single mixer signal path inside Faraday cage.........................................
161
H.3. Dual mixer signal paths inside Faraday cage..........................................
161
I.1.
1.2.
Cavity B . This cavity was tapered in the vertical direction to attempt
to suppress the horizontal TEoi mode.....................................................
162
Cavity C. This cavity was tapered in the horizontaldirection to
attempt to suppress the fundamental TE io mode....................................
162
K. 1. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a
B-field of 1.7 kG. (a) The energy per particle as a function of distance
from the five beamlets emitted. The beamlets are emitted at 800 keV
with a 5 % energy spread, (b) An X -Y perspective of the e-beam
looking down the waveguide (this shows the horizontal reflecting
strips)........................................................................................................
xx
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
172
K.2. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a
B-field of 1.7 kG. (a) The X -Z perspective of the e-beam, (b) TheY Z perspective of the e-beam, (c) This Y-Z perspective tags a small
fraction of those particles in (b) to give a better picture o f the electron
trajectories.................................................................................................
173
K.3. Phasespace plots for the large orbit gyrotron simulations at 100 ns for
a B-field of 1.7 kG. (a) The energy per particle as a function of
distance from the five beamlets emitted. The beamlets are emitted at
800 keV with a 5 % energy spread, (b) A X -Y perspective of the beam
(looking down the waveguide (this shows the horizontal reflecting
strips)........................................................................................................
174
K.4. Phasespace plots for the large orbit gyrotron simulations at 100 ns for
a B-field of 1.7 kG. (a) The X -Z perspective of the e-beam, (b) The
Y-Z perspective of the e-beam, (c) The Y-Z perspective with a small
fraction of the particles in (b). From (b) and (c) scraping is observed
and could lead to the possible formation of plasma................................
175
K.5. Range plots for the large orbit gyrotron at a B-field of 1.7 kG at 100 ns
in the simulation, (a) shows the e-beam current as a function of
distance, (b) shows the e-beam power as a function of distance. The
horizontal strips are at 21 cm.................................................................. 176
K.6. Large orbit gyrotron simulation results at a B-field of 1.7 kGauss. (a)
The current exiting the RCS cavity as a function of time [field integral
J*dA], (prior to the beam dump), (b) Field power (S «dA) at the RCS
cavity exit as a function of time. The decrease in power could show
pulse shortening........................................................................................
177
K.7. Large orbit gyrotron simulation results at a B-field of 1.7 kG. (a) The
integral E-dL of a horizontal line near the exit to the RCS cavity [from
coordinates (-3.6,0,17.8) to (3.6,0,17.8) in cm], (b) the FFT of (a)
showing resonances at 2.16 GHz, 2.88 GHz (small), 3.48 GHz (small),
and 4.27 GHz. These correspond to the TEio, TE0i, TEn, and TE 20
modes respectively...................................................................................
178
K.8. Large orbit gyrotron simulation results at a B-field of 1.7 kG. (a) The
integral E*dL of a vertical line near the exit to the RCS cavity [from
coordinates (0, -2.7,17.8) to (0,2.7,17.8) in cm], (b) the FFT of (a)
showing a resonance at 2.16 GHz. This corresponds to the TEio mode.
179
K.9. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a
B-field of 2.4 kG. (a) The energy per particle as a function of distance
xxi
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
from the five beamlets emitted. The beamlets are emitted at 800 keV
with a 5 % energy spread, (b) A X -Y perspective of the beam
180
K. 10. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a
B-field of 2.4 kG. (a) The X-Z perspective of the e-beam, (b) TheY Z perspective of the e-beam, (c) This Y-Z perspective with a small
fraction of electrons from(b)....................................................................
181
K. 11 Phasespace plots for the large orbit gyrotron simulations at 100 ns for
a B-field of 2.4 kG. (a) The energy per particle as a function of
distance from the five beamlets emitted. The beamlets are emitted at
800 keV with a 5 % energy spread, (b) A X -Y perspective of the ebeam.........................................................................................................
182
K. 12. Phasespace plots for the large orbit gyrotron simulations at 100 ns for
a B-field of 2.4 kG. (a) The X-Z perspective of the e-beam, (b) The
Y -Z perspective of the e-beam, (c) The Y-Z perspective with a small
fraction of the particles in (b)...................................................................
183
K. 13. Range plots for the large orbit gyrotron at a B-field of 2.4 kG at 100
ns in the simulation, (a) The e-beam current as a function of distance.
(b) The e-beam power as a function of distance......................................
184
K. 14. Large orbit gyrotron simulation results at a B-field of 2.4 kG. (a) The
current exiting the RCS cavity as a function of time [field integral
J*dA], (prior to the e-beam dump), (b) Field power (S *dA) at the RCS
cavity exit as a function of time. The initial power in (b) appears to be
generated due to some of the e-beam.......................................................
185
K. 15. Large orbit gyrotron simulation results at a B-field of 2.4 kG. (a) The
integral E*dL of a horizontal line near the exit to the RCS cavity [from
coordinates (-3.6,0, 17.8) to (3.6,0, 17.8) in cm], (b) the FFT of (a)
showing a resonance at 2.88 GHz. This corresponds to the TE0i
mode......................................................................................................... 186
K. 16. Large orbit gyrotron simulation results at a B-field of 2.4 kG. (a) The
integral E*dL of a vertical line near the exit to the RCS cavity [from
coordinates (0, -2.7,17.8) to (0,2.7,17.8) in cm], (b) the FFT o f (a)
showing resonances at 2.25 GHz and 2.88 GHz. These correspond to
the TEio and TEoi modes respectively. From (a) it appears that the
fundamental TE^ mode grows initially, but mode competition from
the orthogonal TEoi mode allows the TEoi mode to grow and beat out
the fundamental mode.............................................................................. 187
xxii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIS T OF TABLES
Table
1.1.
Summary of Microwave Devices................................................................ 3
2.1.
Summary of competing mode parameters [LAU97]...............................
22
3.1
Summary of magnetic cusp characteristics..............................................
38
3.2.
Calculated resonant frequencies for modes in the S-band for
rectangular cavities...................................................................................
44
3.3.
Cavity modes and experimentally measured Q values...........................
47
3.4.
Beam alpha measurements using different diode and cavity B-fields
for the large orbit gyrotron (cusp II) ..........................................................
57
xxiii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIS T OF APPENDICES
Appendix
A.
N E G A TIVE MASS IN S T A B IL IT Y D E R IV A T IO N ........................
129
B.
RECTANG ULAR VA C U U M W A V EG U ID E DISPERSION
R E LA TIO N AND E LEC TR O M A G N ETIC FIELD S
D E R IV A T IO N ........................................................................................
132
M A G IC 2D (1994.5 VERSIO N) IN P U T F IL E FO R LARGE
O R B IT G YRO TRON S IM U LA TIO N S ..............................................
136
SAMPLE EGUN IN P U T F IL E FOR SM A LL O R B IT
G YRO TRO N S IM U LA TIO N S ............................................................
140
ANODE APERTURE SCHEM ATICS AND CATHO DE T IP
D E S IG N .................................................................................................
144
C.
D.
E.
F.
G.
H.
I.
J.
K.
LIB R A (4.0) 500 M H Z FREQ UENCY F IL T E R DESIGNS
C A V IT Y CO LD TESTS, W H IT E TA N K AND COUPLER
C A LIB R A TIO N .....................................................................................
T IM IN G SEQUENCE AND FARADAY CAGE W IR IN G
147
153
159
TAPERED C A V ITIE S USED IN LARG E O R B IT
E X P E R IM E N TS ....................................................................................
162
SAMPLE M A G IC 3D M (SEPTEM BER 1997 VERSIO N) IN PU T
F IL E FO R LARGE O R B IT G YRO TR O N S IM U LA TIO N S
163
SAMPLE M A G IC 3D M RESULTS FO R LARG E O RBIT
G YRO TR O N S IM U LA TIO N S............................................................
172
xxiv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 1
INTRODUCTION
1.1 Preamble
This thesis describes a comprehensive experimental investigation of a rectangular
cross section (RCS) gyrotron oscillator. Experiments were conducted using this
microwave tube to generate high power radiation utilizing two different types of annular
electron beams, small orbit and large orbit. The experiments were conducted at the
University of Michigan’s Intense Energy Beam Interaction Laboratory using the
Michigan Electron Long Beam Accelerator (MELBA) which can generate intense,
annular, relativistic electron beams (e-beams) with the following parameters: peak
voltage = -1 M V , diode current = 1-10 kA, and pulse length = 1 (is.
In the first series of measurements on the small orbit RCS gyrotron oscillator, the
annular e-beam is compressed through adiabatic compression prior to interaction in the
microwave tube. In the second series of measurements, the annular e-beam extracted
from the diode is passed through a magnetic cusp, producing a large orbit, axis encircling
e-beam prior to the microwave cavity.
Gyrotron devices are fast wave devices that do not have slow wave structures,
making fabrication much easier than for slow wave devices. While most gyrotron
configurations employ cylindrical cavities with azimuthal symmetry, the rectangular
cross section gyrotron oscillator offers several advantages over cylindrical gyrotrons and
other coherent radiation sources. Microwave radiation from the RCS gyrotron is linearly
polarized, which is desirable for several potential applications, since this eliminates the
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
need for a mode converter from the cylindrical TEU mode to the rectangular TE10 mode
[RAD93, LAU84, LAU83]. While mode converters can perform efficiently, insertion
losses and spurious mode conversion to unwanted modes can occur [RAD93],
The experiments performed on M ELBA were completed in an effort to study
polarization control o f linearly polarized microwave radiation, pulse shortening
phenomena, and mode competition. This thesis examines these issues for the RCS
gyrotron.
1.2 Gyrotrons and other coherent radiation sources
Many fields have demonstrated needs for high power microwave devices,
including accelerator physics, magnetic confinement fusion, astronomy, and military
applications [BEN92, LEV87], These fields utilize high power microwave sources as
accelerator drivers, for electron cyclotron heating of plasmas, for high resolution radar,
and for microwave processing of materials [GAP94, BEN92, GRA87, GIL80]. Many
different classes of devices for high-power microwaves, millimeter waves, and
submillimeter waves have been under investigation in the past decades. The different
classes of devices are summarized in Table 1.1 [LEV87],
The first basic work connected to cyclotron resonant masers (CRMs) and the
generation of coherent electromagnetic radiation was completed in the late 1950’s
[TW I58, SCH59, GAP59]. The electron cyclotron maser (CRM), which includes
gyrotrons, CARMs (cyclotron auto-resonance masers), and gyrotron backward wave
oscillators, as well as several other devices, produces electromagnetic radiation by
relativistic electrons gyrating about an external B-field. Figure 1.1 shows the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3
Table 1.1 Summary of Microwave Devices.
Slow Wave Devices
Fast Wave Devices
Plasma Devices
Others
magnetrons
Cyclotron resonant
masers .including:
Virtual Cathode
Oscillators
Free Electron Lasers
Cerenkov Masers
gyrotrons,
peniotrons, CARMs,
and gyro-BWOs
Orbitrons
klystrons
Backward Wave
Oscillators (BWOs)
Electric Field for
TEOI Mode
typical
electron
cyclotron
orbits
pasatron
(b)
Metallic
waveguide
(c)
'a , ndged
^ ir waveguide
Metallic
waveguide
Hollow rotating e-beam
Hollow rotating
e-beam
Electron guiding centers placed at
peak Electric field position
Figure 1.1. Cyclotron resonant masers [LAU95]. (a) cylindrical small orbit gyrotron. (b)
cylindrical large orbit gyrotron. (c) peniotron.
cross sections o f a few CRM devices [LAU95], The frequency in the radiation
corresponds to the fundamental or harmonic relativistic electron cyclotron frequency:
ft
J e \B
=
ym
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(l.i)
4
where e is the electron charge, m is its mass, and y - (1 - v 2 / c 2 )"1/2 is the relativistic
factor. Experimental work by Hirshfield and Wachtel successfully demonstrated the
CRM mechanism using a 5 kV electron beam [HIR64]. Several articles review the
theory and history of the CRM [GRA87, LAU82, CHU78, UHM78, UHM77, SPR77,
HIR77, BAI87].
While Hirshfield and Wachtel demonstrated the first cyclotron maser interaction
[HIR64], Gapanov invented the first high power gyrotron in 1967 when he used a
magnetron injection gun (M IG ) with a CRM [GAP67]. In a gyrotron the electron beam
interacts with the TE (transverse electric) mode of a microwave cavity near the cutoff
frequency to produce electromagnetic radiation. A summary of the different CRM
interactions can be observed in Figure 1.2 [SPE91, BAI87], Theoretical efficiencies have
been predicted to be as high as 90 % for some CRM devices [LEV87], While gyrotrons
are normally operated in the fundamental mode, higher frequency devices can be
achieved at higher harmonics, i.e. operating at a frequency c^nQ,. where the integer n >1.
Some power limitations on the gyrotron can be attributed to the e-beam source.
Thermionic cathodes such as those used in a M IG are typically limited in voltage (-500
kV) and current density (~50 A/cm2) [CH091, PAS87]. This source may be optimal for
continuous wave (cw) gyrotron devices however. Using a high current, high voltage,
explosive emission cathode (such as the Michigan Electron Long Beam Accelerator
[M ELBA]) offers the possibility of power levels reaching GW and beyond. A
disadvantage of explosive emission cathodes, however, is the large velocity spread of the
e-beam. In addition, the e-beam’s voltage variation may detune the resonance condition
of the gyrotron [SPE91]. Gold and Black built a gyrotron operating at 35 GHz at 100 to
250 M W with efficiencies as high as 10% [GOL87, BLA90], RF radiation o f 500-1000
M W was reported at frequencies between 700-1200 M Hz for a large orbit cylindrical
gyrotron pE S 89]. Power as high as 120 M W was reported for a fundamental mode RCS
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
gyrotron [RAD93], Lawson, et al. [LAW85] reported 500 M W produced in the K„ band
for a large orbit gyrotron with a 20-slot magnetron-like vane resonator.
Another CRM device is the CARM. In the case of a CARM, the beam-cavity
interaction takes place at a phase velocity close to the speed of light (Fig. 1.2). Adding
the Doppler frequency shift to the phase velocity, the resonance condition is given by
[LEV87]:
(0 = k]lvl + n Q e
(1.2)
where co is the frequency, k// = k* is the axial wave number, Vy is the axial velocity, and n
is the harmonic number.
Despite a great deal of attention, the CARM has had limited success [BEK89,
CH 091], The CARM’s sensitivity to e-beam velocity spread, and mode competition
from the lower frequency gyrotron and gyro-BWO have limited its ability to produce
high-power, high-efficiency microwaves.
The gyrotron backward wave oscillator (gyro-BWO) is a CRM device which is
relatively insensitive to the beam velocity spread [SPE91]. The device operates to the
left hand side of the dispersion diagram with the axial wave number less than zero (kz <
0). For this reason, it has been inferred that the e-beam-cavity interaction can remain in
resonance for longer periods [SPE91]. Powers as high as 55 M W have been reported
[W AL95],
A gyroklystron uses an e-beam that passes through at least two cavities. The
electrons are modulated in the first cavity setting up azimuthal drifts. The drifts lead to
rotating bunches that can give energy to the following cavity (ies). Peak powers above
30 M W and efficiencies greater than 33 % have been reported for fundamental and
harmonic gyroklystrons at the University of Maryland [MAT94, LAW92],
One other class of cyclotron resonant maser under investigation is the peniotron.
While the device looks similar to a large orbit gyrotron, it operates under a different
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
6
mechanism where radial motion is important and relativistic effects are unimportant. In a
peniotron, migration of guiding center orbits occurs while density bunching of electrons
does not. A more complete description can be found in BAI87. Northrop Grumman
scientists performed a series of proof of principal peniotron experiments producing 5 W
of rf power in an oscillator at 91 GHz [GAL96]. A high power peniotron oscillator at
2.75 GHz was reported to produce 30 M W with 60 % efficiency [MUS92].
CARM
intersection
Gyro-BWO
intersection
gyrotron grazing
intersection
gyrotron low
frequency
intersection
—
Figure 1.2. Cyclotron resonant maser interactions. The solid curve represents the
microwave cavity dispersion curve, and the dashed lines represent the ebeam dispersion relations [SPE91, BAI87],
1.3 Previous work on rectangular cross section devices
While cyclotron resonance maser research has been carried out for decades, and
while gyrotrons employing both small orbit and large orbit e-beams have been the subject
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7
of much research, little gyrotron work has focused on the use of rectangular microwave
cavities.
Lau and Barnett [LAU83] calculated the coupling constant e between a relativistic
electron beam and the TEi0 rectangular waveguide mode. Utilizing an axis encircling
beam he demonstrated that the coupling constant could exceed the corresponding value
for the operation of the T E U circularly polarized mode.
A set of experiments were conducted using a tapered-wall gyrotron travelingwave amplifier (gyro-TWA) [BAR81, BAR82], While one experiment [BAR81]
designed and achieved a bandwidth of 13% centered at 34 GHz, the other experiment
[BAR82] operated with a SO cm linearly tapered, fundamental TEio mode rectangular
microwave circuit, and it was designed to operate at 33.5 GHz with 38 % bandwidth.
This wide bandwidth was not observed experimentally prior to the experiment’s
conclusion.
A motivation for use of rectangular microwave cavity structures is the
development of an active circulator-gyrotron traveling-wave amplifier [LAU84], This
design of a reflection amplifier uses an axis encircling beam propagating inside a
rectangular waveguide. A horizontally polarized TE0i signal is launched downstream of
the electrons. By down-tapering the waveguide, the TEoi signal is reflected, but it may
also induce the vertically polarized TE 10 mode through excitation by the e-beam. By
maintaining a grazing condition for the e-beam - TEt0 structure mode interaction, the
vertically polarized TE )0 output signal is amplified and dominates the output window.
Radack, et al. [RAD93] has published the only previous experimental work on a
high-power, large-orbit gyrotron using a rectangular interaction region. This paper
[RAD93] reports on experimental studies to produce high power microwave radiation in
the rectangular TEI0 mode at 650 MHz. Powers as high as 40 M W were reported with an
efficiency of about 16 %. Furthermore, very short duration pulses of 100 M W were also
reported. Unlike the paper, this dissertation concentrates on the lowest two orthogonal
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
(& rectangular) modes ( TEio and TEoi )■ In addition to examining large orbit
experiments on the RCS gyrotron in this dissertation, experimental results on a small
orbit rectangular cross section gyrotron are presented (see Chapter S).
1.4 Present experimental work
The experiments presented in this dissertation were motivated by research on
intense annular electron beams to generate high power microwaves with polarization
control by magnetic field. Polarization control by magnetic field refers to control of the
linearly polarized microwave output (TEi0 versus TEoi) by controlling the B-fields on
both the diode and microwave cavity. Another goal of the research, as discussed
previously, was to initiate work on the development of the Active-Circulator-GyrotronTraveling-Wave-Amplifier (ACGTW A) [LAU84], The experiments in this thesis are the
first steps in this development. While the experiments conducted for this research
centered on frequencies in the S-band, the experiments could easily be scaled to the
millimeter regime by altering the magnetic fields and cavity dimensions used.
In completing the goals above, several objectives guided the experimental work.
The microwave emission in the S-band (2 -4 GHz) that was generated in the RCS cavity
was measured in both the horizontal and vertical polarizations. The ratio of the powers
was then observed as a function of cavity magnetic field and compared with M AGIC
(electromagnetic particle in cell code) simulations [GOP94]. The microwave cavity and
MELBA diode magnetic fields were varied in an attempt to control the polarization of the
generated microwaves. While completing microwave measurements, e-beam alpha
measurements were made and compared with simulations. Alpha is the ratio of the
perpendicular velocity to the parallel velocity (a = Vj_ / v||). Radiation darkening of glass
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
9
plates was used successfully as a beam diagnostic in building and improving the
magnetic cusp used in large orbit gyrotron experiments.
Including the introduction, this dissertation includes six more chapters. Chapter 2
includes the theoretical considerations of the rectangular cross section gyrotron as well as
discussions on the active circulator theory.
Experimental configurations for both the small orbit and the large orbit gyrotron
experiments are discussed in Chapter 3. Furthermore, microwave and beam diagnostics
are described in Chapter 3. Details o f the magnetic field generation are presented.
Chapter 4 reviews the computer simulations used for comparison to experimental
measurement, including both EGUN (Electron Trajectory Program) [HER79] and
M AGIC simulations.
Chapter S provides the experimental results of work on the small orbit gyrotron
oscillator, particularly the comparison of the polarization ratios with simulation results.
The experimental results from the large orbit gyrotron oscillator are covered in
Chapter 6. This chapter includes measurements of microwave power as well as
consideration of conditions where mode competition and pulse shortening occur.
The final chapter, Chapter 7, presents the conclusions and summary of
experimental work on the RCS gyrotron.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 2
RECTANGULAR CROSS SECTION GYROTRON THEORY
2.1 Introduction
Significant theoretical and experimental work has been completed in the past 40
years on the cyclotron resonance interaction. Several approaches have been taken to
describe the cyclotron resonance maser instability including classical mechanics [TWI58,
GAPS9], quantum mechanics [SCHS9], fluid theories [LAU82], and kinetic theories
[CHU80, SPR77],
The gyrotron mechanism is based upon the gyration of relativistic electrons in a
static magnetic field. For gyrotron radiation four required features are needed. These
include an axial magnetic field, rotational energy in the electron beam (ve), relativistic
effects (Eebeam > 5 keV), and a perturbation rf Ej field with an azimuthal component (E)e)
acting on the azimuthal (6) motion of the rotating electrons [LAU95]. The relativistic
cyclotron frequency of the electron is defined by
where e is the electronic charge, m is the electron rest mass, and B is the external
magnetic field. The relativistic factor, y, is defined by
2.2
10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
11
where P= v/c (v is the particle velocity, and c is the speed of light). A synchronous
condition on the frequency 0) of the E)e wave that moves with the rotating electrons
requires
0)=>sne > 0)cutoff
2.3
where s is the integer harmonic number; 0)cuto(r is the cutoff frequency, below which,
fields are exponentially attenuated [GRI89].
Two equivalent mechanisms demonstrating the electron cyclotron maser
instability include the phase bunching mechanism and the negative mass instability
[LAU82], In the phase bunching mechanism consider electrons 1 and 2 in Figure 2.1
rotating about a magnetic field B = Bz pointing out of the plane of the paper. Assume
there is a perturbation rf E field
= y E le J“ where 0 ) is slightly greater than Qe.
Electron 1 is decelerated. This decreases y, and increases
Thus |Qe>1 - co| tends
toward zero. Electron 1 becomes more synchronous, giving more energy to the wave.
Electron 2, however, is accelerated by the perturbation field. This increases y2, decreases
Q.,2, and makes |Qe2 - co| > 0. Electron 2 falls back in phase with time while electron 1
travels forward in phase, and hence, phase bunching. Thus, the beam is modulated in the
A
©direction on the electron orbit.
Figure 2.1 Phase diagram of electron orbits demonstrating the “phase bunching”
mechanism [LAU95, BAI87].
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
For the negative mass instability consider two electrons, A, B, that are in the
vicinity of a localized bunch as shown in Figure 2.2. Electron A is accelerated since it is
repelled by the bunch. This causes yAto increase and QC|Ato decrease, and this in turn
causes particle A to drift closer to the bunch. Similarly, electron B, which is repelled by
the bunch, decelerates causing
to increase, and electron B drifts toward the bunch
azimuthally. The space charge effect of the bunch acts on electrons A and B as if they
had a negative mass, and thus enhances charge bunching.
(localized bunch)
Figure 2.2. Negative mass instability effect showing phase bunching of electrons
[LAU95, BAI87],
A derivation showing the negative mass instability appears in Appendix A. This
derivation results in Equation A. 16:
B2 e
i] = ~
E xa
(2.4)
Yo m0
where i) is the azimuthal displacement of an electron along its cyclotron orbit when it is
subjected to an azimuthal electric field E)e. The subscript “o” represents the zeroth order
quantities, i.e., when the perturbation field E le is absent. Equation 2.4 shows that a force
A
A
applied in the +0direction results in acceleration in the - 0 direction; this looks like the
force acts on a negative mass (as described above) [LAU9S]. Both mechanisms
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13
discussed above modulate the relativistic e-beam, causing the bunched AC current to
grow.
The RCS gyrotron is a fast wave device. For a more complete picture that utilizes
a non-linear analysis of the cyclotron resonance maser, Maxwell’s equations, along with
the non-linearized, relativistic Lorentz force equation, energy equation, and energymomentum relationship can be used to develop a relationship showing the electron
bunching mechanism [BAI87], This derivation includes both slow and fast wave CRMs.
2.2 Gyrotron Dispersion Relations and Coupling Constants
2.2.1 Gyrotron dispersion relation, linear theory
Derivations for a gyrotron dispersion relation have been performed numerous
times and presented over the past decades [SPR77, LAU82, BAI87], Dispersion relations
have been calculated for a large orbit gyrotron [SH087, LAU82], and rectangular
geometry has also been considered in the determination of the dispersion relationship
[LAU83, FER84, LAU95], The following derivation of the gyrotron oscillator dispersion
relation follows from presentations of Lau [LAU83, LAU95], and Sprangle [SPR77],
Subsequent derivations for the coupling constants follow that of Lau [LAU9S] as well.
To simplify initial calculations we will assume a parallel plate geometry as shown
in Figure 2.3. The plates are perfect conductors, separated by a distance b. The electron
beam is a distance a away from the bottom plate, has thickness x = 2rL (rL is the Larmor
radius), and has volume density (n0), surface charge number density (o0), and sheet
current density K ty in the y direction. The externally applied magnetic field is in the
negative z direction. We are interested in the TE modes, and in the case where no —> 00,
b » r L (T —> 0 ), and n0x -<S0 ~ finite. Consider the region below the e-beam (x < a)
region I, and above the e-beam region n. We assume the perturbation E field, E t is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
approximated by E ^ " 1, and the tangential E field, EIy, that the thin electron sheet
experiences, is constant.
iE „
n
t,
Figure 2.3. Simplified geometry for gyrotron dispersion relation determination.
First consider the condition that voz=k2=0. Utilizing Maxwell’s equations (B.6a - B.6d),
applying boundary conditions, and assuming a=b/2 results in the dispersion relation
[SPR77, LAU82]
B2
( Q ) - 0 ) 0) 2(Q)2 - Q ) ) ) = —^ - ( 0 2
b(o] = - Q ) ' E
o
(2.5)
where (0 q= |e|Bo/(moY0), coc= nrcc/b , 0)b= e2n0t/( m0eob), e0 is the permittivity of free
space, and e is called the coupling constant which is to be derived below. The cutoff
frequency for the TEn0 mode is toc (for the fundamental mode, n=l). Assuming that the
streaming velocity is non-zero ( v0t t- 0 ), the gyrotron dispersion relation may be simply
written as
(o>~k2v0z - (t)0)V
- k}c2 - 6) c ) = ~<o$e
(2.6)
The first set of terms in the dispersion relation of Equation 2.6 represents the
beam mode [Fig. 2.4], The e-beam line shown in Figure 2.4 may be shifted by raising or
lowering the magnetic field, which in turn shifts the e-beam mode by changing coo- Thus,
the magnetic field for gyrotrons acts as a tuning parameter. Gyrotrons may also be tuned
by adjusting the beam voltage. The second set of terms on the left hand side of Equation
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15
(structure mode)
<o2= k £ 2+
+
(0
2
c
(beam mode)
co=k^0z+ <o0
0
k
z
Figure 2.4. Beam and stmcture mode of dispersion relations.
2.6 represents the structure mode. As in Figure 1.2, Figure 2.4 demonstrates the
dispersion relation of Equation 2.6. To convert Equation 2.6 to a realistic geometry for
the rectangular cross section gyrotron, the coupling constant, e, must be determined for
both small and large orbit gyrotron configurations. The next section is used to develop e
for the fundamental mode (TEio) of these 2 types of gyrotrons.
2.2.2 Fundamental mode gyrotron coupling constants
To determine the coupling constant, £, for the fundamental mode (TE10) of the
small orbit gyrotron, a few assumptions are required. First consider the geometry shown
in Figure 2.5a. We will assume the guiding centers are distributed at a constant radius, r0,
from the center axis of the waveguide, and we assume that the Larmor radius is small.
Furthermore, we will consider interactions near cutoff, and hence kt ~ 0 . By taking the
curl of one of Maxwell’s equations (V x H z = J\ + j'qkqEi ), multiplying the curl by
//,*„, integrating over x and y, and using some vector identities, we can show
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
16
where we have assumed H x = H w (the vacuum mode). If kz= 0, / / , is only in the z
direction. Furthermore, we have assumed no current intercepts any surfaces. If we
assume the magnetic field is of the form
JDC
H u = - A sin —
a
(2.8)
where A is an arbitrary constant, the form for E )y is
„
1 f .K
10i\
£ ly = ------- A —cos — ej0*
jo x 0 V a
a J
(2.9)
The current density, Jiy, is given by
A , = « . ( ', )
(210)
where the current < iy > is given by [see (2.4); also LAU82]
, .
{ h ) = -A
e2p l E ly {-(0)
.
T2
(2-11)
(b)
(a)
b/2
-b/2
-b/2
Figure 2.S. Rectangular cross section gyrotron geometry, (a) small orbit configuration,
(b) large orbit configuration.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17
Substituting Equation 2.11 into Equation 2.10 and plugging 2.10 into Equation 2.7 results
in:
(O
J
(O£0e 2p l(D
\A\2n 2
4 y 0w0(ffl-fli0)2
a2
( 2. 12)
\ 2
cos'
The beam current, Ib, is given by
Ib=
JJ dxdyen0v
(2.13)
where n0 = D5(r-R). The constant D results in
h
D =
(2.14)
I n Re v,
Both the small orbit and large orbit gyrotron electron beams are cylindrical, making the
problem easier to solve using cylindrical coordinates. By switching from Cartesian to
cylindrical coordinates and evaluating the right hand side of Equation 2.12, leads to the
following result
{CO2 -
C02
e )(0) -
G)0 ) 2 =
f 1r n ( p i ] fKa cb 4a 2 j] n 2 JT + —1 / .
U7k A ) UoJ
( 2 nR
j
(2.15)
a
= COc£
where Jo is the zeroth order Bessel function. From Equation 2.15, the coupling constant,
e, for the fundamental mode (TEi0) of the small orbit gyrotron is shown to be
£
vpl
(2.16)
—
v /o
r
where v is the dimensionless Budker parameter {v=(Ib/17 k A )(l/p t|)}.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
18
A similar approach can be used to determine the coupling constant for the
fundamental mode o f the large orbit gyrotron. Under the geometry of Figure 2.5b, the
vacuum mode electric field may be expressed as
f TEC
= yE 0y H
17/
(2.17)
Remembering that at resonance the stored magnetic energy equals the average stored
electrical energy,
^ ■ j j O c d ^ H „ \ 2 = ^ j j d x ^ E „ \ :‘
(2.18)
then Equation 2.7 may be rewritten as
( 0 )2
2
U
2a
0 ) 2e ]
b —
2
c
)
* 0 ,
j“ o
2
(2.19)
In the large orbit case, the electron sees mostly an azimuthal field. The azimuthal
component of the electric field can be shown to be [LAU83]
e
w =
(2 .20)
where Jt is the Bessel function of order 1, and the prime notation indicates a derivative
with respect to the argument. The current in the azimuthal direction is found to be [Eq.
(2-4)]
(2.21)
where T| is the azimuthal displacement, and o0 is the surface charge density. Substituting
Equations 2.20 and 2.21 into Equation 2.19, converting to cylindrical coordinates, and
solving results in the large orbit gyrotron dispersion relation for the fundamental mode
[ ( d ) - Q ) q) 2 (a)2 - (o\ ) = -(Q*£] where the coupling constant is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
19
£
—
(V I
8 fa'
j
W o ; J t\b
(2 .22)
:
,
where v = (V 17 kA)(l/p||) is the Budker parameter.
2.2.3 Large orbit gyrotron linear growth rates
Consider the large orbit gyrotron with the following parameters: Ebe«n= 800 keV,
a= 7.2 cm, b= 5.4 cm, Ibe«m= 200 A, and a = vl / v // = 1. From these parameters the
relativistic factor, y, is determined to be 2.57 [where y= 1 + E/(e‘ rest mass) ]. From
Equation 2.2, p = 0.92. Since a = 1 and /3 2 = f$l + /?*, /3/; = p L = 0 .6 5 . The Budker
parameter (v) used in Equation 2.16 is determined to be 0.018.
The gyrotron dispersion relation in Equation 2.6 can be simplified to obtain a
growth rate. Assuming that we are looking at the fundamental mode (s= l) near cutoff
where kt ~ 0 and G)0 = 6)e, Equation 2.5 may be approximated as
fi)
(Vc o - c oe)) = — 2- e
(2.23)
I f the frequency has both real and imaginary components (to =
,
cdr +
( e V 'T K . V r
5 ±,T
icOj),
(2.24)
The solution will grow exponentially in time if the imaginary component has a positive
value. The large orbit gyrotron’s fundamental mode results in
1/3
CO =
1
V3 (O
2
'
(2.25)
.
v a yj
Radiation darkening on glass plates, which is described in Chapter 3, demonstrates that
the Larmor radius is approximately 1.5 cm. The frequency 0 )j can be estimated from
MELBA e-beam parameters provided and R = 1.5 cm as
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
coi =
0.084oc = 1 .096 jc109 s ' 1
(2.26)
where the cutoff frequency is defined in Equation B.20 of Appendix B. The e-folding
time for this growth rate is defined as the inverse of G )j. Hence, the e-folding time for the
fundamental mode of the large orbit RCS gyrotron is 0.913 ns.
2.2.4 Mode competition in the large orbit gyrotron
A rectangular cross section gyrotron exhibits the possibility of mode competition
just as a cylindrical gyrotron. In subsequent chapters, frequency measurements will
indicate that such mode competition does exist. In order to evaluate these as potential
problems for future active circulator experiments, coupling constants and growth rates
need to be determined and compared with the fundamental mode for the large orbit
gyrotron. This discussion follows the work of Lau [LAU97],
Besides the two orthogonal modes ( TEi0 and TEoi) for the RCS gyrotron,
operation at higher harmonics (i.e. the second cyclotron harmonics TE20, TE02, and TEn)
is possible. The gyrotron dispersion relation of Equation 2.5 may be rewritten to include
the harmonic number such that the dispersion relation reads (valid only when kz = 0)
(t0 - SQ)0) Z(C02 ~ ( 0 2) = —ECO*
(2.27)
where s is the cyclotron harmonic number. Using the same large orbit gyrotron e-beam
parameters as listed in the previous section (i.e. Ebeam= 800 keV, etc.), as well as Equation
B.20 of appendix B, the cutoff frequencies for the higher order modes may be
determined. These data for the TEt0, TE0i, TE n, TE20, and TE02 modes are presented in
Table 2.1. If we assume that so)0= coc the magnetic field at cutoff can be determined from
Equation 2.1. These data are shown in Table 2.1. The Larmor radius for the large orbit
gyrotron is given by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and are listed for the various modes in Table 2.1.
The results of the calculations for 0 )c, B, and R suggest that the TEn mode is of
the most concern since the coupling constant £ for the TEn is larger than those of the
other competing modes, and radiation darkening on glass plates, which is discussed in the
next chapter, shows darkened patterns at radii in this range. Furthermore, the TEU mode
is closest in frequency to the TEio and TEoi modes.
The coupling constant for the fundamental (TE t0) mode is given by Equation
2.22. To obtain the coupling constant for the orthogonal TEoi mode the parameter a must
be changed to b, and the parameter b is replaced by a in Equation 2.22. To calculate the
coupling constant for the TEn mode, the magnetic field can be stated as
(2.29)
The coupling constant, £, can be determined in the same manner as that presented for the
fundamental mode, and the result is
(2.30)
u=0.78
where
1 *
a
p(u) = — f d0{ sin 20) sin(-w sin 0) sin(w cos 0)
2k
b
(2.31)
and u= 7tR/a. Using R from Table 2.1, u results in 0.78. Equation 2.31 can be solved
using MAPLE (or another mathematics program) [ELL92]. For the TEn mode, then,
dp/< ^ |-=a7g ~
0.39. Equation 2.30 can then be determined and compared against the
fundamental mode. A similar derivation for the coupling constant of the TE^o mode
results in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
22
1
c* -I
hr
(2.32)
i—
*<
o
oo
E (re » U =
where
1 *
p 2 = — f dd
In
cos 20 cos 6 sin(2^/? cos B i d )
(2.33)
The coupling constant for the TEo2 mode may be determined by interchanging a and b in
Equations 2.32 and 2.33.
The results of these calculations are summarized in Table 2.1 where the coupling
constants of the various modes are compared (in ratio form) to the fundamental mode.
Since the temporal growth rate, G)j, is proportional to e1/3coC) a comparison of the growth
rates as compared with the fundamental mode is also presented in Table 2.1.
Table 2.1. Summary of competing mode parameters [LAU97],
Mode
(i)c (xlO10 rad/s)
B (kGauss)
R (cm )
E/E(TE io^.i )
oVaicCrE™,*-!)
T E 10<^ i
1.31
1.91
1.49
1
1
TEoi,*-!
1.75
2.55
1.12
0.563
1.103
T E ll4. 2
2.18
1.59
1.79
0.215
0.997
IE 20^-2
2.62
1.91
1.49
0.081
0.865
T E o2j -2
3.50
2.55
1.12
.046
0.953
The results listed in Table 2.1 include several assumptions. While
(5L, y 0,Ol = \, and v are assumed constant, the magnetic field, B, is adjusted in order to
assure (o = sto0= coc. The results from Table 2.1 suggest that mode competition is
possible. The first point to note is that the coupling constant ratio decreases with
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
23
increasing frequency, or with increasing mode or harmonic number. The most important
point to note is that the temporal growth rates for competing modes are nearly the same
as the fundamental mode. The quality factor, Q, however, is very different for the
competing modes. This is discussed in Chapter 3, with results summarized for the RCS
uniform cavity in Table 3.3. (A low pass filter at the receiver in the Faraday cage
removes some of the higher order competing modes.)
2.3 Active Circulator Applications
The RCS gyrotron oscillator experiments are the initial experiments for possible
future work on the Active Circulator-Gyrotron Traveling Wave Amplifier. A proof-ofprinciple experiment in 1981 demonstrated that a gyrotron traveling wave amplifier
(gyro-TW A) could produce a small signal gain of 18 dB over a 13% bandwidth
[BAR81]. The wide bandwidth was achieved by tapering the microwave cavity cross
section in step with a tapered magnetic field. This gyro-TWA acted as a reflection-type
amplifier, where input signal is injected downstream, travels upstream, and is reflected by
the constriction of the tapered waveguide.
The “9 dB launching loss” of a gyro-TWA was absent in the reflection-type
amplifier [BAR81]. There are three solutions to the dispersion relation of Equation 2.23;
in an amplifier only one mode represents the amplifying mode. The amplitude of each
component of the input wave is on the order of 1/3, and power, which is proportional to
the square o f the E-field, is on the order of 1/9. Hence, this is the origin of the “9 dB
launching loss”. In the reflection-type amplifier case, the incoming wave retains its
identity when the input mode is launched and does not share its energy with other modes.
Therefore, no “launching loss” occurs [LAU84],
In previous research a problem with the reflection amplifier remained in the inputoutput coupler, separating input mode and output mode. A traditional circulator that
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24
could solve this cannot handle wide bandwidths or high power. In the Active Circulator
Gyro-TWA a horizontally polarized TE0| mode wave is launched upstream in a
rectangular, tapered waveguide. The constriction of the waveguide reflects this signal,
and while the horizontally polarized TEoi wave propagates downstream, it induces the
vertically polarized T E I0 mode through excitation by the electron beam. Maintaining the
grazing condition for the T E i0 mode by the tapered magnetic field allows for a strong
cyclotron maser interaction mostly in the TEi0 mode. While both the TEt0 and TEoi
modes are amplified, the vertically polarized TE|0 signal is amplified more and can be
separated from the lower power, orthogonal TEoi mode by a standard technique such as
mode selective side wall coupler or wire grids. Figure 2.6 shows a view o f the active
circulator with appropriate dispersion relations.
(b)
a)
Horizontally
polarized
waveguide mode
(TE01)
vertically
/
polarized
waveguide
mode (TE10)
Figure 2.6. (a) Axial view of the active circulator gyro-TWA. (b) Waveguide modes and
beam mode for a tapered rectangular waveguide with a tuned beam grazing
the vertically polarized TE10 mode [LAU84].
Whether the TE i0 mode could be excited and amplified was answered
theoretically as follows. Under the assumption that the large orbit electron beam is an
infinitesimally thin mono-energetic electron layer where the propagation constant in the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
25
tapered magnetic field is given by kB(z)= ( cd -Cflb(z))/vte, the fields, Ey(z) and E^z) and
the RF surface current K e(z), evolve as [LAU84]
*
dz
-j)k.dz
,2
2 "*■ kwa ( z ) Ey (z)e
“
- j ] k tdz
= K e(z)e
"
-j)k>dz
■ j j + klbU) Ex (z)e -
dz2
I
- j \ k kdz
= K e (z)e
*
dz
d 2K e (z)
(2.34)
H
QJ if ?
= P E J z ) J [ — \ - j E x {z)J{
3
\ a )
(2.35)
(2.36)
where J [ is the derivative of the Bessel function of order unity, the prime notation
indicates a derivative with respect to the argument, P = -jOHG0e \ \ / (m 0y Qvltc 2), kwa
and kW5 are the local propagation constants for the TEoi and TE10 modes where
k2
wtt(z) = ((CQ/c)2 - ( 7 C / a ( z ) ) 2) and j £ ( z ) = ((( 0 / c ) 2 - ( * / b ( z ) ) 2),
Q=jo)|i047tR/ab, and p0 is the permeability of free space. Numerical integration of
Equations 2.34 through 2.36 demonstrated excitation of the TEI0 mode by a launched
TE0I mode is a strong possibility utilizing the geometry of the active circulator [LAU84].
The RCS gyrotron oscillator experiments have examined polarization control,
mode competition, and the effects of tapered cavities as a precursor to a possible Active
Circulator Gyro-TWA. The results will be discussed in subsequent chapters.
2.4 Quality Factor Determination
The quality factor, Q, is an important parameter in resonant circuits and
microwave cavities. A simple expression defining Q is [BAL89, POZ90, SLA50]:
average energy stored
(
dissipated power
)
(237)
)
where co is the frequency in radians. Q is a measure of the loss of a resonant device,
where lower losses imply a higher Q. Waveguide cavities are attractive since they
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
26
generally have high quality factors [BAL89], Since a resonant circuit is not independent
of the system in which it is placed, external effects such as the impedance mismatches at
the input and exit of the microwave cavity must be taken into account such that
( i
Q=
V
V1
' o *£e«,al y
<238)
Q , incorporates wall losses and dielectric losses (Q,=(1/Q w»ii + 1/Qdieiectnc)'1) and is called
the unloaded Q for the mode in question [SLA50]. Qwal| takes into account resistive wall
losses, coming from walls that are not perfect conductors, and Qdieiectric comes from the
medium filling the waveguide. The term g is the real part of the reduced admittance
looking out of the cavity and is derived in Chapter 4 of [SLA50], Qextial is called the
external Q of the a111mode of the cavity and the first mode of the guide. The quantity Q
in Equation 2.38 is called the loaded Q of the cavity. A derivation from Microwave
Electronics shows [SLA50]
(0 - (Oa
<».
l
11
= T7T
2Ql
<2-39>
where QL is the loaded Q, coa is the frequency of the resonant mode and co is the
frequency at the half power point. Measurements for the loaded Q’s of the RCS gyrotron
cavity are shown later in this dissertation.
2.5 Pulse Shortening
The RCS gyrotron demonstrates a phenomenon known as pulse shortening. Pulse
shortening appears common to most high power microwave tubes [MIL96, AGE96,
GRA96], In pulse shortening the microwave pulse duration is shorter than the e- beam
driver’s pulse length. While the e-beam pulse may be up to several microseconds, the rf
radiation is typically no more than -100 ns for high power pulses [GRA96].
Many experiments studying the cause and effects of pulse shortening suggest that
pulse shortening in high power microwave devices occurs due to the formation of plasma,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
27
electron streaming, high E-field breakdown, and beam disruption [BEN97]. Plasma is
formed where the beam intercepts surfaces, and the plasma disrupts coupling between the
beam and electromagnetic modes, and from e-beam collection, where the e-beam
dumping against a collector generates a plasma [BEN97], In high E-field breakdown,
high microwave electric fields within the cavity produce surface breakdown and disrupt
microwave production. Beam disruption due to instabilities or beam drift and diffusion
have also been observed to destroy microwave radiation due to perturbation of beam
electron orbits. Plasma emission inside the microwave cavity appears to be related to
pulse shortening on the RCS gyrotron [GIL98],
Some experiments have demonstrated rf radiation in excess of 1 GW where the
pulse length was limited only by the duration of the voltage source (Sandia IM P pulser,
300 ns) [HEN97], Furthermore, investigation suggests that subtleties of source operation,
i.e. voltage, current, and impedance fluctuations, could be responsible for pulse
shortening, and stray plasma could be a symptom of design errors [HEN97].
Experimental work in S-band shows that if a plasma exists or is created by ebeam interaction in the microwave cavity, microwave pulse disruption is likely to occur
[GIL98, GRA96], As the beam is dumped to a waveguide wall in the RCS gyrotron, it
causes hydrogen plasma expansion, and once plasma emission starts, the beam could be
amplified by multipactoring [BEN97, KIS9S, KIS98], A minimum plasma density
threshold for pulse shortening has not been observed, but is hypothesized to be the
critical (cutoff) density which corresponds to the radiation frequency (the critical (cutoff)
density for 4 GHz radiation is 2 x 1011cm ‘3). Investigation into surface coatings has
suggested that coatings which suppress secondary emission increases microwave pulse
width [GRA96]. Finally, “conditioning” of microwave tubes, i.e. high-temperature
bakeout or plasma processing, could also reduce the problem of pulse shortening
[M IL96]. Further research into the causes and mitigation of pulse shortening are
underway.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 3
EXPERIMENTAL CONFIGURATION AND DIAGNOSTICS
The description o f the experimental setup is given below for the individual parts
of the small and large orbit gyrotron experiments, where the configurations are shown in
Figure 3.1 and 3.2 respectively.
3.1 MELBA Diode
Large and Small Orbit Gyrotron experiments to produce high power microwaves
were performed on the Michigan Electron Long Beam Accelerator (MELBA). The high
voltage electron beam generator has the following diode parameters: voltage = -0.7 to
-1.0 M eV, diode current =1-10 kA, and pulselength = 0.3 - 4.0 psec. MELBA’s voltage
and current profiles have been fully described since its start of operation [PSI83],
[GIL85], [SPE91], and [WAL95]. MELBA is a Marx generator, a bank of capacitors
charged in parallel, but discharged in series. M ELBA contains sixteen l|iP, 100 kV
capacitors; fourteen of the capacitors produce a seven stage Marx generator, and two are
reverse-charged with an Abramyan resistor to constitute the Abramyan stage [ABR77].
The Abramyan stage is used to create a flatter (more uniform) pulse over longer
pulselengths (> lpsec). An equivalent circuit for MELBA can be found in [PSI83], and
[CH091]. The capacitors are charged to + 57 keV to provide a flattop voltage of
approximately -800 keV. A typical voltage pulse is shown in Figure 3.3, where the
length o f the voltage pulse is set by the adjustable delay on a crowbar switch.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Dumping
magnets
Maser Solenoidal
Coils
To
Diffusion
Pump
Rogowski Coil
(Entrance Current)
30 dB coupler
attenuator and
crystal detector
Cathode
Stalk
Carbon
Anode
1
Diffusion
Pump
Rogowski Coil
(Aperture Current)
30 dB coupler
to
DSA
N>
attenuator and
crystal detector
Rectangular
Waveguide
Interaction region
S-Band Rectangular
Waveguide
Diode Magnetic
Field Coils
Figure 3. 1. Experimental configuration for small orbit gyrotron experiments.
VO
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Diode ^
Magnetic
Field Coils
CUSP
m
Maser Solenoidal Coils
Rogowski Coil
(Entrance Current)
to screen
room
Dumping magnets
Cathod
Stalk
$
r= 2.25+/
Carbon Anode
(w/ 3 radial slots
at 2.2+/- 0.2 cm)
reflector
pieces
Rectangular Waveguide
Interaction region
Cryo pump
to screen
room
S-Band Rectangular
Waveguide
iitput
window
E^(kGauss)^
1
-1
Figure 3. 2. Large orbit gyrotron experimental configuration with axial magnetic field profile.
31
MELBA’s voltage pulse is applied to a glyptal-coated aluminum stalk. The stalk
has a glyptal-coated aluminum tip with a bare aluminum annular ring for an explosive
emission cathode. A schematic of the cathode tip is shown in Appendix E. The glyptal,
(1201-A ) red insulating enamel is used to prevent unwanted electron emission. A
description of M ELBA’s firing and cathode plasma formation, where electrons are then
ejected by the high negative voltage can be found in [PAR74], [CUN89], and [SPE91].
An electron trajectory computer code, EGUN [HER79] was used to model this cathode,
and results are discussed later in this thesis.
-200
-400
o
>
-600
-800
1000
Time (100 ns/div)
Figure 3.3. MELBA voltage pulse generated by the Marx generator.
The electric field produced across the A -K gap (10.7 cm) accelerates the electrons
toward the grounded anode. Three graphite anode apertures were used in different
gyrotron experiments and measurements. The stainless steel anode plate has a 24 cm
radius, and it is covered by a recessed 0.32 cm-thick graphite plate. A POCO graphite
anode is used to reduce bremsstrahlung x-rays. The three different apertures were placed
behind the graphite plate to control e-beam injection through the center of the anode.
Figures and descriptions of these anodes are found in Appendix E. For small orbit
gyrotron measurements a circular aperture o f 4.6 cm radius was used; for large orbit
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
gyrotron measurements, a slotted aperture was used; the annular slot was cut at a radius
of 2 . 2 +
0 .2
cm; and for electron beam diagnostics, an aperture with eight
1
mm pinholes
at a radius o f 2.25 cm was used.
3.2 Diode and e-beam transport magnetic fields
Magnetic fields are used to focus and control the electron beam. Two sets of field
coils are used to produce B-fields on the diode and in the interaction region. Five pulsed
“pancake” electromagnets control the field in the diode. A full description of these
magnets can be found in [CUN89]. A magnetic field is produced independently on the
maser solenoid. The magnetic field on the 10 cm diameter, stainless steel drift tube is
provided by two layers of 12 gauge copper wire wrapped around the tube. Fields of up to
4 kG may be obtained using a Marx-like two-stage, double-polarity (+ 450 V ) SCR
switched electrolytic capacitor bank which provides a high voltage pulse to the
solenoidal windings. The 2 sets of magnetic fields were varied for both small and large
orbit gyrotron experiments, as well as by modifications made in the large orbit
measurements. They are described separately below. Fields were measured both axially
and radially using a Bell Gaussmeter model 610 equipped with a Hall effect axial
magnetic probe and radial magnetic field probe.
The magnetic fields are pulsed independently on the diode and the maser solenoid
to control the e-beam velocity ratio, a ( vx / v„). This is discussed later in e-beam
diagnostics.
3.2.1 Small orbit e-beam magnetic fields
The diode B-field created by the ‘pancake’ type magnets is shown in Figure 3.4a.
in units o f Gauss per Amp (G/A) as a function o f axial position relative to the outer anode
plate. The solenoidal B-field profile in G/A is shown in Figure 3.4b; this, too, is plotted
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
as a function of axial position relative to the anode. The magnetic field is nearly uniform
starting just prior to the interaction region at 4S.5 cm. Figure 3.5 shows a typical profile
for small orbit gyrotron measurements with a superposition of the diode and solenoidal
fields.
50
(a)
40
O
2
30
'£
20
<o
c
on
10
0
-20
20
0
40
60
80
100
Distance from Anode (cm)
12
(b)
10
a
2
13
8
E
o
•w
m
m
<u
c
6
4
0
20
0
20
40
60
80
100
Distance from Anode (cm)
Figure 3.4. (a) Diode magnetic field (G/A) and (b) maser solenoid magnetic field (G /A)
as a function o f distance from the anode. The cathode position is at -12.2 cm
(A -K gap =10.7 cm).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
2.5
/—s
2.0
RCS
cavity
region
O
2
E
u
a)
s
00
2
0.5
0.0
-10
110
Distance from Anode (cm)
Figure 3.5. Magnetic field as a function o f distance from the anode for a small orbit
gyrotron measurement. This is a superposition of diode and maser fields.
The rectangular cross section cavity region is between 45.5 and 66.5 cm.
A single measurement o f the currents, calibrated by Figure 3.4, is sufficient to
produce the fields as demonstrated in Figure 3.5 since the magnetic fields are
proportional to the current flowing in the electromagnets. Thus, the strength o f the 13field on the interaction cavity is measured on each shot by the current in each of the
windings, monitored on a Tektronix storage oscilloscope.
3.2.2 Large orbit e-beam magnetic fields
Three different magnetic cusps (IA , IB, & II) were built, each one improving on
the previous one. Figure 3.2 shows the final configuration of the experiment with cusp II.
In order to improve the diode field characteristics, the diode magnets were pushed back
towards the accelerator and evenly spaced with 1.25 cm gaps between the ‘pancake’
electromagnets. Three 0.64 cm-thick steel plates were placed at the end o f the diode
magnets to guide the field lines from the diode magnetic field. This minimized the
effects of the large electromagnets on the solenoidal drift tube. Figure 3.6. shows the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
field response in G/A of the diode magnets. This was not altered for any of the cusps.
Table 3.1 summarizes the characteristics o f the three cusps. The maser solenoid field was
then reversed, and extra windings were added around each side of the steel plates to
enhance the field reversal. In Cusp 1 ,19 different sets of windings were used to enhance
the field reversal. The rectangular interaction cavity was left in the same place as in the
small orbit gyrotron measurements. Axial magnetic profiles for two different diode and
maser solenoid charging voltages are shown in Figure 3.7. The magnetic field reversal
occurs over a distance of approximately 14 cm, and the field has some oscillations due to
a metal flange between the interaction cavity and the cusp.
O
2
cathode
o
•aHi
e
2
start RCS cavity
-15
0
15
30
Distance from Anode (cm)
45
Figure 3.6. Diode magnet field response in G /A as a function of distance from the anode
plate for the large orbit gyrotron measurements. Cusp IA ’s interaction region
started at 45.5 cm, but the cavity was moved forward towards the anode to a
position of 28.5 cm for cusp IB and II.
In cusps IB and II, the maser solenoid windings were rebuilt, removing the metal
flange and all of the excess windings. One set of windings was then placed on both sides
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
2.0
0.5
Cathode
Anode
0.0
u
e
60
-0.5
S
-1.0
RCS cavity
position
03
-
2.0
’ -20
-10
0
10 20
30 40
50
Distance from Anode (cm)
60
70
Figure 3.7. Superposition o f diode and maser magnetic fields for Cusp IA at different
charging voltages, (a) The solenoid charging voltage was 320 V, and the
diode charging voltage was set at 2.76 kV. (b) The solenoid charging voltage
was set at 240 V , and the diode charging voltage was 1.8 kV.
of the steel plates, each with approximately 25 turns o f 12 gauge wire. Furthermore, a
cryopump was placed beneath the experiment and the diffusion pump at the end of the
experiment was removed. This shortened the overall maser solenoidal tube. The
solenoidal field profile was then measured as a function of distance from the anode as
shown in Figure 3.8. This magnetic field was not altered between cusps IB and II. The
superposition o f the magnetic fields for cusps IB and II for a typical MELBA shot is
shown in Figure 3.9. Cusps IB and II have a sharper field inversion that occurs over an
axial distance o f 9 cm on the centerline, as opposed to 14 cm. The aperture in the steel
plates for the drift tube in cusps IA and IB was rectangular. This led to radially periodic
magnetic field variations of approximately 20% every 45 degrees around the drift tube.
This asymmetry was corrected in cusp II; there is no specific, azimuthally periodic
oscillation in cusp II and the worst variation within the cusp is + 4.5%. A radial field
distribution going through cusp II is shown in Figure 3.10.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
o
-10
4U-
-12
10
0
20
30
40
50
Distance from Anode (cm)
Figure 3.8. Maser Solenoidal profile in G/A as a function o f distance from the anode for
cusps IB and II. The rectangular interaction region was placed at a distance of
28.5 cm from the anode.
1.0
/"•S
a
a
0.5
2
0.0
13
2
•2
-0.5
I
-1.0
0)
s
-1.5
RCS Cavity
M
-
2.0
5
0
5
15
25
35
45
Distance from Anode Plate (cm)
55
Figure 3.9. A typical axial magnetic field profile for cusp IB and II as a function of
distance from the anode. The rectangular interaction region was placed at a
distance of 28.5 cm from the anode.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
15
Distance
from
Anode(cm)
10
U
a
c
5
on
c
0
n
o ■
ao
Od
5
ffl -10
-15
-15
-10
5
5
10
15
10*Bfield*sin(angular position) [kG]
Figure 3.10. Radial magnetic field profile for cusp II. Positions indicated on the right
side of the figure indicate distance from the anode. The center of the cusp
is 14 cm from the anode. The axes were converted from angular positions
to X -Y Cartesian coordinates and multiplied by a factor o f 10.
Table 3.1 Summary of magnetic cusp characteristics.
Cusp
Characteristics
IA
19 sets o f windings; axial distance for field inversion: 14 cm; distance from
anode to RCS cavity: 45.5 cm: radial B-field variation: ~20% every 45° in theta
IB
2 sets o f 25 turns of 12 gauge wire; axial distance for field inversion: 9 cm;
distance from anode to RCS cavity: 28.5 cm: radial B-field variation: -20%
every 45° in theta
II
2 sets o f 25 turns of 12 gauge wire; axial distance for field inversion: 9 cm;
distance from anode to RCS cavity: 28.5 cm: radial B-field variation: -4.5%
every 45° in theta
Figures 3.5,3.7, and 3.9 show typical magnetic field profiles for measurements on
the small and large orbit gyrotron experiments. However, measurements at several
charging voltages were done with the Hall effect probe to estimate the cavity magnetic
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
field during experimental runs. Both the diode field magnets and the maser solenoidal
field windings were considered, and as stated before, the fields responded linearly with
changes in the current to the different sets o f windings.
3.3 Trigger sequencing
Timing for the magnetic fields to reach their peaks needs to be properly adjusted
in order set the proper fields during the firing o f the Marx generator. The diode magnetic
field coils take 116 ms from the time the capacitor bank is triggered to discharge the
current and produce the maximum field on the diode. Since these coils are the slowest
part o f the experiment, the diode magnetic field capacitor bank is triggered first. A
Systron Donner Pulse generator triggers the experiment. A BNC delay generator (BNC
7050, Berkeley Nucleonics Corp.) triggers the maser solenoid for cusp II 108.3 ms after
the diode coils to reach a maximum B-field at the same time as the diode. This timing
Time (20 ms/division)
Figure 3.11. Magnetic field coil currents for a large orbit gyrotron measurement as a
function of time, (a) represents the diode magnetic field current (5.25
A/div). (b) shows the coil current o f the maser solenoidal field windings
(25 A/div). (c) demonstrates the gate pulse used as a reference for the
MELBA Marx trigger and all o f the triggers and time delays.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
delay was adjusted from 109.6 ms for the small orbit gyrotron experiments because the
field windings were altered for the large orbit experiments. Magnetic field coil currents
as a function of time are demonstrated in Figure 3.11. The Marx bank is triggered 116
ms after the diode magnet coils. The time required for the Marx bank to erect is
approximately 450 ns, and the crowbar switch is set to trigger 960 ns after the Marx
trigger, giving an e-beam voltage pulse of approximately 500 ns. The timing circuits and
delays with the various BNC generators are shown in Appendix H.
3.4 Electron beam extraction and cavity structure
The e-beam that is extracted from the diode is compressed adiabatically in small
orbit gyrotron measurements by increasing the magnetic field in the cavity region. The
radius o f an annular e-beam after adiabatic compression can be given as [CH092],
(3.1)
where ru (rL2) is the Larmor radius in the diode (in the interaction region), and
is the
cathode e-beam radius. By using this adiabatic invariant argument, the relationship of
the e-beam a ( vx / v„ ), where v is the veolcity, between the diode and cavity regions may
be determined [SPE91] by,
(3.2)
where otm is the e-beam’s velocity ratio in the maser solenoidal B-field, ctd is the diode’s
velocity ratio, and Rn, is the magnetic field ratio = B2/B i.
The e-beam extracted from the diode in large orbit gyrotron measurements is run
through the magnetic cusp producing an axis-encircling e-beam. The e-beam is then
transported down the drift tube where it enters the rectangular cross section cavity. The
e-beam interacts with the RCS cavity, which is shown in Figure 3.12. The uniform
rectangular interaction cavity has dimensions of 7.2 cm by 5.4 cm, which is made by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
modifying and joining 2 sections of S-band waveguide. The cavity entrance is 28.5 cm
from the anode for cusps IB and II, but 45.5 cm from the anode for cusp IA and small
orbit gyrotron measurements. The entrance o f the cavity has a circular aperture of 2.6 cm
radius. The exit o f the interaction cavity region has removable copper strips (1 cm x 7.2
cm and 1 cm x 5.4 cm) at 21 cm downstream o f the entrance, which are used for varying
the cavity Q. The e-beam is dumped to a wall after leaving the interaction region, using
permanent magnets.
\VVVvV\V
aperture in
reflector strips
(used in some of
the measurements)
a (7.2 cm)
Figure 3.12. Uniform rectangular cross section interaction cavity.
Two different tapered cavities were built and tested in cusp II. They are
illustrated in Appendix I. Cavity B was tapered in the vertical dimension, where the
entrance of the cavity had dimensions o f 7.2 cm x 4.8 cm, and the exit of the cavity had
the same dimensions as the uniform cavity (A). This was done in an effort to suppress
higher order modes ( i.e. TE 0 n). Cavity C was tapered in the horizontal dimension,
where the entrance of the cavity had dimensions of 5.6 cm x 5.4 cm, and the exit was the
same as the uniform cavity; this was attempted to suppress the fundamental TE|0| mode.
3.5 Microwave extraction and cavity cold tests
High power microwaves generated in the RCS cavity are directed out through
waveguide of the same transverse dimensions as the uniform interaction cavity. A large
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
chamber lined with microwave absorber is located at the end of the waveguide. Two Sband waveguides oriented with wide dimensions perpendicular to each other at the end of
the chamber are used to collect the high power microwave emissions. The waveguides
have thin copper wires across the long dimensions to prevent cross-polarized microwave
electric fields from entering the waveguide. In some measurements microwave signals
go through S-band 30 dB couplers prior to being transmitted to a Faraday cage.
Otherwise, microwave signals are transmitted to the Faraday cage via RG-214/U Type
E l5402 coaxial cable directly. Coaxial attenuators, low pass filters, and calibrated
crystal detectors (HP8470B) are used to measure total power in both waveguide
orientations. The frequency responses of the large microwave chamber, a 30 dB coupler,
and a 4 GHz low pass filter are shown in Appendix G.
Frequency spectra were diagnosed by different methods in the gyrotron
experiments. The small orbit gyrotron experiments and cusp IA used a four channel 500
M Hz filter system designed using LIBRA (4.0). The individual bandpass microstrip filter
components were initially determined using methods described in Microwave
Engineering [POZ90]. The filters were then optimized using this program. These filters
were designed to have 500 M Hz bandwidths starting at 2 GHz, i. e., filter A was designed
to respond from 2.0 to 2.5 GHz, filter B was designed to respond from 2.5 to 3.0 GHz,
filter C from 3.0 - 3.5 GHz, and filter D from 3.5 - 4.0 GHz. The design parameters,
design response, and actual response are reviewed in Appendix F.
Frequency measurements for cusp IB and II gyrotrons were completed by use of
two heterodyne mixer systems. Two different microwave oscillators (HP8350B sweep
oscillator with a HP83590S RF plug-in and General Radio microwave oscillator) are
sources for the mixers' local oscillators (LO), and the rf source from the gyrotron is from
an incoming coaxial line. The incoming line uses attenuators, a 4 GHz low pass filter,
and a 3dB power splitter prior to going to the 2 mixers (Minicircuit 15542 type). The
mixers intermediate frequency (IF ) signals are directed to a digital signal analyzer
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
(Tektronix DSA-602) using a 2Gsample/s sampling rate. The signal is then Fast-FourierTransformed (FFT) for frequency spectra to show operating frequencies and respective
bandwidths. This set-up is demonstrated in Figure H.3. of Appendix H.
Measurements using only one microwave mixer did not require the General Radio
microwave source nor the 3 dB power splitter. Schematics of this heterodyne mixer
diagnostic can be found in Appendix H (Figures H.2.). For low S-band frequencies, the
local oscillator was set below the cutoff frequency of the cavity. For higher frequencies,
two experimental shots had to be taken at different local oscillator signals to remove any
ambiguity in sum and difference frequencies o f the IF signal response.
Cold testing of the RCS cavity (cavity A ) and the two tapered cavities (B & C)
was performed with an HP8722D network analyzer. For each of the RCS cavities, a
12 Apr 1997
CHt
S
11
log
MAO
441/
0 *3 2 :0 9
R EF 0 4 8
3 .M 3 .2 3 6 48
11 12 200 012 GHx
PRm
1j
I
Cor
23.372 48
115 G H i
1.65 d l
3.503 GH<
5 .•2 1 .7 ) 1 48
3.970 G H i
H I4
ST A R T 1 0 0 0 000 000 OHx
STOP 4.000 000 000 G H i
Figure 3.13. Cold test frequency spectrum o f the RCS cavity (cavity A). Marker 1
appears at a frequency o f 2.15 GHz. This corresponds to the TE10i mode.
Marker 2, which appears at 2.88 GHz, corresponds to the TE0n mode.
Marker 4 shows the TEm mode at 3.50 GHz, and marker 5 is apparently
due to either the TE0u mode or possibly the TE 201 mode at 3.97 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
small hole was placed in the center o f a wall, and a small loop antenna was inserted into
the experimental cavity. The ends of the cavities were also blocked o ff with copper
plates. The resonant frequencies were determined by dips in the SI 1 scattering parameter
as a function of frequency. Figures 3.13,3.14, and 3.15 show the frequency response of
the rectangular cross section cavity A, as well as the two tapered cavities, cavity B and
Table 3.2 Calculated resonant frequencies for modes in the S-band for rectangular
cavities.
Cavity
Calculated Resonant
Calculated Resonant
Calculated Resonant
Mode
Frequency (G Hz)
Frequency (GHz)
Frequency (G H z)
7.2 x 5.4 cm cavity (A)
7.2 x 4.8 cm cavitv (B)
5.6 x 5.4 cm cavitv (C)
TEioi
2 .2 0
2 .2 0
2.76
TEio:
2.52
2.52
3.02
TEon
2.84
3.19
2.84
T E im
2.99
2.99
3.43
TEon
3.12
3.43
3.12
TE o,3
3.51
3.79
3.51
T E im
3.53
3.53
3.92
TE |n
3.54
3.82
3.92
TEou
3.98
4.23
3.98
TE 201
4.21
4.21
5.40
cavity C. Appendix G contains further results o f cold testing on cavity A, the RCS
cavity. The cold test frequency spectrum o f the RCS cavity (cavity A) shown in Figure
3.13 shows the different mode resonances clearly. The cavity resonant modes may be
defined for the TE modes as follows [BAL89]:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
(\Jr>mnp
f ) TE =
wherem,n=0 , 1 , 2 ,
1
2V/uT
J
+ P1
—
7 ,2 +
\bj
p=l , 2 , 3 , but m = n &
0
(3.3)
.
Table 3.2 summarizes the resonant frequencies for the TE modes of rectangular
cavities of different dimensions. The resonant frequencies calculated for the tapered
cavities are based on rectangular cavities. Note that the table lists resonances based on
dimensions at either end of the tapered cavities. Equation 3.3 assumes perfect conductors
for the cavity walls, rectangular symmetry, and no apertures in the end plates.
I I Apr 1997 01:49:22
CHI
S
,,
k>| MAO
idil
RET lO d l
3.190 000 000 OH*
PR*
1 .>24.171 dB
I
2.11 GH*
Cor
3.89 G H z
Hid
s ta r t inno ono ono gh<
s to p 4.000 non non gh<
Figure 3.14. Cold test frequency spectrum o f the tapered cavity B. Marker 1 appears at a
frequency of 2.18 GHz. This corresponds to the TE |0| mode. Marker 2,
which appears at 3.11 GHz, corresponds to the TE0u mode. The frequency
has shifted due to the taper in the vertical dimension. Marker 4 at 3.77 GHz
shows the TE| 11 mode, and marker 5 at 3.89 GHz appears to be due to either
the TE014 mode or possibly the TEu 2 mode.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
Marker 1 in Figure 3.13 appears at a frequency o f 2.15 GHz which corresponds
to the TEioi mode as calculated from Equation (3.3). Marker 2, which appears at 2.88
GHz, corresponds to the TE0| i mode. Marker 4 shows the TE |11 mode at 3.50 GHz,
andmarker 5 at 3.97 GHz is apparently due to the TEoh mode or possibly the TE 201 mode.
During cold testing o f the cavities, the TE 102 mode was not observed because the TE 102
mode has a null field at the center of the cavity where the probe was placed for cold
testing [JAY97].
13 Apr 1997 01:15:44
3.>21.197 dB
It
3.790 000 001 GHi
Pfta
I
Cor
3.163 4B
I 2.360 GHi
Hid
START 1000 000 000 GHi
STOP 4.000 000 000 GHx
Figure 3.15. Cold test frequency spectrum o f the tapered cavity C. Marker 1 appears at a
frequency of 2.36 GHz. The frequency shift from 2.18 GHz is due to the
taper in the horizontal dimension. Marker 2, which appears at 2.85 GHz,
corresponds to the TE0| 1 mode. Marker 3 shows the TEm mode at 3.79
GHz.
Figure 3.14, which shows the cold test frequency response of cavity B,
demonstrated more characteristics o f a cavity with dimensions of 7.2 cm x 4.8 cm. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
TE0|i mode appeared in cold tests at 3.11 GHz as opposed to 2.84 GHz. The TE !!!
mode shifted up to 3.77 GHz as opposed to 3.50 GHz in the uniform cavity (A)
case.Figure 3.15 also demonstrated frequency shifts due to the taper in the cavity electric
field. The TEioi mode shifted up to 2.36 GHz and the TE| 11 mode shifted up to 3.79
GHz.
The quality factor, Q, which is defined by the following equation [SLA50],
0)Qx to ta l stored energy
_
decrease o f energy p e r u n it time
^ 4
is closely related to the frequency o f the resonances in a cavity. The cavity Q relates the
energy stored within a cavity to energy losses such as due to end-leakage and to
imperfect conductors. The cavity Q can be measured experimentally, where
C0-Q)a
(0
11
FW HM
2QL
f0
= -------- = -------------
(3.5
Q l is called the loaded Q. FW HM refers to the frequency separation at the half power
Table 3.3 Cavity modes and experimentally measured Q values.
Mode
Cavity A
_______
Cavity B
Resonant
Q
Resonant
Cavity C
Q
Resonant
Frequency
Frequency
Frequency
(GHz)
(G Hz)
(GHz)
Q
TEioi
2.15
512
2.18
770
2.36
68
TEon
2 .8 8
656
3.11
199
2.85
891
T E in
3.503
28
3.77
393
3.79
512
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
points. Table 3.3 lists the cavities, with their modes, frequencies, and Q values. The Q
values were determined from the cold test frequency spectra presented in Figures 3.13
through 3.13.
The cavity cold tests resonances were confirmed in e-beam microwave generation
experiments using heterodyne measurements. Cold testing suggested that tapering the
cavities would lower the Q to suppress the modes to some degree. However, the modes
were not completely suppressed; rather the resonant frequency shifted due to the differing
cavity dimensions. Cavity B, which was tapered in the vertical dimension to suppress the
TE0| i mode, had a Q o f 199 in cold test measurements, as opposed to 656 in the uniform
cavity case. The frequency was shifted up to 3.11 GHz in cavity B from 2.88 GHz
(cavity A).
Cavity C, on the other hand, had a Q o f approximately 6 8 in the fundamental
mode as opposed to 512 in the uniform cavity, and the frequency shifted from 2.15 GHz
(cavity A) to 2.36 GHz (cavity C). For both tapered cavities, the T E 111 mode was shifted
from 3.5 GHz to 3.79 GHz.
3.6 Electron Beam Voltage and Current Diagnostics
3.6.1 MELBA Voltage
MELBA’s e-beam voltage is measured across the insulating stack in the diode. A
copper sulfate/water solution is used to fill a 60 cm plastic tube, and this tube is used as a
balanced resistive divider between the supporting aluminum back plate at the start o f the
insulating stack and the grounded wall at the front of the stack. The voltage signal is then
attenuated through another resistive divider, a 10 x attenuator, a 50 £2 splitter, and
displayed on a digital signal analyzer, which is terminated in 50 Q. Figure 3.3 shows a
typical voltage response. The voltage signal response has a calibration o f approximately
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
310 kV/V. Calibration and operation o f the voltage monitor are described in more detail
elsewhere [LUC 8 8 ].
3.6.2 Diode current
Diode current is monitored by a small magnetic probe, a B-dot loop, located in
the grounded front wall of the MELBA tank. The probe extends into the oil for
approximately 1 cm. The probe has five turns o f thin magnet wire around a 1.1 cm rod.
The probe responds to the current flowing in the cathode stalk which causes a timechanging azimuthal magnetic field. The signal is integrated to yield a voltage signal
proportional to the current, 9.62 + 0.48 mV/kA. More detail on this diagnostic appears
in [CUN89].
3.6.3 Aperture current, cavity entrance current, and exit plate current
Both aperture current and cavity entrance current are monitored by Rogowski
coils. The aperture current monitor is placed on the downstream side of the anode plate.
The cavity entrance Rogowski coil is placed at the entrance to the rectangular interaction
cavity. The signals generated due to the e-beam current passing through the Rogowski
coil are then integrated to give voltage signals proportional to the current. The aperture
monitor uses integrator #21 which has a 5 psec time constant, and the entrance Rogowski
uses integrator # 8 with a 9.3 psec rise time. The coils are calibrated using a Febetron
pulser module operating in a self-breakdown mode. A full description o f calibration and
principles of operation can be found in [CH091]. The aperture Rogowski’s calibration
was determined to be 1.03 kA/V, and the entrance Rogowski’s calibration was
determined to be 1.61 kA/V.
When transported current measurements were performed, the output waveguide
which is connected to the RCS cavity was removed, and the dumping magnets were also
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
removed. A graphite exit collector paddle was placed immediately after the RCS cavity.
Figure 3.16 shows the set-up for these measurements. Current exiting the cavity was
determined using a Pearson coil with a response o f 0.1 V/A (0.05 V /A into 50 Q).
r=2.25+/-0.25 cm
Iron pole
piece
Maser Solenoidal Coils
exit plat
Rogowski Coil
(Entrance Current)
Cathod
Stalk
S *E
Pearson
Carbon Anode
r=2 .2 cm+/-0 . 2
Cryo
pump
Rogowski Coil
(Aperture Current)
Diode Magnetic
Field Coils
RCS cavity
Figure 3.16. Experimental set-up for transported current measurements for the large orbit
gyrotron.
3.7 Beam alpha diagnostics
To observe the e-beam and its positioning in the drift tube, the RCS cavity was
removed, and a glass witness plate was placed in front of the graphite exit plate (shown
above in Figure 3.16). This was done for the large orbit gyrotron. By replacing the anode
aperture by an aperture with eight 1 mm pinholes at a radius of 2.25 cm, radiation
darkening of glass witness plates may be completed to determine the radius (R), and
hence the e-beam a . This is completed by repeating the same MELBA pulse for 10 to 20
shots in order to achieve a dark enough pattern for analysis. The anode aperture used for
these measurements is demonstrated in Figure E.4 of Appendix E. A schematic for this
darkening during large orbit measurements can be seen in Figure 3.17.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
By using radiation darkening on glass witness plates to find the e-beam Larmor
radius (R), the e-beam’s a (a = v_l / v//) can be determined [CH092], [HOC96]. Using
the following equations:
(3.6)
>
E =
- 7
- H
me
(3.7)
where Ebeam= 800 keV, and y= 2.57, the e-beam a may be determined by:
1
a =
(3.8)
v
- l
{ pymc
- 1
A
e-beamlet
anode
Eight 1mm
pinhole apertures
glass
plate
B
Figure 3.17. Schematic showing radiation darkening for the large orbit gyrotron. Each
beamlet is given a large kick in the theta direction as it passes through the
cusp.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52
Figure 3.18. Radiation darkened glass witness plate for the large orbit gyrotron. The
eight beamlets clearly show coherent o ff centering.
Figure 3.19 Radiation darkened pattern for the small orbit gyrotron.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
A radiation darkened pattern for the large orbit gyrotron is shown in Figure 3.18,
and a radiation darkened pattern for the small orbit gyrotron is shown in Figure 3.19.
Figure 3.20 shows radiation darkening on the glass plate after going through cusp II; this
shows the entire e-beam after a single shot. Figures 3.18,3.19, and 3.20 used computer
contrast enhancements in scanning to allow the patterns to be more distinguishable.
Figure 3.20 Radiation darkened glass witness plate of the e-beam for the large orbit
gyrotron after passing through cusp II.
The e-beam a was determined to be approximately 0.3 for the small orbit
gyrotron using Equation 3.8. Similarly, the e-beam a was determined to between 0.8 and
1.2 for cusps IA, IB, and II at low magnetic fields (~1.5 kG), showing the velocity spread
of the e-beam. The darkest patterns in the large orbit gyrotron suggested that an average
e-beam a o f 1.0 was a good approximation at low magnetic fields. Another clear effect
demonstrated in Figure 3.19 is the coherent off-centering caused by this cusp [RHE74],
A relativistic single particle computer code compared spatial distributions o f the e-beam
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
to the experimental glass witness plates [JAY97]. The model for this code is the
schematic shown in Figure 3.18. The program numerically integrates relativistic
equations of motion of a single particle. The particle in the code is started at the anode
and stopped at an axial distance corresponding to the position of the glass witness plate.
One thousand particles were used, given the same initial position (radius and 6 ), but
different initial directions in velocity with spread in angles less than 5° from the axis
[JAY97]. This spread is set such that beta (v/c) is equal to 0.914. The code determined a
ranged between 0.6 to as high as 3.5 with a dominant range of 1.0 to 1.2, which is in good
agreement with the large orbit experiment. A comparison of a single beamlet with the
simulation is shown in Figure 3.21.
Y (cm)
2.0
X (cm)
Figure 3.21. Comparison of simulation results with experimental results in e-beam a
simulations for the large orbit gyrotron (cusp IA). The cross-hatched area
is due to the radiation darkened pattern of one e-beamlet. The simulation
also demonstrates the coherent off-centering (simulations from Jaynes
[JAY97]).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
A comparison of one e-beamlet in the small orbit gyrotron is shown in Figure
3.22. The simulation showed an e-beam a distribution that was dominant between 0.2
and 0.4. This agreed well with the experimentally determined value, ~0.3, for a.
0.0
-
-
1.0
2.0
-3.0
- 2.0
-
1.0
0.0
1.0
2.0
X (cm)
Figure 3.22 Comparison of simulation results [JAY97] with experimental results in ebeam a simulations for the small orbit gyrotron. The cross-hatched area
represents the radiation darkened pattern of one e-beamlet.
Experiments to measure the e-beam a were repeated at several values of cavity
magnetic field using cusp II, and they were repeated after changing the diode magnetic
field. The results are summarized in Table 3.4 and plotted in Figures 3.23 and 3.24.
These data show the magnetic field on both the diode and cavity have significant effects
on the e-beam’s velocity ratio. The e-beam a at 1.5 kG had the darkest pattern where the
e-beam a was equal to 1.0. This was performed by setting the diode B-field to 1.1 kG
prior to the cusp. When the diode B-field was raised to 1.2 kG and the cavity B-field
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
2 .0 ...............
+ diode B field 1.1 kG (min/max)
o diode B field 1.2 kG (min/max)
1)
I
Q*
8
1'5
.
1.0
U
09
0.5
L
1.4
1.6
1.8
2.0
Cavity Magnetic Field (kG)
2.2
2.4
Figure 3.23. Electron beam a as a function of cavity magnetic field for the large orbit
gyrotron (cusp II). This shows the range over which a varies. The data is
based on minimum and maximum radii of the radiation darkened glass
witness plates.
kept at 1.5 kG, the e-beam a showed more variance, ranging from 0.8 to 2.0 with the
darkest pattern indicating a around 0.95. At 1.9 kG solenoidal field, the dominant a for a
diode B-field of 1.1 kG was around 1.5, but a was only about 1.1 with the higher diode
field (1.2 kG). Figure 3.23 shows the full range of a measurements as a function of
cavity B-field. Figure 3.24 highlights where the most radiation darkening occurred, thus
giving the dominant or average a value.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
Table 3.4 Electron beam a measurements using different diode and cavity B-fields for
the large orbit gyrotron (cusp II).
Aperture B-
Cavity B-field
Beam a
Beam a
Beam a
Field (kG)
(kG)
(minimum)
(maximum)
(average)
1.1
1.50
0.8
1.2
1.0
1.1
1.60
1.06
1.49
1.1
1.1
1.71
0.84
1.44
1.3
1.1
1.87
0.93
1.61
1.5
1.1
2.24
0.72
1.6
1.6
1.2
1.49
0.75
1.95
0.95
1.2
1.70
0.75
1.22
1.0
1.2
1.86
0.93
1.79
1.1
1.2
2.23
0.97
1.38
1.3
+ diode field 1.1 kG
° diode field 1.2 kG
u
>
a
S
o
PQ
0.8
1.4
1.6
2.0
Cavity B Field (kG)
1.8
2.2
2.4
Figure 3.24. Average e-beam a as a function o f cavity magnetic field for the large orbit
gyrotron (cusp II).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER4
C O M PU TER SIM U LA TIO N S
Several codes have been used to both model and guide laboratory work as well as
to compare experimental results with computer simulations. In the previous chapter, a
relativistic single particle code was used to compare spatial distributions of the electron
beam with radiation darkened glass plates [JAY97]. From the radiation darkened
patterns and this single particle code, the beam a ( a = vx / v„) was determined.
Another code used to examine the beam and diode characteristics was the Stanford
Linear Accelerator Electron Optics Program which is also known as EGUN, or
Hermannsfeldt Code [HER79].
The Magnetic Insulation Code, referred to as MAGIC, was used to look at the
electromagnetic effects, kinematics, and dynamics of an annular e-beam in a rectangular
cross section cavity.
4.1 EGUN simulations for the small orbit gyrotron
The results of EGUN simulations are shown in Figures 4.1 through 4.3. An input
file without the applied, external, axial magnetic field is demonstrated in Appendix D.
EGUN iteratively solves Poisson’s equation and includes space charge effects. The code
uses finite difference methods, and the electric fields are determined from the potential.
Trajectories are then solved by using the relativistic force law.
For the simulations, the applied magnetic field (Bz) is an input parameter. This is
assumed to be the only external field. The code utilizes cylindrical symmetry with
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
Z, f
( x , y ) axes plotted in Figures 4.1 to 4.3. The cathode, where the e-beam is
emitted, is set at 750 keV, the axes are set as vacuum boundaries, and the outer walls are
set at ground potential. The area simulated in Figures 4.1 to 4.3 represents the diode,
diode aperture, and the drift tube without the microwave cavity as shown in Figure 3.1.
Each grid cell in both the radial and axial dimensions is 0.054 cm with an anode-cathode
gap of 10.7 cm. The cathode has an emitting surface at a radius of 2.25 + 0.25 cm.
The magnetic fields in Figures 4.1 to 4.3 were varied to determine the effects on
beam transport (i.e. to see if any reflections occur) and to simulate the beam a (v x / v/;).
In Figure 4.1 the magnetic field was set at a uniform field o f 1 kG. Figure 4.2 and 4.3
begin with a diode magnetic field o f 800 Gauss that is ramped to 1 kG at the anode
aperture to model experimental measurements. Prior to the interaction region (see Figure
3.1), the magnetic field (Bz) is ramped to 2 kG (Figure 4.2) or 4.5 kG (Figure 4.3) to
represent experimentally measured fields along the axial dimension. EGUN, being a
quasi-static code, allows simulation of the beam a at any point along the trajectory.
For a uniform magnetic field of 1 kG, the e-beam a in the region where the
microwave cavity would be placed (45.5 cm from the outer anode surface) was low with
an a spread between 0.05 and 0.23 (average a o f 0.15). When the e-beam was
adiabatically compressed and the magnetic field raised to 2 kG in the region of the
interaction cavity, the e-beam a spread increased to range between 0.10 and 0.29 with an
average a o f 0.23. Adiabatically compressing the e-beam further by raising the
interaction region magnetic field to 4.5 kG resulted in an a spread ranging from 0.19 to
0.59 with an average a of 0.32. As mentioned in Chapter 3, the experimental beam a
was determined to be approximately 0.3 at a cavity region magnetic field of 2 kG. This
agreed well with the EGUN simulations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
400
S.O
4.0
300
3.0
•200
2.0
100
0.0
1000
Z (MESH UNITS)
Figure 4.1. EGUN result showing the e-beam trajectory for a uniform 1 kG B-field. The
cathode emits at 2.25 + 0.25 cm with a voltage of -750 kV. The average a
without adiabatic compression is 0.15.
400
i - 5.0
300
200
ac
100
0.0
500
1000
-
1500
1.0
Z (MESH U N IT S )
Figure 4.2. EGUN result showing the e-beam trajectory as the B-field is increased to 2
kG on the interaction region (other parameters are the same as Figure 4.1).
The average a with adiabatic e-beam compression is 0.23.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
400
300
200
2. 0«J
oc
TSJ
-CD
100
0
500
1000
1500
Z (MESH U N I T S )
Figure 4.3. EGUN result showing the e-beam trajectory as the B-field is increased to 4.5
kG on the interaction region (other parameters are the same as Figure 4.1).
The average a with adiabatic e-beam compression is 0.32.
Under the conditions shown for each case, the simulations showed that the beam
transported 1.84 kA of current to the interaction region without reflections. The actual
experimental results produced approximately 3.5 kA (see Figure 5.8).
4.2 M A G IC 2D simulations
MAGIC code simulations were performed on both the large and small orbit
gyrotron oscillators to examine the effects o f the cavity and magnetic fields on the
polarization o f microwave emission. MAGIC is an electromagnetic particle-in-cell code
that is fully relativistic, time-dependent, and two dimensional [GOP94]. These gyrotron
simulations were performed in x-y coordinates, assuming the rectangular cavity infinite
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
62
in the Z direction; under this assumption, kz is zero. Figure 4.4 shows the model used for
M AGIC simulations. The 7.2 x 5.4 cm2 simulation area was divided into a mesh
Perfectly
x conducting
walls
V
A
/
/
/
'
yA
Large-orbit
sU
— Electron Beam
i/i
small-orbit
-►H
7.2 cm
Figure 4.4. Model used for MAGIC 2D code simulations of the RCS gyrotron oscillator
for both the small orbit and large orbit cases.
where the mesh spacings were 0.5 mm in each dimension. Four beamlets were used to
simulate an annular electron beam. For the small orbit and large orbit simulations, the
beamlets (as shown in Figure 4.4) populated the rectangular cavity at a distance o f 1.8 cm
from the center o f the cavity. The walls of the RCS cavity are assumed to be perfect
conductors for the code simulations. In the small orbit simulations the electron beam
energy was set at 750 keV, with a beam a of 0.3 and current of I kA for the four
beamlets (total). In the large orbit simulations the e-beam voltage was set at -800 kV,
with a beam a set at 1.0 and current of 200 A for the beamlets (total).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
63
The magnetic field was varied from 1.5 kG to 2.5 kG for different simulations.
The time step was fixed at 90 % o f the Courant stability criterion, which resulted in
5.4cm
(•)
5.4cm
(b)
.ft*•>>•
0
7.2 cm
0
7.2cm
5.4cm
0
<d)
7.2 cm
Figure 4.5. Trajectory plots from M AG IC 2D code simulations for the large orbit RCS
gyrotron case. While four beamlets were used to initially populate the
simulation space, the beam appeared to demonstrate bunching and the
formation of an annular e-beam similar to the one depicted from radiation
darkening on a glass plate (see Figure 3.20). Electron beam trajectories are
shown at 1 ns (a), 13 ns (b), 20 ns (c), and 27 ns (d).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
1.1 ps time steps for the majority of the simulations, and the simulation time was allowed
to vary (> 30 ns). A sample input file for the large orbit simulation is shown in Appendix
C.
Electron beam position as a function of time is shown for one case of the large
orbit simulations in Figures 4.5a through 4.5d. In the large orbit simulations the e-beam
appeared to show bunching (Figure 4.5b) followed by the formation of a rotating, annular
e-beam similar in appearance to the radiation darkened glass plate as shown in Figure
3.20. This was in contrast to the small orbit simulations, which showed the four beamlets
smearing out and rotating around the center of the cavity.
The time resolved Ex and Ey wave electric fields were found by the M AGIC code,
as well as the peak amplitudes of the Fast Fourier transforms (FFTs) of the electric fields.
Figures 4.6a - 4.6d show the FFTs of the Ex(h) and Ey(V) fields for a small orbit gyrotron
simulation and Figures 4.7a - 4.7d show the FFTs for the electric fields in a large orbit
simulation.
In order to study polarization control, Figures 4.6a and 4.6b show FFTs in the
small orbit simulation with an external magnetic field o f 1.85 kG, while Figures 4.6c and
4.6d show the same simulation with the external B-field changed to 2.3 kG. The figures
demonstrate that the magnitude of the electric field from the fundamental TEio mode
decreases as the B-field is raised while the magnitude of the orthogonal TE0| mode
increases between these magnetic fields. The dispersion relations that correspond to
these modes can be seen in Figure 5.6.
The large orbit gyrotron electric field FFTs demonstrate similar polarization
control results as in the small orbit simulations. Figures 4.7a and 4.7b show that at an
externally applied B-field of 1.5 kG, the fundamental TEi0 mode is dominant with the
TE0| mode lost in the noise. Again, when the B-field is raised to 2.1 kG, as in Figures
4.7c and 4.7d, the orthogonal TE0| mode dominates the fundamental TE)0 mode. The
corresponding dispersion relations for the large orbit gyrotron are shown in Figure 6.16.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
(a)
(b)
in
r*»
a
s
\
>
m
> «
9
e
a . 25
9
a .5
FREQUENCY
( Hz )
e*t9
(C)
2.25
9 .7 5
FREQUENCY
( Hz )
£•19
(d)
ns
n m
i
U (M
e
\
>
>
01
a
« . 25
f l. 5
5 .7 5
1
s
9 .2 5
9 .5
9 .7 5
£*19
FREQUENCY
( Hz )
1
£ ♦10
FREQUENCY
( Hz)
Figure 4.6. Fast Fourier transforms (FFTs) o f the electric fields from the small orbit
gyrotron MAGIC 2D code simulations, (a) Ev at a B-field (Bz) o f 1.85 kG.
The cyclotron frequency occurs at 2.10 GHz and the fundamental TE10 mode
has a resonance at 2.22 GHz. (b) EH at a magnetic field of 1.85 kG. The
cyclotron frequency and the fundamental mode are present as well as the
TEoi mode at 2.82 GHz and the TEn mode at 3.6 GHz. (c) Ev at a B-field of
2.3 kG shows only a resonance at 2.12 GHz (TEi0). (d) EHat a B-field o f 2.3
kG, where the cyclotron frequency is seen at 2.61 GHz and the TE0i mode is
present at 2.82 GHz. Figure 5.6 shows the dispersion relations for the small
orbit gyrotron.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
(a)
0»)
01
CM
m
s0
8
\
>
> *"
aa
<s
to
a
CM
■«r
a
0
1
0.25
FREQUENCY
£ ♦10
FREQUENCY
(H z I
(c)
1
0.5
£♦10
(H z I
(d)
CM <0
I
•
u m
Ii
]i
1
i
\6
>
i
;
;
i
|
........... i............i---------I
[
N
> -
<n
9
i
(
J
0
3
6
1.2
E*t9
FREQUENCY
(Hz)
|
(
l
v.— A ii——X j J
.3
.6
.9
1.2
E .ia
FREQUENCY
( Hz)
Figure 4.7. FFTs of the electric fields from the large orbit gyrotron M AGIC 2D code
simulations, (a) Ev at a B-field (Bz) o f 1.5 kG. The cyclotron frequency
occurs at 1.63 GHz and the fundamental TE l0 mode has a resonance at 2.34
GHz. (b) Eh at a magnetic field of 1.5 kG. The cyclotron frequency and the
fundamental mode are present but the TE0| does not appear except in the
noise, (c) Ev at a B-field o f 2.1 kG shows only a resonance at 2.3 GHz which
appears due to both the cyclotron frequency (2.3 GHz) and the fundamental
TEio mode, (d) EH at a B-field o f 2.1 kG, where the TE0i mode is present at
2.82 GHz. Figure 6.16 shows the large orbit gyrotron dispersion relations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
67
To compare the power generated in the orthogonal TEio and TE0i modes, the
corresponding power was calculated using [HAR61]:
" “
.2
m=l n=0
ab
(4.1)
Z fc .
where
_ - H x _ k - (m n I a)
O&U =
Ey
(4.2)
a)fxkz
(Yo)mn are the TE™ wave admittances, a and b are the horizontal and vertical
dimensions respectively, E is the permittivity, and k is the wave number. The ratio of the
powers was then calculated, PVerticai(v){TE10}/ Phorizontai(h){TE0i}. The polarization power
ratio as a function of externally applied magnetic field is shown for the small orbit
simulations in Figure 4.8 and for the large orbit gyrotron simulation in Figure 4.9.
©
100
1
g
10 r
□
C3
04
<5
£
£
c
o
.1
B
N
?
cu
i
01
1.7
1.9
2.1
1 i
2.3
i
.
i
2.5
Magnetic Field (kG)
Figure 4.8. Microwave polarization power ratio for the small orbit RCS gyrotron as a
function of B-field from M AGIC 2D code simulations. The model assumes
kz=0, e-beam a = 0.3, and the current = 2 kA.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68
The results from Figure 4.8 can be compared with experimental results in Figure
5.7 for the small orbit gyrotron experimental measurements. Simulation (Figure 4.8)
predicts that the fundamental TE I0 mode is dominant at low B-fields and flips to a
dominant orthogonal TE0| mode at B-fields above 2 kG. However, experimentally this
was not seen. This is discussed further in Chapter 5.
cd
qc
<3
£
s
o
3
N
O
0U
1.6
1.8
2.0
Magnetic Field (kG)
2.2
Figure 4.9. Microwave polarization power ratio for the large orbit RCS gyrotron as a
function of B-field from M AG IC code simulations. The model assumes
kz=0, e-beam a = 1.0, and the current = 200 A.
The large orbit gyrotron simulation results appeared to agree qualitatively with
experimental results. Figure 4.9 shows the fundamental TEi0 mode is dominant at lower
magnetic fields but rapidly transfers to the TEoi mode, which dominates at higher fields.
Figure 6.18 demonstrates experimental results that can be compared with Figure 4.9
(simulation results). The change in polarization at 1.9 kG in Figure 4.9 agrees with large
orbit experimental measurements, and this is discussed further in Chapter 6.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
Due to assuming kz= 0 in the simulations, the TElt mode became dominant over
either of the previous orthogonal modes at higher magnetic fields (~ 2.5 kG). This
occurred in both simulation cases.
4.3 MAGIC 3D simulations
The large orbit RCS gyrotron was modeled using MAGIC 3D code. This version
(September 1997) is fully relativistic, time-dependent, and three dimensional [GOP97].
The RCS cavity was modeled and shown in Figure 4.10. The inner cavity dimensions are
7.2 x 5.4 cm2 in the X - and Y-coordinates. The cavity is 21 cm long in the Z-coordinate,
followed by two metal, 8 mm thick, horizontal strips (7.2 x 1 cm2), which is then
followed by an output waveguide of the same dimensions as the RCS cavity. A constant,
output waveguide'
reflectinj
strips
direction of beam propagation
Figure 4.10. M AG IC 3D cavity generated for large orbit gyrotron simulations.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
externally applied magnetic field in the Z-coordinate (Bz) is applied along the entire
simulation volume. A dumping magnetic field (By) o f 1 kG is applied for 6 cm following
the horizontal strips.
Appendix J is a sample input file for M AGIC 3D simulations, and Appendix K.
shows the results from 2 simulations at different magnetic fields, 1.7 kG and 2.4 kG. For
the large orbit simulations the grid spacings were 4 mm in X , 4 mm in Y, and 8 mm in Z.
The cavity shown in Figure 4. 10 is constructed of a perfect metal conductor. The
annular large orbit e-beam is injected into the cavity from five beamlets at - 800 kV with
a 5 % energy spread. The sum of the current injected from the five large orbit beamlets is
200 A. The simulation was allowed to run for 100 ns. The beam is emitted using a
1000000
100000
§
I
10000
s
w
o
s
04
U
0)
*
£
s
0
sN
1
£
.0001
1.5
1.7
1.9
2.1
Cavity Magnetic Field (kG)
2.3
2.5
Figure 4.11. Polarization power ratio from M AGIC 3D simulations. Below 2.1 kG the
fundamental TGi0 mode is dominant, and above 2.1 kG the orthogonal TE0)
mode becomes dominant.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
71
GYRO emission process which allows a rotating beam to be emitted from a metal
conductor. The output waveguide is terminated with a vacuum boundary. The a
(velocity ratio) of each beamlet was set at 1.0. Phasespace plots, trajectory plots, current
diagnostics, power plots, and field plots with FFTs are demonstrated for simulations in
Appendix K. From the FFTs of the electric fields the polarization power ratio was
calculated using Equations 4.1 and 4.2. The polarization power ratio (PwrTEio/PwrTEoi) is
shown in Figure 4.11.
The simulation results demonstrated sharp polarization ratios. Below 2.1 kG the
fundamental TEio mode was dominant. The peak polarization power ratio occurred for a
magnetic field (Bz) of 1.7 kG with a ratio o f approximately 800,000. Below this
magnetic field, the fundamental TEI0 mode was dominant, but the magnitude o f the
electric fields in both modes were at least an order o f magnitude lower than at 1.7 kG.
Above an external B-field of 2.1 kG the orthogonal TE0i mode dominated the
fundamental mode. The polarization power ratio dropped to a minimum of 0.0006
(~1/1700) at 2.4 kG. In several o f the simulations mode competition from the TEu and
TE2o modes was observed; however, the magnitude o f the fields for both o f these modes
was several orders o f magnitude below the dominant mode.
These 3D simulation results agree qualitatively with experimental results, as did
the MAGIC 2D results. In these simulations the point where the polarization power ratio
flips from the fundamental TE)0 being dominant to the TE0i being dominant occurs near
2.1 kG, but experimentally (as w ill be discussed in Chapter 6) the ratio flips at
approximately 1.9 kG. The simulation results assume a constant a , and a uniform energy
spread, as well as other idealized conditions, and this could account for the difference
between simulation results and experimental results.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 5
SM ALL O R B IT RECTANG ULAR CROSS SECTIO N G YR O TR O N
EXPERIM ENTS
Chapter five examines the initial experiments on the rectangular cross section
gyrotron in which the magnetic field acting on the experiment resembled Figure 3.5. The
experimental configuration for these measurements was demonstrated in Figure 3.1. Two
sets of measurements were completed using this geometry. First, the cavity was used
without reflecting strips just prior to the beam dump (see Figure 3.12). The second set of
measurements was completed with reflecting strips placed in the horizontal dimension.
This was done in an effort to raise the rectangular interaction cavity’s Q. A discussion of
this is found in Chapter 3. Figure 5. la shows the microwave power measured at the
output of the linearly polarized waveguides as a function of the magnetic field for the
small orbit gyrotron without reflecting strips. Figure 5.1b shows the peak power
achieved for the case with horizontal reflecting strips. The highest power achieved
without reflectors was estimated at 40 M W in the vertical polarization. However, this
power was uncalibrated, as there were no frequency filters. Power measurements are
based on measured attenuation in the waveguide and directional couplers; but, higher
frequency signals may not be attenuated properly, giving higher than actual results. Once
a frequency filter was placed in the vertical polarization, the peak power measured in the
vertical polarization was 5 MW , using 6 GHz low pass filters. When a 4 GHz low pass
filter was substituted, the peak power measured in the vertical polarization was 4 M W
without reflectors. The peak power measured in the vertical polarization was 3.5 M W
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
(a)
45
T
' V
I
I
|
1I
I
I
|
I
+
o
x
o
40
35
u
:$t; + I
1
O
. . .p." . A , ? - B. . j , . fe
20
2.5
Cavity B-field (kG)
2.0
I
I
I
l“
l
I'"
I „ I"
X
+
16
1
H polarization
V polarization (w/ 6GHz LP)
H polarization (w/ 6GHz LP)
V polarization
10
1.5
{2
I
+
+
0
%
0
k*
I
x
5
u
*o
3
00
u
5
I
m
eo 25
u
s
20
*
9
0
15
u
(b)
|
I
30
■g
'3
1
0*
I
+ +
12
f
I
I
I
+
o
x
°
I
I
3.0
I
I
3.5
I
I
I
H polarization
V polarization (w/ 6 GHz LP)
H polarization (w/ 6 GHz LP)
V polarization
+*
+
.
♦
4
+
* ♦
X
o
0o O o
°
aa 0 o
.o a A f t ° o ° P
0
1.5
2.0
o
a
o
o 0
2.5
Cavity B-field (kG)
3.0
3.5
Figure S. 1 Peak power measured in the vertically and horizontally polarized waveguide
systems for the small orbit gyrotron. (a) without reflecting strips; (b) with
reflecting strips.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
when the horizontal reflectors were added. The reflectors did not have any real effect on
the vertical polarization.
The peak power measured in the horizontal polarization with low pass filters was
23 M W for the case without reflecting strips. The maximum power measured with the
reflecting strips in the horizontal polarization was approximately 20 M W , as shown in
Figure S. lb. Below 1.8 kG, negligible microwave power was measured in either
polarization. As Figure S. la and S. lb demonstrate, the power drops o ff rapidly after the
sharp rise in power in both polarizations at 2.2 kG for both cases. Microwave
measurements were not taken above 3.2 kG since mode competition and higher order
modes were expected based on the dispersion relations. The reflecting strips did not have
a significant effect on power in either polarization, but they did define the cavity
dimensions and Q by reducing the coupling to the output waveguide.
Time (lOOns/div)
Figure 5.2. Rectangular cross section gyrotron data signals from shot 4841. (a) Voltage
monitor signal (310 keV/div). (b) Entrance current signal (2 kA/div). (c)
Vertically polarized power signal. The peak power corresponds to
approximately 1 M W . (d) Horizontally polarized power response. The peak
power in the horizontally polarized mode was approximately 15 MW .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
Figures 5.2 and 5.3 show typical data from a high power rectangular cross section
gyrotron shot taken on MELBA. The data for M ELBA shot 4841 were taken at a B-field
of 2.16 kG on the cavity. Figure 5.2a shows a typical voltage pulse on the accelerator.
Another voltage trace is shown in Figure 3. 3 and discussed in Chapter 3. Figure 5.2b
shows the current entering the rectangular interaction cavity. The peak current was
measured to be approximately 4 kA. Figure 5.2c is the vertically polarized microwave
power signal with a peak of 1 MW. Figure 5.2d is the horizontally polarized microwave
power in the S-band waveguide which represents a peak power of 15 MW . Figure 5.3
shows the microwave pulse responses of gyrotron shot M4841 in the 500 M Hz bandpass
filters. Figures 5.3a and 5.3d clearly show that no microwave signals were observed in
the ranges of 2.0 - 2.5 GHz and 3.5 - 4.0 GHz. The peak response from filter B (2.5 - 3.0
GHz) was approximately 1.8 M W [Figure 5.3c], and filter C’s (3.0 - 3.5 GHz) peak
Time (lOOns/div)
Figure 5.3. Microwave Filter response for M ELBA shot 4841. (a) Filter A (2.0 - 2.5
GHz), (b) Filter B (2.5 - 3.0 GHz), (c) Filter C (3.0 - 3.5 GHz), (d) Filter D
(3.5 - 4.0 GHz). The filters were placed in the horizontal polarization.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
76
response was 2.3 MW . The filtered gyrotron signals were lower (6 -10 dB) than other
measured power results. This could be due to several factors including: (1) higher order
modes not contributing to a filter response, (2) signals with opposite polarization not
contributing (the signal to the filters originated from only one S-band line as opposed to
both lines), and (3) using an average of the filter attenuation response to calculate signals,
where the filter responses varied as shown in Appendix F (Figures F. 3 to F. 6).
However, the filters were used as a frequency diagnostic and not for power
measurement. Shot 4841 shows microwave emission power between 2.5 and 3.5 GHz.
As will be seen later in the dispersion relations, this corresponds to the forward wave of
the TEoi mode.
The gyrotron emission’s filtered relative power responses are shown in Figures
5.4a, 5.4b, 5.5a, and 5.5b. Cases studied included both the vertical and horizontal
polarizations, and a cavity without/with reflecting strips. A comparison of Figure 5.4a
(without strips) versus 5.5a (with strips) where the bandpass filters are both in the
horizontal polarization shows the power in Filter C (3.0 - 3.5 GHz) almost doubles from
3 to 6 M W with strips added. This indicates that the reflectors did increase the power in
the TEoi mode. But this is apparently due to the backward wave interaction of the second
harmonic in this mode. A dispersion relation, in Figure 5.6, shows the various
interactions for the small orbit gyrotron at different magnetic fields. The magnitude of
the forward wave interacting with the TEoi mode appears unchanged with a peak value
near 2 M W by the presence of the reflecting strips. There is moderate power in Filter D
(< 1 M W , 3.5 - 4.0 GHz) at B-fields in excess of 2.6 kG for both sets of measurements in
the horizontal polarization. This is due to the contribution of the beam interaction with
the TEu mode. However, dispersion relations show that the presence of the lower order
modes has diminished at this magnitude o f B-field. In summary, with the filters in the
horizontal polarization, mode competition exists between the forward TE0i mode, the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
3.5
(a)
a Filter Bpwr (2.5-3.0 GHz)
• Filter Cpwr (3.0-3.5 GHz)
A Filter D pwr (3.5 - 4.0 GHz)
3.0
e
M
E
2.5
2.0
s
S
I
fa
1.5
Urn
O
*
o 1.0
CU
.! >
□
V
>
&
•
a
a
O fl
0.5
a ci
■ ■ ■ * » . * » « » ■ ■ ■ ■ D i . .?. .
0 .0
1.8
2.0
2.2
2.4
i . . .* ■ i ■tT *
2.6
2.8
i . ■ .* .
3.0
3.2
Cavity B-field (kG)
(b) ^
i i i i • i •
2.0
i i i i
£
S
|
1.5 1-
tu
e
•a
a
2
3
•
*
1.0
Filter Bpwr (2.5-3.0 GHz)
Filter Cpwr (3.0-3.5 GHz)
Filter D pwr (3.5-4.0 GHz)
-
S
□
u
I
£
o
>
0.5
o»
;
«
o
-4—L.
0.0
1.8
2.0
2.2
I*
A
2.4
2.6
2.8
Cavity B-field (kG)
3.0
3.2
Figure 5.4. Microstrip bandpass filter results for the small orbit gyrotron without
reflecting strips, (a) Filters placed in the horizontal polarization, (b) Filters
placed in the vertical polarization.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
i i i i I i r»i i | i i i i 1| i i i i | i i ■i i | i i i i
(a)
w
a Filter Bpwr (2.5-3.0 GHz)
• Filter Cpwr (3.0-3.5 GHz)
* Filter D pwr (3.5 - 4.0 GHz)
5
2
ra
A
G 4
T3
K
H
3
w
3 ■
I
2
• •
s
£
o
•a 1
CQ
13
04
0
2.0
(b) _
B
a
tPa
* * * ■1 * * ■
2.2
11
a
□
a
* ■ ‘ * 1* ^
» 1 * ■* ■1 * ■* ■
2.4
2.6
2.8
Cavity B-field (kG)
3.0
3.2
i ■• 1 • i •
2*°
£
2
'w'
£
S 1.5
E
tc
T3
£
I
IU
a
o Filter Bpwr (2.5-3.0 GHz)
•
*
'- 0
Filter C pwr (3.0 - 3.5 GHz)
Filter D pwr (3.5-4.0 GHz)
Im
I
Icu 0.5
o
>
fl □ 0
13
*
8
□
□
• ■■ • 1 ■ ■ ■ ■1 ■ ■ • • 1• • • • 1 • ■ ■ ■ 1 ■• ■ ■
□
0.0
2.0
2.2
2.4
2.6
2.8
Cavity B-field (kG)
3.0
3.2
Figure 5.5. Microstrip bandpass filter results for the small orbit gyrotron with reflecting
strips, (a) Filters placed in the horizontal polarization, (b) Filters placed in
the vertical polarization.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
backward TEoi mode, and the TEu mode. When the filters were placed in the vertical
polarization, other modes that could compete were also observed.
Figures S.4b and S.Sb show the results of the gyrotron emission analyzed by the
frequency filters in the vertical polarization. The absence of any response in filter A (2.0
- 2.5 GHz) proved that the forward wave of the fundamental TEI0 mode was absent. The
largest measurements of power were recorded in the third filter, filter C (3.0 - 3.S GHz).
Figure S. 6 shows that the mode observed was the backward wave of the TE|0 mode from
4.5
TE20
4.0
X
3.5
T E ll
S
£ 3.0
c
<o
TEOI
£ 2.5
TE10
Om
2.0
80
-60
-40
-20
0
Kz (1/m)
20
40
60
80
Figure 5.6. Dispersion diagram for the small orbit RCS gyrotron. The e-beam is assumed
to have a beam a of 0.3 and a beam energy of 750 keV. (a) the beam line for
the first harmonic at a B-field of 2.25 kG. Observed frequency interactions
are: TE01 (FW) =2.8 GHz, and TEu (FW ) = 3 . 7 GHz. (b) frequency
interactions for the first harmonic o f a 2.9 kG B-field. Observed interactions
include the TE01 (BW ) = 2.9 GHz, and the TE „ (FW ) = 3.5 GHz. (c)
frequency interactions for the second harmonic of a 2.25 kG B-field.
Observed interactions include the TEio (BW ) = 3.0 GHz, the TEoi (BW ) =
3.3 GHz, and the TEu (BW ) = 3.7 GHz. (d) frequency interactions for the
second harmonic of a 2.9 kG B-field. Observed interactions include the TE10
(BW ) = 3.7 GHz, and the TEoi (BW ) = 3.9 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
the second cyclotron harmonic o f the beam interaction. This mode interaction was
observed as the field was raised from 2.2 kG to 3.2 kG. The results from measurements
taken with and without reflecting strips are similar, as seen in Figures S.4b and S.Sb.
This was expected, as the horizontal strips should not have enhanced the vertical
polarization.
The small orbit gyrotron did not meet the motivation of gaining polarization
control of the output microwaves. Figure S.7 plots the polarization power ratio as a
function of magnetic field. M AGIC2D simulations demonstrated (see Figure 4.8) that
polarization control should be exhibited as a function of magnetic field. M AGIC 2D
code results showed a polarization power ratio that changed from IS at 1.9 kG to 0.04
(1/25) at 2.2 kG with the polarization ratio flipping at 2.0 kG. Figure S.7 shows this did
not occur experimentally. The fundamental TEi0 mode was not evident in any
measurements. For the forward wave to intersect the fundamental mode, the B-field
10
.
I
v
i
i
i
|
I
M
I
I
I
I
I
I
I
|1
t
i
i
x no reflectors
o reflectors
X
o
C3
Od
U>
u
*
S,
e
o
|
0 *
•
a«
o
.1
03
N
•c
o
«0
og o
a
ft- .01
1.5
ooo
CD o o o
ooo
2.0
2.5
Cavity B-field (kG)
3.0
3.5
Figure 5.7. Polarization power ratio (V /H ) as a function of B-field. The horizontal mode
was dominant at all field values, and the fundamental TEI0 forward wave was
not observed in the vertical polarization.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
would need to be below 1.8 kG. When the magnetic field was lowered to find the
intersection, no microwaves were produced. This could be due to several factors. First,
at low magnetic fields, the e-beam’s Larmor radius is large, causing significant scraping
and plasma formation. This could impede the e-beam cavity interaction. Second, the ebeam a is very small since there is very little adiabatic compression, and thus, very little
kinetic energy existed in the perpendicular velocity to interact with the cavity.
The reflecting strips did not appear to modify the polarization ratio results over
the measured magnetic fields significantly. The strips did not cause a change in polarity.
However, the strips did appear to decrease the ratio slightly (increase in horizontally
measured signals).
Transported current measurements were made with a Rogowski coil on the
entrance to the RCS cavity (see Figure 3.1); results are plotted in Figure 5.8. These data
show that the average current entering the RCS cavity was 3 kA, which did not increase
with increasing B-field, as expected [MEN93].
1 • •
1.5
■ •
1 ■ ■ ■ ■ 1 ■ ■ ■
2.0
2.5
Cavity B-field (kG)
3.0
3.5
Figure 5.8 Transported current to the RCS cavity entrance as a function of B-field.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
The RCS small orbit gyrotron’s efficiency is plotted in Figure 5.9. The power
efficiency, r\, is calculated as the ratio of peak microwave power to the beam power,
where:
Tl=P(4w.vyPbe«n*100.
(5.1)
The peak efficiency measured was 2.0 %, but was generally below 1 %. This
was based on beam voltage of 800 keV and a beam current of 3.6 kA. This experiment
was conducted without reflecting strips on the cavity output. With reflecting strips at the
cavity exit the peak efficiency was typically less than 0.6 %.
■■ ■
2.0
'w'
>»
o
e
1)
*M
u
£
w
• ■1 • • • • 1■
.
.
.
X
x no reflectors
o reflectors
1.5
1.0
%
0.5
0.0
1.8
*
O
X
0
2.0
£$.
xx
••
2.2
X8
.
a
o
: i «r
2.4
2.6
2.8
Cavity B-field (kG)
3.0
3.2
Figure 5.9. Power efficiency for the RCS small orbit gyrotron as a function of B-field.
The efficiency may also be stated in terms of perpendicular efficiency, 1 ) ^ , since
microwave power for a gyrotron is driven by the perpendicular energy of the beam. This
efficiency may be defined as [WAL95]:
(5.2)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
83
Using this relation, the small orbit gyrotron yields a peak perpendicular power
efficiency of approximately 24 % (typically < 12 %) without reflecting strips and
typically less than 7 % with the strips.
~ 50
— i-----■
1 40 • o
i
-
+ H polarization
o V polarization
T3
So 30
<0
>
S3
*
w
3
O
oo
20
S3 10
£
<£
0
0
100
200
300
400
500
Microwave pulse length (ns)
600
Figure 5.10. Power versus microwave pulse length for the small orbit gyrotron. Pulse
shortening is clearly visible.
Figure 5.10 shows the microwave power as a function o f the length of the
microwave pulse. Pulse shortening is clearly observed, as the higher power shots
demonstrate shorter pulse lengths (recall that MELBA’s pulse length is in excess of 600
ns). The highest power ( > 20 M W ) pulse lengths are less than 200 ns. As discussed
previously in Chapter 2, pulse shortening is thought to be related to plasma generation by
e-beam scraping [BEN97, GRA96, LOZ93]. Optical spectroscopy on the large orbit
gyrotron has measured light produced by a plasma. This demonstrated the formation of
plasma in the RCS cavity collector. Furthermore, the microwave signals cut off abruptly
with the formation of this plasma. This will be discussed later in Chapter 6.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
CHAPTER 6
LARGE O RBIT RECTANG ULAR CROSS SECTIO N GYROTRON
EX PE R IM E N TS
Chapter six reports the results of experiments on the large orbit gyrotron. This
chapter is divided into the three magnetic cusps built and used for experiments. The
different cusps are reviewed in Chapter 3. The third cusp’s (II) axial and radial profile
were the most uniform in the development o f the axis encircling e-beam. The first cusp,
IA , used the 500 MHz bandpass frequency filters in gyrotron microwave emission
analysis. Cusps IB and II used heterodyne mixer signals for gyrotron frequency analysis.
Results for cusp II will also be presented which show a comparison of effects on
microwave emission by changing the diode magnetic field, as well as using tapered
cavities in an attempt to suppress unwanted modes. A summary of the different cusp
characteristics is provided in Table 3.1
6.1 Large O rbit RCS gyrotron results for Cusp IA
Using an axis encircling e-beam with a higher a than compared with the small
orbit experiments (>1 vs 0.3), mode control of the high power microwave emission as a
function of magnetic field was observed. Because the axis encircling e-beam used an
anode aperture that was slotted with a width o f 0.4 cm as opposed to a fully open circular
aperture, current from the large orbit gyrotron decreased by an order of magnitude as
compared with the small orbit gyrotron. Figure 6.1 plots the transported current entering
the RCS cavity as a function of magnetic field. The average current exiting the anode
aperture was on the order o f 500 A. The average current entering the rectangular
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
85
interaction cavity is approximately 250 A. This current loss could be due to cuspreflections in the e-beam current as well as e-beam scraping against the drift tube and
cavity walls.
400
350
Epa
w 300
| 250
a □□
8 200
I
150
t§ 100
1.2
1.4
1.6
1.8
2.0
2.2
Cavity B-field (kG)
Figure 6.1. Transported current to the entrance o f the RCS cavity using cusp IA in axis
encircling e-beam measurements. The entrance current appears to decrease
with increasing B-field.
Figure 6.2 shows the gyrotron microwave emission power in both the vertical and
horizontal polarizations as a function o f the field; (note: all of the measurements for this
cusp were taken with reflecting strips in the horizontal polarization). Figures 6.3 and 6.4
show signals from two shots that demonstrate power in the fundamental TE)0 mode and
in the next order TE0i mode. Peak power achieved in the vertically polarized,
fundamental mode was 6.2 M W . This occurred for a field of 1.47 kG. At this point peak
contributions from the horizontal mode were less than 2 M W . This trend reversed as the
field was raised to 1.66 kG. At this point a peak power measured in the horizontal
polarization was 10.8 M W , but the contribution from the fundamental TE10mode was
under 1 M W . These contributions were confirmed using the bandpass filters to determine
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
86
the e-beam-cavity mode interactions. A t lower B-fields (~ 1.5 kG) the fimdamental TE |0
mode dominated and other competing modes were minimal, but at higher B-fields ( ~ 1.7
kG) the polarization flipped and the horizontal TE0| mode was dominant.
The magnetic fields on the cavity using magnetic cusps as shown by figures in
Chapter 3 are opposite those of the diode (negative); in the large orbit measurements and
graphs in this chapter, the cavity fields are expressed as positive values (magnitude only).
However, the B-fields on the cavity are the reverse of those on the diode and aperture.
11
10
9
<u
'3
H polarization
7
6
<->
5
4
3
s
o
u
<u
£
o
Cu
V polarization
+
8
cuq
a
>
a
o
2
1
0
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
Cavity B-field (kG)
Figure 6.2. Peak power measured in vertical and horizontal polarizations for the large
orbit gyrotron (cusp IA ; reflecting strips were used in the horizontal
dimension).
Data was not taken below 1.3 kG cavity field as the microwave output was
negligible since the e-beam interaction is below fundamental cyclotron wave cutoff.
Furthermore, data was not measured above 2.1 kG, as the higher B-fields lead to mode
competition based on the dispersion relations (see Figure 6.7).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
87
—
1
—1
—1
—1
—
1
-1
—1
—1
—1
—-1
--1
--1 i i i--1
-= \____
r
n
a
„
•M JV H.
;
-
h '■
<«)
'^ — nA— (0
■
.
A.
lh> A .Afl_ ___:
Time (100 ns/div)
Figure 6.3. Data from MELBA shot
5183. This data was taken with a cavity
B-field of 1.66 kG. (a) voltage monitor
response (400 keV/div). (b) RCS cavity
entrance current (200 A/div). (c)
Vertically polarized microwave output
(0.2 MW/div). (d) Horizontally polarized
microwave output (4 MW/div). (e) Filter
A response (2 MW/div; 2.0 - 2.5 GHz),
(f) Filter B response (2 MW/div; 2.5 3.0 GHz), (g) Filter C response (0.1
MW/div; 3.0 - 3.5 GHz), (h) Filter D
response (0.67 MW/div; 3.5- 4.0 GHz).
Time (100 ns/div)
Figure 6.4. Data from MELBA shot
5191. This data was taken with a cavity
B-field o f 1.46 kG. (a) voltage monitor
response (400 keV/div). (b) RCS cavity
entrance current (100 A/div). (c)
Vertically polarized microwave output
(2 MW /div). (d) Horizontally polarized
microwave output (0.1 MW/div). (e)
Filter A response (0.5 MW/div; 2.0 - 2.5
GHz), (f) Filter B response (0.1
MW/div; 2.5 - 3.0 GHz), (g) Filter C
response (0.1 MW/div; 3.0 - 3.5 GHz),
(h) Filter D response (0.1 MW/div; 3.54.0 GHz).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
88
Figure 6.3 shows the horizontally polarized TE0t mode is dominant over the fundamental
T E 10 mode at 1.66 kG (MELBA shot 5183). The peak transported current is 290 A. The
peak power in this shot is 9.6 M W in the horizontal polarization, but only 0.3 MW in the
vertical polarization. The filters connected to the horizontal polarization cables and
microwave responses were seen in filters B (2.5 to 3.0 GHz) and C (3.0 to 3.5 GHz).
When the cavity magnetic field was changed to 1.46 kG (MELBA shot 5191), the
microwave polarizations reversed. The peak microwave emission in the horizontally
polarized TE0i mode dropped to 0.2 M W , while the TE|0 fundamental vertically
polarized power increased to 3.2 MW . As Figure 6.4 shows, the only filter response is
from Filter A (2.0 to 2.5 GHz). For this shot, the filters were connected to the vertically
polarized signal cables.
£
2
W'
C
UA
2.5
2.0
M
E
e
k.
1.5
£
1.0
°
+
Filter A power (2.0-2.5 GHz)
Filter B power (2.5-3.0 GHz)
Filter D power (3.6-4.1 GHz)
4)
£
1)
>
wm
£
0.5
04
0.0
•
1.4
1.6
Cavity B-field (kG)
1.8
Figure 6.5. Gyrotron microwave power out the bandpass filters with the filters in the
vertical polarization. The filters indicate a clear resonance at 1.47 kG with an
emission frequency response between 2.0 and 2.5 GHz. This corresponds to
the forward wave of the fundamental TE|0 mode.
Figures 6.5 and 6.6 show the relative gyrotron microwave emission power
response through the microstrip filters. Figure 6.5 shows the results o f the measurements
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
89
with filters in the vertical polarization. Whereas in the small orbit gyrotron, no signal
was seen below 1.8 kG, here the fundamental TE |0 mode is clearly evident at 1.47 kG.
The peak power measured between 2.0 and 2.5 kG was approximately 2.0 M W as
opposed to 0.3 M W for any other frequency filter. This relative difference indicates that
the fundamental TE|0 mode is the dominant mode at the lower magnetic fields. Figure
6.7 shows the waveguide mode and e-beam cyclotron dispersion relation interactions for
this cusp.
■I ii
£
i i i i i
+
+
s' 3
o Filter C power (3.0-3.5 GHz)
B
£
• Filter D power (3.6-4.1 GHz)
Z
2
<o
£
a.
« 1
£
13
04
□ Filter A power (2.0-2.5 GHz)
+ Filter B power (2.5-3.0 GHz)
•
t+
++
0
1.3
1.5
1.7
1.9
Cavity B-field (kG)
2.1
2.3
Figure 6.6. Gyrotron emission microstrip bandpass filter response as a function of cavity
magnetic field. The filters were placed in the horizontal polarization. The
resonance at 1.67 kG is from the backward wave (B W) of the second
harmonic o f the second order TE0| mode.
The horizontally polarized TEoi gyrotron emission is dominant at 1.67 kG. This
is evident in Figure 6.6 where the diagnostic response is between 2.5 and 3.0 GHz.
However, by observing the interactions on the dispersion diagram in Figure 6.7, it is
evident that the backward wave of the second harmonic of the TE0i mode dominates
over other interactions in the RCS gyrotron at this magnetic field. In this case, the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
forward wave of the TEoi mode was observed but its magnitude was an order lower than
the backward wave interaction.
Figures 6. 5 and 6 .6 show that the filters measured some gyrotron emission in
both Filter C (3.0 - 3.5 GHz) and Filter D (3.5 - 4.0 GHz) even when the dominant signal
came from Filter A or Filter B. These emission signals, when compared with e-beam
4.5
TE20
4.0
TEl
.TEOI
3.5
X
o
TE10
» 3.0
0
a
<u
1 2.5
2.0
80
-60
-40
-20
0
20
40
60
80
Kz (1/m)
Figure 6.7. Dispersion diagram for the large orbit RCS gyrotron using cusp IA. Marker
1 indicates the dominant interaction o f the fundamental mode. Marker 2
indicates the dominant interaction o f the second harmonic TE0| mode. The
e-beam interactions are based on an a (V pe^/V p^,) o f 1.0 as measured
experimentally ( see chapter 3). (a) e-beam interaction using a B-field of
1.47 kG. (b) e-beam interaction using a B-field of 1.67 kG. (c) second
cyclotron harmonic using a 1.47 kG B-field. (d) second cyclotron harmonic
interaction using a 1.67 kG cavity B-field.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
structure interactions on the dispersion diagram o f Figure 6.7, suggest some mode
competition from the TE| i and the TE 20 modes from harmonics of the e-beam cyclotron
wave interaction. Experimental results have demonstrated that the second harmonic can
be excited by a threshold value of current, but that the current must be increased further
to excite the fundamental mode [BRA94]. I f the current is then increased further, the
fundamental mode can grow at the expense o f the second harmonic [BRA94].
This first cusp showed that the gyrotron’s high power microwave emission
exhibits a linearly polarized output that is dependent on the magnetic field. Figure 6.8
shows the polarization power ratio for this cusp. It is very clear from this plot that
> i 1 1 1 p 1 1 1 1 I i 1 1 1 I ■! 1 1 1 I 1 1 1 1 I 1 r f f ; 1 1 1 1 | 1 1 1 1 .
□:
1.3
1.4
1.5
1.6 1.7 1.8 1.9
Cavity B-field (kG)
2.0
2.1
Figure 6.8. Polarization Power ratio for the large orbit RCS gyrotron (cusp IA ) as a
function of cavity B-field. The shift from one dominant polarization in the
TE 10 vertical mode to the TEoi mode in the horizontal polarization is clearly
visible above.
microwave emission polarization is flipped from a vertically dominant output at 1.47 kG
to a horizontally dominant output at 1.67 kG. The peak polarization ratio was
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
(Pverticai/Phorizontai) approximately 20, and this dropped to 0.02 (1/50) as the field was
raised.
The large orbit gyrotron’s peak electronic efficiency o f 5.6 % was much higher
for cusp IA as compared with the small orbit gyrotron (< 2%). Furthermore, the peak
efficiency improved with the other cusps built. In Figure 6.9, the peak power efficiency
is plotted as a function of cavity B-field for cusp IA . The efficiency was calculated
using Equation 5.1. The peak perpendicular efficiency,
, was 11.2 % for cusp IA.
This was calculated using Equation 5.2 and assumed that a was equal to 1.0.
6 -------------------------
5 -
B
a
B
S'
E, 4 ■
*
4 :
u
c
2
£
w
a0
0
:
□
3 ’
I0 #
'
;
2 i
Be
B0
0
i
■0 a
0°
jjj
J|1
a9
21
21
CP | □_
|D B g
%
0
11
(ID
03
0
D
□
□
0300
0 0
0
0
00
0
0
n B
GL □
B
u
0o ■ 0
IQ B^L
q
e ■
. >B
in.t* . . .
y 1 ** ** *‘ ** 1 ** *1 ‘1 ■ 1 ‘• ■
‘ w
1.2
1.4
:
a
□
1.6
1.8
Cavity B-field (kG)
f
i . . .
2.0
.
2.2
Figure 6.9. RCS large orbit gyrotron efficiency as a function of cavity B-field (cusp IA ).
The peak efficiency for this cusp was 5.6 %.
The peak microwave power is plotted as a function of microwave pulselength in
Figure 6.10. As in the case of the small orbit RCS gyrotron, microwave pulse shortening
is evident. The pulse lengths for microwave pulses with magnitudes greater than 4 M W
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
are less than 150 ns. However, MELBA’s voltage pulse lasts for an average of
approximately 700 ns.
1 1 1 1 1 1 1 1
£
u
TJ
m
m
s
&o
0)
S
£
•
4-1
9
O
<0
£
+
10
’
o V polarization
+ H polarization
+
+
8
++
6 L
4
:
2 ■
£
+ o
o + ++ +
+ ^0
o o > ; +: :
° +o# ++
O+40$*® +ot*8++
° + +
. . + . ?+? to+°.*pO?
0
0
-
o
to . t ♦ „ 0
100
200
300
400
Microwave Pulse length (ns)
500
Figure 6.10. Peak gyrotron microwave power as a function of pulse length for cusp IA.
Pulse shortening is clearly evident.
6.2 Large Orbit RCS gyrotron results for Cusp IB
Cusp IB brought several advantages over cusp IA. First, for a large orbit
gyrotron, the field reversal of the cusp was reduced from 14 cm to 9 cm. Second, the
distance to the interaction cavity was reduced to 28.5 cm from 45.5 cm. Axial field
variations were also smoothed out. These differences were seen in Figures 3.9 versus
Figure 3.7 and discussed in Section 3.2.2. The 500 M Hz bandpass filters were not used
in cusp IB experiments. Instead, a heterodyne mixer system with higher accuracy was
used for frequency analysis. This is discussed in Section 3.5 and shown schematically in
Appendix H.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
Time (100 ns/div)
Figure 6.11. Data from MELBA shot 5711. This data was taken with a cavity B-field of
1.49 kG. (a) voltage monitor response (400 keV/div). (b) RCS cavity
entrance current (100 A/div). (c) Vertically polarized microwave output (2
M W /div). (d) Horizontally polarized microwave output (0.2 MW/div).
i
i
Time (100 ns/div)
IF frequency (122.07 MHz/div)
Figure 6.12. (a) Heterodyne mixer signal from shot M 5711 (100 mv/div). (b)FFT of the
mixer signal. The resonance at 160 M Hz corresponds to a signal o f 2.16
GHz, and the resonance at 850 M H z corresponds to a signal at 2.85 GHz.
The mixer signal was taken with the mixer in the horizontal polarization.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
95
Figures 6.11 and 6.12 show typical data for the large orbit gyrotron for one shot.
Figure 6.11 represent the voltage, current, and microwave output (for both polarizations).
This data was collected for M ELBA shot 5711 which was taken with a cavity magnetic
field of 1.49 kG. To contrast this, Figures 6.13 and 6.14 show the results when the
cavity magnetic field is raised to 1.88 kG. Figure 6.11 shows a flattop voltage pulse
Tim e (100 ns/div)
Figure 6.13. Data from M ELBA shot 5870. This data was taken with a cavity B-field of
1.88 kG. (a) voltage monitor response (400 keV/div). (b) RCS cavity
entrance current (200 A/div). The initial spike was due to the current
monitor being struck by the e-beam, (c) Vertically polarized microwave
output (0.5 MW /div). (d) Horizontally polarized microwave output (1
MW/div).
around 800 keV, a peak entrance current o f approximately 150 A, a peak microwave
power in the vertical TE)0 polarization of 5 MW , and a horizontally polarized signal that
resulted in less than 0.3 MW . This can be compared with Figure 6.13 where the flattop
voltage was similar, and the entrance current showed a spike due to the e-beam striking it
prior to providing a current o f 180 A. At higher B-fields, the entrance current Rogowski
coil showed spikes from being struck by the e-beam. With the higher e-beam a and
higher solenoidal magnetic field, more of the e-beam could be reflected, and thus strike
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
the Rogowski coil. At the higher B-field, the vertically polarized power measured in
Figure 6.13 was 0.8 MW while the horizontally polarized signal jumped to 3 MW.
Figure 6.12(b) shows the Fast Fourier Transform (FFT) of the mixer signal from Figure
6.12(a). The FFT performed on the Tektronix DSA602A shows a difference frequency at
160 MHz. The local oscillator was set at 2.00 GHz, below the cavity cutoff frequency for
the modified S-band waveguide. Thus, the gyrotron microwave emission frequency was
determined to be 2.16 GHz. This corresponded well with the cold test resonance
frequency presented in Chapter 3. The dispersion diagram (see Figure 6.16) shows this
interaction is due to the gyrotron forward wave of the fundamental TE |0 mode. A second
resonance appeared at 850 MHz, corresponding to the TE0i i mode. Even with the mixer
in the horizontal polarization, the cross polarized signal from the fundamental TE ioi
mode dominated at lower B-fields.
(a)
Time (100 ns/div)
IF frequency (122.07 MHz/div)
Figure 6.14. (a) Heterodyne mixer signal from shot M5870 (100 mV/div). (b) FFT of
heterodyne mixer signal from shot M5870. The FFT shows two strong
difference frequencies at 60 M H z and 350 M Hz, which correspond to
signals of 2.56 GHz (TE 102) and 2.85 GHz (TE0n). Other modes are clearly
visible in this FFT. The heterodyne mixer was in the horizontal polarization
for this MELBA shot.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
Figure 6.14 (b) shows the FFT of the mixer signal from M5870; here, several
possible modes are competing. The local oscillator for this MELBA shot was set at 2.5
GHz. While four possible difference frequencies appear in Figure 6.14(b), two are small
and over 20 dB down from the two dominant signals. The first difference frequency
occurs at 60 MHz, which, when compared with other data showed the interaction to be
due to the forward wave of the TE | 02 mode and possibly a contribution from the
backward wave of the TE)0i mode from the second cyclotron harmonic. The
4.5
x mixer signal V polarization
mixer signal H polarization
0
o
c
(0
s
<T
4>
£
3.5
0
X
N
X
o
0
4.0
^
TTP111
IM 1 1
00
3.0
cocfe
O faftg E*
0
x
*
; x>* * 0 * a
1 jn X M h L a ih
2.5
____TE103
^ -------- TE011
<
:
x
1
x
8x *
*
®
ft)
8
*
x
*
*
<
2.0
1.5
J
1.4
1.6
_
1
i
1.8
i
i
lu X v A
------ TE101
i
2.0
Cavity B-field (kG)
Figure 6.15. Frequency response o f the RCS large orbit gyrotron (cusp IB ) as a function
of magnetic field. These results came from heterodyne mixer measurements
with the RF supplied from either the horizontal or vertical polarizations. The
TEiot, TE102, TEon, and TEm cavity modes were observed. Power levels
were not measured with the mixer, however, below 1.6 kG, the fundamental
mode dominated by a minimum of 1 order of magnitude. Above 1.8 kG, the
T E 102 and TE0n modes dominated competing modes.
T E |02 mode did not appear in cold testing o f the microwave cavity, since the TE 102 mode
has a field null at the center where the probe was placed during cold testing [JAY97].
The second FFT difference frequency was at 350 MHz. This corresponded to a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
98
frequency measurement of 2.85 GHz. This was due to the TE0| i cavity mode. The third
FFT difference frequency peak observed was thought to be due to the fundamental TE 101
mode and the fourth difference frequency in Figure 6.14(b) was thought to be due to the
TE| 11 mode, but these last two signals were weak, and the local oscillator frequency was
changed to examine these possible modes. Figure 6.15 shows the results of frequency
measurements completed using the heterodyne mixer. The mixer signal responses were
not reviewed for power levels; however, at lower magnetic fields the magnitude o f the
4.5
TEH
4.0
,*■
TE01
'n '
SC
O
3.5
TE10
» 3.0
o
a
9i
2.5
£
2.0
Kz (1/m)
Figure 6.16. Dispersion diagram for the large orbit RCS gyrotron using cusp IB. The ebeam interactions are based on an a (Vperp/Vparaiiei) of 1.0 for the lower field
interactions. These include (a) and (c) which are the e-beam lines for a Bfield of 1.47 kG and the second harmonic of this field interaction. The
higher B-field interactions (b) and (d) assume a beam a of 1.3. The ebeam interaction in (b) is at 1.95 kG and (d) is the second cyclotron
harmonic of (b). The dominant interactions observed were the forward
wave of the fundamental mode(TEio) at 1.47 kG and the forward wave of
the oppositely polarized TEot mode at 1.95 kG.
fundamental mode was at least 2 orders of magnitude greater than any competing mode.
When the B-field was raised above 1.8 kG, the dominant modes were the TE0u and the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
99
T E ,02 modes. This is evident in Figure 6.14(b). Figure 6.16 shows waveguide and ebeam cyclotron wave dispersion relations for this cusp. Based on glass-plate
measurements, the e-beam a is 1.0 at the lower B-field (1.5 kG) interaction, but it is 1.3
for the upper magnetic field (1.9 kG) interaction. Figure 6.15 clearly shows the different
cavity modes that were excited in this gyrotron experiment. The TEioi, TE|02, TE0|i, and
TE m cavity modes were observed. However, at low magnetic fields (i. e., 1.5 kG), the
TEioi mode was dominant. The microwave polarization did flip to the horizontally
dominant TE0i i mode as the field was raised to 1.9 kG. The fundamental TE|0| mode did
not turn off, although its value decreased at the higher fields, and this presented mode
competition which was evident in Figure 6.14. Figure 6.16 shows that at lower magnetic
fields, the fundamental TE|0| mode was dominant. As the B-field was raised, the TE | 02
mode, the TEjoi backward wave, the TE0n, and the TEm mode appear to compete.
However, the TE0n mode appears dominant by its grazing intersection at approximately
14
<D 12
“O
‘3
<U
£
£
•o
<L>
N
eP
8
6
4
s
2
o
<5
£
o
a-
o
10
O
a
+ Horizontal Polarization
o Vertical Polarization
0
1.3
*
+
o
■rrf.+
g-a>. *
l» NtHll ffllfrll 0
1.4
1.5
1.6
+
1.7
1.8
1.9
2.0
2.1
Cavity B-field (kG)
Figure 6.17. Peak power measured in vertical and horizontal polarizations for the large
orbit gyrotron (cusp IB; reflecting strips were used in both dimensions). The
peak power measured in the fundamental mode was 13.8 MW.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
1.9 kG. At this field the polarization o f the microwaves is dominated by the horizontal
(TE0|) mode as opposed to the fundamental TE|0 mode. At this 1.9 kG field the TEioi
mode has an axial wavelength that is too long (kz ~ 0) to be fitted in the rectangular
cavity [HOC98].
The power measured in the linearly polarized waveguides is shown in Figure
6.17. The dominant mode was the fundamental mode (TEioi) which achieved powers as
high as 13.8 MW at a magnetic field of 1.47 kG. In these measurements, reflecting strips
were placed in both polarizations. This peak power was more than double that measured
in the fundamental mode of the first cusp. The power measured at 1.92 kG in the
horizontal TE0i i reached a maximum o f 6 M W . This was a decrease as compared with
the first cusp, but as opposed to the previous backward wave interaction, the forward
wave was observed.
The polarization power ratio is shown in Figure 6.18 as a function of cavity
magnetic field. The maximum power ratio increased significantly using cusp IB. The
polarization ratio (PwrmjCrowaVe, v / PwrmjCrowavei h ) climbed as high as 300 at lower
magnetic fields and dropped to as low as 1/30 when the microwave power output flipped
polarizations. When these results are compared with M AGIC 2D simulations completed
in Chapter 4 (see Figure 4.9), the polarization power ratios compare well. Both
experimentally and in simulation the polarization is flipped at approximately 1.9 kG.
M AG IC predicted power ratios on the order o f 100 for low magnetic fields and 0.3 at
fields near 1.9 kG, which are on the same order as those measured experimentally.
M AG IC 3D simulations in Chapter 4 (see Figure 4.11) also demonstrate the ability to flip
polarizations as a function o f externally applied magnetic field.
The current transported through cusp II to the entrance of the RCS cavity is
shown in Figure 6.19. Unlike the small orbit gyrotron, this cusp showed a decreasing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
101
current as the solenoidal magnetic field was raised. This is due to several factors. First,
increasing the e-beam a with the increasing solenoidal B-field increased the amount of
1000
5
>
o
s
100
04
<3
£
10
£
a
o
1
03
N
£
.1
01
1.3
1.4
1.5
1.6 1.7 1.8 1.9
Cavity B-field (kG)
2.0
2.1
Figure 6.18. Polarization power ratio for the large orbit RCS gyrotron (cusp IB) as a
function of cavity B-field. The shift from one dominant polarization in the
vertical mode (TEt0i) to the horizontal polarization is clearly visible above.
The peak ratio achieved was 300. As the B-field was raised, the ratio
dropped to 0.03 (1/30).
<
500
200
100
-
1.3
1.4
1.5
1.6
1.7
1.8 1.9
Cavity B-field (kG)
2.0
2.1
Figure 6.19. Transported current to the entrance o f the RCS cavity using cusp IB in axis
encircling e-beam measurements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
102
the e-beam that was reflected [JAY97], and secondly as the e-beam’s a was raised, the
amount o f coherent off-centering increased, which allowed the e-beam to scrape more.
This is visible by the spike in entrance current in the M ELB A shot demonstrated in
Figure 6.13. The average current at lower magnetic fields (~ 1.5 kG) was approximately
250 A, and this decreased to an average o f 200 A at higher B-flelds (~1.9 kG).
Cusp IB ’s efficiency improved over the first cusp.; this is seen in Figure 6.20
where the peak efficiency was 6.2 %. This corresponds to a peak transverse efficiency
o f approximately 12.5 %. Unlike cusp IA , however, cusp IB demonstrates two areas of
increased efficiency. Both of these efficiency peaks occur where the microwaves are
dominant in one polarization (TEi0) or the other (TE0|). These peaks occur at fields of
1.47 and 1.92 kG respectively.
□
a
% bJb
a l%q*wl 0
0
qEB
i I i i i 11 i B i
1.3
1.4
1.5
□
a
□
tP |0
I
-0
0
1.6 1.7 1.8 1.9
Cavity B-field (kG)
□
□ □
B
□
2.0
2.1
Figure 6.20. Power efficiency as a function of cavity B-field (cusp IB). The large orbit
gyrotron’s peak efficiency was 6.2 %. The efficiency was highest at the
points where the two dominant resonances occurred.
Pulse shortening is observed in this cusp, as it was in cusp IA and in the small
orbit RCS gyrotron. The microwave power as a function o f pulse length is shown for
cusp IB in Figure 6.21. Spectroscopy showed that plasma was formed with the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
103
16
/—
\
+
°
o
£
H polarization
V polarization
o
o
o
o
+
s
o
p i o + H frfr
0
100
200
300
400
Microwave pulse length (ns)
500
Figure 6.21. Microwave power as a function of pulse length for the large orbit gyrotron
(cusp IB). As in previous cases, pulse shortening was evident in cusp IB.
microwave pulse. The plasma has several sources including the explosive emission
cathode, the e-beam scraping in the drift tube and cavity entrance, and the e-beam
collector where the e-beam is dumped against one wall of the waveguide after exiting the
cavity. The spectroscopic results w ill be discussed later, in the cusp II results.
6.3 Large Orbit RCS gyrotron results for Cusp II
As described in Chapter 3, cusp IB had some azimuthal variations in the magnetic
field of the cusp region; these were corrected in cusp II. The azimuthal magnetic field
profile was shown in Figure 3.10. With the improvements in the fields of cusp II, several
experiments were conducted. The effect o f the reflecting strips was tested by taking
experimental measurements without the horizontal strips. In an attempt to raise the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
microwave power and minimize reflections, the diode magnetic field was varied and
microwave results compared with that of the magnetic fields used in the other large orbit
measurements. Another set of experiments using cusp II was completed to attempt to
suppress unwanted modes. This was done by using tapered cavities in either the vertical
or horizontal dimension. Spectroscopy was performed on cusp II by placing a fiber optic
line in the output window to view the RCS cavity during microwave measurements, and
running the fiber optic line into a 0.75 m spectrograph with a CCD camera attached. The
fiber optic was used to observe plasma formed by the cathode explosive emission as well
as the plasma formed by the e-beam being dumped to the wall after exiting the RCS
cavity.
6.3.1. Cusp I I results utilizing the uniform RCS cavity
Transported current measurements were conducted on cusp II using the
rectangular interaction cavity; the experimental configuration is shown in Figure 3.16.
The results for this are shown in Figure 6.22. As mentioned earlier, the average aperture
current was approximately 500 A. The current that was transported through cusp II
(without being reflected) that entered the RCS cavity ranged between 200 and 300 A, and
approximately 80 % o f that was measured after exiting the cavity. In the tapered cavities,
currents were on the same order as in the uniform cavity case.
Figure 6.23 shows the results of microwave power measurements for the large
orbit RCS gyrotron using cusp II. The peak power in this gyrotron with cusp II measured
9.2 M W in the fundamental TEioi mode, and the peak power measured in the horizontally
polarized TEoi i mode was 3 M W . This gyrotron with a uniform cusp did not reach as
high a power as in cusp IB (~14 M W ), but the microwave emission here demonstrated
wider resonance magnetic field, varying over 100 Gauss range (1 .4 -1.5 kG) as opposed
to a specific magnetic field (i.e. 1.47 kG), as in cusp IB. This gyrotron cusp II produced
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
600
,1 1 | r
T
rT—* ' ' 1 '
T"
500
□
1 400
|
:
0
□
'w'
□
?
□
□
-
1' '
T r
□
0
□
X
B □
'
1
'
Aperture
entrance
exit
•
□
□
-
□
□
300
73
s
0
,
£
0
X
100
0
0
X
1.2
i i.
1.3
8
X
X
X
X
’
o
8
X
0
X
□
□
X
X
8 200
£
o
0
I t
0
X
0
X
□
a
0
X
8
0
*
8
a
. 1
1.4
lJLj
l_l_t ■ ■ 1 ■
1.5 1.6 1.7 1.8
Cavity B-field (kG)
i . . . i .
1.9
2.0
2.1
Figure 6.22. Transported current measurements for cusp II. The aperture current shows
the current prior to going through the cusp. The average aperture current
was approximately 500 A. The entrance current which was measured with
a Rogowski coil averaged around 220 A for cusp II. The exit plate current
was measured with a graphite paddle at the exit of the RCS cavity. The
average exit current was approximately 180 A.
9 M W in the fundamental TE 10i mode between magnetic fields of 1.4 and 1.5 kG on the
cavity. The higher order modes were suppressed more effectively at the lower magnetic
fields. This can be seen by the frequency measurements in Figure 6.24 and by the
polarization ratio shown in Figure 6.25.
The results of heterodyne mixer signals are shown in Figure 6.24. Some of these
measurements were taken using two heterodyne mixers at the same time in order to get
the exact frequencies (resolve sum or difference) without repeating measurements. The
experimental configuration for the heterodyne measurements is shown in Appendix H.
At low B-fields, there is little mode competition with the fundamental TE10i, but as the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
106
s
10
t
£
9
8
■8
7
3>
6
1
5
I
4
o
3
+
°
s>
H polarization
V polarization
o
CP o o
00
o
o
O O
o
O
0
1.3
J ++
<t>o
O
■M
1.4
1.5 1.6 1.7 1.8
Cavity B-field (kG)
1.9
2.0
Figure 6.23. Power out linearly polarized S band waveguide for the RCS large orbit
gyrotron (cusp II). The peak power measured was 9.1 M W in the vertical
polarization and 3.0 M W in the horizontal polarization.
magnetic field is raised, mode competition becomes significant. The dispersion diagram
that shows the modes’ interactions is shown in Figure 6.16. At high magnetic fields,
frequency components from five different modes were observed: TE0n, TEioi, TE |02 ,
TE m , and the TE 201. The dominant mode at the higher magnetic fields was the TE0n,
which dominated the other modes by a factor o f two or more.
Figure 6.25 shows the polarization power ratio for the large orbit gyrotron (cusp
II). The polarization ratio, Pwrvertica/ Pwrhorizontal, shows a much stronger fundamental
mode interaction. The polarization ratio jumped from 300, which was measured in cusp
IB, to as high as 2000 in cusp II. The polarization ratio did flip at higher magnetic fields;
the minimum of the polarization ratio was approximately 0.12 (-1/9). The mode
competition from the TE 102 mode and the backward wave o f the fundamental mode
sustained the vertically polarized microwaves. Clearly, this mode competition is not
desired since it apparently reduces the microwave production from the horizontal mode at
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
107
4.5
/n
X
o
w'
I
x = V polarization
o = H polarization
4.0
TE201
T E lll
■TE103
TE011
30
I 2,
2.0
X
1.2
X q jlo X
»
M X W N fl& X
*
1.4
1.6
1.8
Cavity B-field (kG)
-T E 102
-T E101
2.0
Figure 6.24. Frequency response of the large orbit gyrotron (cusp II) as a function o f
cavity B-field. As is clearly evident, mode competition was much worse at
higher magnetic fields.
the higher magnetic fields. M AG IC 2D simulations showed strong mode competition at
higher magnetic fields (since kz is set to zero in the simulation) from the TEu mode;
these did not demonstrate the mode competition as strongly at fields around 1.9 kG.
The electronic efficiciency o f the RCS large orbit gyrotron in cusp II improved
approximately 25 % over the previous cusp. This is shown in Figure 6.25 where the peak
efficiency was approximately 8 %. Using Equation 5.2 for the transverse electronic
efficiency, this would be approximately 16% assuming a e-beam a of 1.0. This gyrotron
(using cusp II) produced the highest efficiency results o f all o f the experiments conducted
on RCS gyrotron devices.
In an effort to further increase the power o f the fundamental TEioi mode and raise
the polarization ratio, the horizontal reflecting strips were removed from the cavity exit
prior to the e-beam dump. While this did reduce the peak power in the horizontal
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
108
a
10000
>
~
1000
*
100
o
Oon o
0 O
OO
*
<0
I
00o °o a
0
§
10
O
o
0
o
o o
o
o'
* ■■ 1■ • * ■ 1■ • ■ * 1• ■■ ■1 ■ ■* ■1 ■■ • ■1 • • • ■
.1
1.3
1.4
1.5 1.6 1.7 1.8
Cavity B-field (kG)
1.9
2.0
Figure 6.25. Polarization power ratio as a function o f cavity magnetic field for the large
orbit RCS gyrotron (cusp II).
o
o
o
o
0
e
.
00
o
>>
o
S
<0
o
0
o
0°o
°
$3
w
: o
00
8°
•
0
1.3
1.4
1.5
o
0
0
® 0
0
03 ° °
0 O 0 .
8e
08
00
i.9 »i . i 9i i i 1
1.6
1.7
1.8
Cavity B-field (kG)
1.9
2.0
Figure 6.26. Efficiency for the large orbit gyrotron (cusp II).
polarization from 3 to 2 M W , the peak power in the fundamental mode dropped to under
7 MW . The results o f microwave power measurements without the horizontal reflecting
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
109
strips is demonstrated in Figure 6.27. Only one shot on MELBA achieved 7 MW , and
the remainder were under 5 MW. This showed that removal of the strips was not
desirable because the Q was too low. Since the output waveguide was of the same
dimensions as the RCS cavity, coupling effects may have played a large role in the
results, i.e., changing effective cavity wavelengths.
The polarization power ratio is shown in Figure 6.28 for the RCS gyrotron
without the horizontal reflecting strips. Similar to the power measurements, these results
were not anticipated. While it was expected for the polarization ratio to increase as the
1 1 ■ I 1 1 1 pi 1 1 I 1 I I I 1 I I I ' » ' I I I I I
a>
!2
‘3
+
H polarization
o o
3
3
o
o
<0
£
V polarization
o o
u
s
£
°
o«
1
£
0
1 .3
1.4
1.5 1.6 1.7 1.8 1.9
Cavity B-field (kG)
2.0
2.1
Figure 6.27. Power out of the RCS gyrotron when the horizontal reflecting strips have
been removed.
horizontal mode was not as strong, this did not occur. The highest polarization ratio
achieved was approximately 300. The lowest ratio achieved was approximately 1/3.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
no
1000
o oo
° o
%
100
%
C3
Qd
<D
Io
o
oo
o «P
10
O
0 °8
0
0 .0
°o
cu
e
o
s
N
I
£
l
O
O
o
o
.1
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
Cavity B-field (kG)
Figure 6.28. Polarization ratio for the large orbit gyrotron (cusp II) with the horizontal
reflecting strips removed.
6.3.2. Diode magnetic field optimization measurements
Measurements were taken in order to optimize the magnetic field on the diode.
This field was varied between 0.9 kG and 1.8 kG. The microwave power results did not
improve over those taken using a field of 1.1 kG in most cases. Some o f this was due to
increasing reflections o f the e-beam in the cusp, or more e-beam scraping prior to
reaching the RCS interaction cavity. However, the power in the fundamental mode did
improve slightly in one case, where the diode magnetic field was raised to 1.2 kG; the
peak power measured in the fundamental TE)0| mode was 9.8 M W . This was at a cavity
magnetic field of 1.51 kG. Using this diode B-field did not improve results for the
horizontal polarization, where the reflecting strips were again placed in the cavity output.
The peak power in the horizontal TE0i i mode was 1.8 MW. These microwave power
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
measurements with the diode magnetic field of 1.2 kG are summarized in Figure 6.29
(which is plotted as a function o f cavity B-field).
r—■>
£
<U
■o
10
9
o o
8
7
’3 6
eo
U
5
£
4
£
<->
s
3
o
u 2
£
1
£
0
1.3
0
V Polarization
+
H Polarization
oo°
o
O
o
o
co°o
O
o
<b
<V
■♦ 1■+
1.4
i ■*
1.5 1.6 1.7 1.8
Cavity B-field (kG)
1.9
2.0
Figure 6.29. Power out linearly polarized waveguides for the large orbit gyrotron (cusp
II) when the diode magnetic field was raised from 1.1 kG to 1.2 kG.
The polarization ratio only flipped (to a ratio of less than one) for two cases using
the higher diode B-field. The polarization ratio was as high as 1000 for these
measurements but only dropped to approximately one as the cavity B-field was raised
from 1.5 to 2.0 kG. Thus, mode competition from the TE 102 and the TE|0i backward
wave reduce the microwave power generated from the TE0i 1 mode. These interactions
can be seen on the dispersion relations in Figure 6.16. The polarization ratio is plotted as
a function of cavity B-field for the large orbit RCS gyrotron (cusp II) with a higher diode
B-field in Figure 6.30.
The power efficiency of the RCS gyrotron did not improve with varying the diode
B-field. The best case, next to the original 1.1 kG on the diode was when the field was
raised to 1.2 kG. This case is shown in Figure 6.31 which plots the power efficiency as a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
112
function of cavity B-field. The highest power efficiency measured in these experiments
was 6.2 %.
10000
> 1000
o«P ° o
100
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Cavity B-field (kG)
Figure 6.30. Polarization ratio for the large orbit gyrotron (cusp II) with the diode
magnetic field raised from 1.1 kG to 1.2 kG.
7
6
0
1.3
1.4
1.5 1.6 1.7 1.8
Cavity B-field (kG)
1.9
2.0
Figure 6.31. Efficiency o f the RCS large orbit gyrotron (cusp II) when the diode field
was raised by 100 Gauss to 1.2 kG.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
6.3.3. Tapered cavity experiments utilizing cusp I I
Tapered cavities were built in an attempt to suppress undesirable modes in the
RCS large orbit gyrotron. The tapered cavities are shown schematically in Appendix I,
Figures I. 1 and 1.2. Cavity B was tapered in the vertical dimension to suppress the TE0i
horizontal mode. This cavity also did not have horizontal reflecting strips. Cavity C was
tapered in the horizontal dimension and had only horizontal reflecting strips to suppress
the TE | 0 vertical mode. The tapered cavities did suppress microwave emission at the Bfields and frequencies where the uniform cavity produced microwaves, but with a shift in
B-field or frequency, these modes were not completely suppressed.
Figures 6.32a and 6.32b show the microwave power measurements for cavities B
and C as a function o f cavity magnetic field. The diode magnetic field was set at 1.1 kG
as in the uniform case and as in cusp IA and cusp IB data. Figures 6.33a and 6.33b give
the gyrotron emission frequency results from mixer measurements for the two cavities.
Cavity B did not produce horizontally polarized microwaves at 1.9 kG as in the uniform
cavity case. As the magnetic field was raised, it was apparent that the TEoi horizontally
polarized mode produced microwaves at 2.1 kG. This is shown in Figure 6.32a; the peak
power was 3 M W in this polarization. The peak power in the fundamental TE |0| mode
was 6 M W with the cavity (B) tapered in the vertical dimension. The fundamental mode
T E 10i frequency remained at 2.17 GHz, but the horizontally polarized TE0n mode shifted
to range between 2.9 and 3.2 GHz. This is observed in Figure 6.33a. This corresponds
with the results shown in Table 3.2 where the resonant mode o f the TE0n mode for the
uniform case was 2.84 GHz, but a uniform cavity with the smaller dimensions had a
TE0i i resonance of 3.19 GHz. The results of tapering the cavity (B) did not produce a
highly polarized result in the fundamental TEioi mode with the TEon mode suppressed. It
did, however, shift both the frequency and magnetic fields required for interaction.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
(a)
(b)
t i1i i [O
£
2
o
u
!2
‘3
oo
0)
>
(3
*
3
o
u
U
£
£
«>
o
o o
o_
o
0
o
CO
o o
V polarization
+
H polarization
°
°o 0
+
0
%«®o°
P
o° +
+ o
1.3
0
o+
cP
o
°0
> + ■ ih i^ ^ W
12
I I I I I I I I I I I I I I I I
*
ii
ii
®
++'
£
'w'
<u
73
3
00
4>
>
C3
£
s
o
u
<u
o V polarization
10
+
8
6
4
o o
2
o '* ? ? •
n4m *
1■■■■1 *
1.5 1.7 1.9 2.1 2.3
Cavity B-field (kG)
£
H polarization
0
+1
1.5
o
nH|4n
. * 1 ,1
1.7 1.9 2.1 2.3 2.5
Cavity B-field (kG)
Figure 6.32. Power measured in the large orbit gyrotrons when tapered cavities were used
to replace the uniform cavity, (a) Cavity B power measurements where the
vertical dimension is tapered, (b) Cavity C power measurements; here the
horizontal dimension was tapered.
When the taper was changed in order to attempt to suppress the fundamental
mode (this used cavity C) the results were different, as in Figure 6.32b. The vertical
polarization still dominated, however, the forward wave of the fundamental TEioi mode
was suppressed. Instead, the TE | 02 and backward wave of the TE)0i modes dominated.
Heterodyne frequency measurements demonstrated the vertically polarized signal
appeared at 2.47 GHz. The peak power achieved in the vertical polarization was 12 MW .
Here, as in the cavity B case, the resonance occurred at higher magnetic fields (~ 1.8 kG
as opposed to 1.5 kG). Furthermore, below 1.5 kG, no gyrotron microwave production
was observed (this was below the cutoff frequency for the fundamental mode). The
horizontally polarized mode only reached a peak power of 1.5 MW . Hence, cavity C did
not enhance its mode selection in any manner. Figure 6.33b shows the modes present in
gyrotron emission frequency measurements completed on tapered cavity C. Both tapered
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
115
(a)
4.5
| I I I | I I I | I I I
x Mixer in V polarization
Mixer in H polarization
0
~ 4 .0
°„
- x i r -0 - 0 - 0 -------------------
0
TE201
N
X
S 3 .5
TE111
>»
U
S
o 00
0 0 0
§ .3 .0
" V
XO
tL,
rS
2.5
oxm x
W i k &> * * * *
— 0 0
oo 0 0 0
0
0
«o o x
* * °x X X * 0
1 1 I 1 1 1 I 1 -« — 1— L —1— 1— 1—
2.0
1.2
1.4
1.6
0
^
1.8
0 -0
0 o
TE011
(note freq.
shift)
o
, 0- 0-
L —»—
TE102
TEIOI
1— j -
2.0
2.2
2.4
Cavity B-field (kG)
<b)
4.5
1
1
■
!
1
|
1
4.0
1
1
1" y
X
r t
i”
i'
|
1
1
1
i
i
;
i
TE201
O
"S'
X
CD
S 3.5
TE111
-o--------------o~
x Mixer in V polarization
0 Mixer in H polarization
i,,
O'
r2
u.
ox, : )P x% ° o 9 0 0
2.5
"0
2.0
* ■■ ■
XC « *
)0CXX«X x X x
<d 0
TE011
o
TE102
Sl
TE IO I
1.5
1
1.7
. . . .
1
. . . .
1
1.9
2.1
Cavity B-field (kG)
•
1
2.3
. . . .
1
■ •
2.5
Figure 6.33. Frequency measurements for the tapered large orbit gyrotrons. (a) Cavity B
results; note the frequency shift for the TE0i 1 mode, (b) Cavity C results;
here, the fundamental TE 101 mode was supressed.
cavities showed multiple modes as in the uniform case. The taper in cavity B shifted the
TEou mode, and the taper in cavity C shifted microwave power to the TE 102 mode.
Cavity C produced higher power than the uniform cavity (A) case in the vertically
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
polarized modes. This appears due to reducing the mode competition from the two TG | 0
competing modes.
10000
i
> 1000
O
a
u
<3
£
0
*
:°
<^o
“ o,
i i
100 o
ox
a
* * o
° o
Mx
° ° oO*
£
o
cavity B ratio
cavity C ratio
10
•
°
^ o ®o
..O
° °o **
°°» K
o A
,«
,« 8
*
C3
N
O
° „ ox
Q_S_
1
x
0
0
X* x
t
£
.1
1.3
*
1.5
1.7
1.9
8
2.1
2.3
2.5
Cavity B-field (kG)
Figure 6.34. Polarization ratios for the tapered RCS gyrotron experiments.
The polarization power ratios for both Cavity B and Cavity C are shown in Figure
6.34. The results here were similar to those of the uniform cavity case. The dominant
vertically polarized mode achieved much higher powers than the higher order
horizontally polarized modes. The polarization ratios ranged as high as 1000, and with
increased magnetic fields the polarization ratios shifted below
1
to as low as 0 . 2 (1/5).
The polarization ratio is shifted to higher magnetic fields for cavity C. As mentioned
earlier, this was due to the suppression of the fundamental TEioi mode at lower magnetic
fields.
The power efficiencies o f the two tapered cavities are shown in Figure 6.35.
Neither tapered cavity produced higher efficiencies than the uniform cavity. This could
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
117
be due to more e-beam scraping or possibly irregularities in the cavity. Also, since the
walls are tapered in one dimension, the e-beam cavity interactions might not be as
6
I I I I | I I I I Jfl I I I | I I f V | I I I I | I I I I | I I
Q cavity B (%)
5
*
S'
o
C
U
'o
cavity C ( %)
4
T.
J
□
0
1
a p
D
□i
_ja
a
□ c&cftxii
“ D n*
0
.................... ..
1
.3
1.5
X
“□ IP
X
x
—
0
°
□ □
o ar,*
a.
at
0 oD
*V
X
X
■ * ...........
1.7
1.9
2.1
2.3
Cavity B -field (kG)
2.5
Figure 6.35. Power efficiencies for the tapered cavity experiments.
efficient, since tuning to specific resonances is not possible in one dimension. The peak
power efficiency measured was 6 % for Cavity C and 4 % for Cavity B; the average
power efficiency appeared to be on the order o f 1.5 %.
6.3.4. Microwave pulse shortening and spectroscopy results
Figures 6.36 and 6.37 demonstrate microwave pulse shortening in both the large
orbit gyrotron uniform cavity case (cusp II) and in the large orbit tapered cavity cases.
These are plots of microwave power produced as a function of microwave pulse length
for microwave signals of both the vertical and horizontal polarizations. The pulse length
was determined by measuring the duration o f the microwave signal at half of its signal
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
118
strength. MELBA’s pulse length has been shown in several figures and varies in length
from 300 ns to over 1 ps, yet the longest microwave pulses are all much shorter in
10
+*
+ + +
8 ■+ +
u
s
o
&>
<D
S
O
6
♦ *
+
+ Vpolarization
o Hpolarization
++
+
■ +
4
. ++t + *
*+ +
+ :>
2
+
*
OW Otri- 0
0
0
-
. .
'r + * ±
+
.» Q .* O ■____
100
200
300
400
Microwave Pulse length (ns)
500
Figure 6.36. Microwave power as a function of pulse length for the uniform cavity, large
orbit gyrotron (cusp II). While the voltage pulse o f M ELBA was on the
order of 700 ns, large microwave power signals did not last more than 200
ns. Higher power microwave pulses were shorter than ones with low power.
duration than the voltage pulse. In the large orbit RCS gyrotron (cusp II) the higher
power microwave pulses (>
8
M W ) are on the order of 100 ns while low power pulses (<
1 M W ) can be as long as 400 ns (see Figure 6.36). The same results are seen in both
Cavity B and Cavity C in Figure 6.37, where both cavities’ microwave power as a
function of pulse length is plotted.
Optical emission spectroscopy was performed on the large orbit RCS gyrotron
(cusp II), as well as for the tapered cavities. Plasma was detected by placing a fiberoptic
bundle ( four fibers) against the lucite microwave output window oriented down the
gyrotron axis in order to observe both the RCS cavity as well as the cathode and anode
(backside). The output end o f the fibers are then placed at the entrance slit o f a three
quarter meter spectrograph with a gated, intensified, CCD camera system. Figure 6.38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
119
12
P "
10 i a
+ V polarization (cavity B)
□
□
□
□
0
100
200
0
H polarization (cavity B)
°
V polarization (cavity C)
*
H polarization (cavity C)
300
400
500
600
Microwave pulse length (ns)
Figure 6.37. Microwave power as a function o f pulse length for the tapered cavities (B &
C, cusp II). Microwave pulse shortening is apparent.
shows the optical emission spectra for aluminum, where the neutral lines from two
ground state lines (394.4 nm and 396 nm) are exhibited. These aluminum lines were
observed with the fiberoptic bundle set to observe the cathode plasma formed. Figure
6.39 is the optical emission spectrum for H-alpha [GIL98]. The H-alpha gave the
strongest emission in the spectroscopic data, observed at 656.3 nm. Along with the Halpha, two signals from singly ionized carbon were visible. The ionized carbon lines
observed occur at 657.8 nm and 658.3 nm respectively. The ionized carbon lines
observed could be due to the e-beam scraping the carbon anode as it leaves the diode. Or
the lines could be due to hydrocarbons from the plasma when the e-beam dumps against
the waveguide wall.
Mass spectroscopy data taken on M ELBA diodes have shown that water is a
major impurity in the system [GIL98]. The H-alpha spectra is probably due to the
electron beam induced decomposition o f water vapor when the e-beam strikes the
waveguide wall at the e-beam dump, or from e-beam scraping in the cavity.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
120
wm ■
396.15nm - A11
5C0Q ■
5
U
1
'O
394.40nm - A11
4(300'
3X 0 -
O
«
•5 2GOO'
£
tS
1000 ''
lli
UIamjiLojuO
uA
o-t—
392
393
394
395
396
397
398
399
400
Wavelength [nm]
Figure 6.38. Optical emission spectra o f aluminum for MELBA shot 6199. The two
aluminum lines are due to the explosive emission cathode, made of
aluminum.
Formation of plasma in the microwave cavity is thought to be a major suspect of
pulse shortening. I f a plasma formed at the cavity output due to the e-beam dumping
against a waveguide wall exceeds the critical density, nc, then the plasma becomes highly
reflecting and could prevent output transmission o f microwaves produced in the cavity.
The critical density is defined as [GIL94, CHE84]:
At 2.15 GHz, the critical density is on the order of 5 x 10 10 cm *3. Thus, microwaves at
2.15 GHz w ill be cut o ff at plasma densities exceeding this value. Figures 6.40 and 6.41
show the results o f a photomultiplier (pm) tube signal set to respond to the H-alpha
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
121
s
1
V 30000
0
1
20000 *'
I
04
10000*
■
rt°
655
6553
656
6563
657
6573
658
658.5
659
Wavelength [nm]
Figure 6.39. Optical emission spectrum o f Hydrogen (H-alpha) for MELBA shot 6236.
The H-alpha peak appears stronger with higher microwave production. The
two carbon lines are due to the e-beam hitting the graphite anode and
producing a plasma from scraping.
signal from the spectrograph as compared with the voltage response of MELBA and the
microwave signals [GIL98]. Figure 6.40 results in an abrupt end to the microwave signal
shown in Figure 6.40 trace b as the H-alpha signal rises sharply. The peak microwave
power in this shot was 2.3 MW. In contrast to this, Figure 6.41 shows a slower falling o ff
of the microwave signal as the H-alpha signal increases slowly. However, in both cases
the plasma signal intensity grows after the microwave signal starts and appears to remain
during the pulse while the microwave signal is cut off. The general trends in optical
emission measurements show that as the H-alpha intensity increases, microwave
production decreases, and at some point is cut o ff completely. Plasma density
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
600
500
700
800
900
1000
1100
1200
1300
1400
1300
Time (ninoseconds|
Figure 6.40. Signal response from M ELBA shot 6512 demonstrating the voltage pulse
(a), the vertically polarized microwave signal (b), and a PM tube response to
H-alpha optical emission (c). The vertically polarized signal here had a
peak power of 2.5 M W .
600
700
800
900
1000
1100
1200
1300
1400
1300
1600
Time (nanosecond*)
Figure 6.41. Signal response from M ELBA shot 6523 demonstrating the voltage pulse
(a), the vertically polarized microwave signal (b), and a PM tube response to
H-alpha optical emission (c). The vertically polarized signal here had a
peak power of 2.8 M W .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
measurements have not been conducted yet, however, Figures 6.40 and 6.41 suggest the
increase in plasma density may cut o ff the microwave production. The correlation
between microwave power and optical emission is still under investigation, although
initial results suggest that some correlation exists.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 7
CONCLUSIONS
Gyrotron devices have been demonstrated to be efficient and high power sources
of microwave radiation. A gyrotron utilizing a rectangular cross section geometry offers
potential advantages over other geometries, such as linearly polarized microwave output.
Control of the linearly polarized output might be useful for a rapid scanning radar or
perhaps in fusion plasma startup (x-wave) and heating (o-wave).
This thesis presents comprehensive experimental research conducted on a
rectangular cross section gyrotron oscillator. Microwave measurements were conducted
for both small and large orbit gyrotron configurations; radiation darkening on glass plates
was used for electron beam diagnostics, and optical spectroscopy was performed to
observe the effects of plasma on microwave generation.
Radiation darkening showed that adiabatic compression o f the e-beam produced a
beam a (vj_/v||) of approximately 0.3 for the small orbit gyrotron. EGUN simulations
agreed with these results, showing the e-beam’s a to be between 0.2 and 0.3, increasing
with the magnitude of adiabatic compression. The small orbit e-beam a also agreed with
the results of simulations using a single particle electron trajectory code. The e-beam a
increased significantly in the large orbit gyrotron measurements. Experimentally, the
average e-beam a was approximately 1.0 at a magnetic field o f 1.5 kG and rose to an
average of approximately 1.3 for a B-field of 2 kG. These results also agreed with the
single particle trajectory code.
MAGIC 2D simulations predicted that polarization control o f microwave
emission from a rectangular cavity could be achieved by controlling the magnetic field in
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
the cavity. In the small orbit simulations, the polarization power ratio in the fundamental
TE 10 mode was dominant at lower B-fields with a peak polarization power ratio
(Pteio/Pteoi) of 15 at 1.85 kG; the TE0i mode became dominant at higher magnetic fields,
and the polarization ratio dropped to 0.07 (~1/14) at a magnetic field of 2.3 kG. The
large orbit gyrotron M AGIC 2D simulations produced similar polarization control results
to the small orbit simulations. A peak polarization power ratio of 90 was achieved at 1.5
kG with MAGIC and this flipped to a minimum o f 0.003 (~l/300) at 2.1 kG. Similarly,
M AG IC 3D simulations showed a high degree of polarization control. At 1.7 kG the
peak polarization power ratio was approximately
8
x
105
and this flipped to a minimum
o f0.0006 (~1/1700) at 2.4 kG.
The small orbit gyrotron did not demonstrate polarization control.
Experimentally, the forward wave of the fundamental mode was not observed. The
highest power achieved was on the order o f 23 M W in the horizontal polarization; this
appears to be due to the TE0i mode. The highest power achieved in the vertical
polarization was approximately 5 MW , and we assume that the power is a combination of
the TEn mode and the backward wave o f the TEio mode. The addition o f reflecting
strips did not have a major effect on the results of the small orbit gyrotron measurements.
The average current transported to the interaction region for these measurements was
~3.0 kA, and the efficiency o f this gyrotron device was on the order of 0.5 %. Pulse
shortening was observed during the microwave measurements.
Polarization control was successfully achieved in the large orbit gyrotron
oscillator. Three different cusps were built, each improving over the previous version.
The highest power achieved in the fundamental TEi0 mode was 14 M W . The highest
power achieved in the orthogonal horizontally polarized TE0| mode was 6 M W .
Heterodyne frequency measurements confirmed these modes, as well as demonstrating
mode competition. The fundamental TEioi mode appeared at 2.18 GHz at magnetic
fields o f ~1.5 kG on the microwave interaction cavity. Mode competition demonstrated
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
126
that the TE 102 mode was present at -2 .5 GHz at slightly higher magnetic fields.
Furthermore, the TEon was dominant at B-fields of 1.9 kG and a frequency of 2.85 GHz,
but significant mode competition existed from the backward wave o f the fundamental
TE 10| mode, from the TE 102 mode, and from the TEm mode at -3 .6 GHz. The
polarization power ratio (Pwrvpoiarizatioi/PwrHpoiarizaiion) reached a peak value o f
approximately 2000 at a magnetic field o f 1.5 kG. The polarization ratio flipped to make
the TE0| mode dominant at -2 kG; at this B-field the polarization power ratio was 0.03
(1/30). MAGIC 2D code simulations agreed qualitatively with these experimental
results. In Cusp II an average o f 220 Amps was transported to the RCS cavity entrance,
and approximately 80 % o f the current was measured prior to dumping the beam. The
peak efficiency of the large orbit gyrotron was 8 % with a transverse efficiency of -1 6 %.
To reduce mode competition tapered cavities were introduced to replace the
uniform RCS cavity. These experiments met with limited success. Cavity B, which was
tapered in the vertical dimension to attempt suppression of the higher order, horizontally
polarized TE0| mode, lowered the peak power in that mode to a peak value of 3 MW;
furthermore, the mode frequency was shifted up from 2.85 GHz to above 3 GHz. This
did not cause the power in the fundamental mode to increase, and tapering did not
enhance the polarization ratio. Cavity C was tapered in the horizontal dimension to
suppress the TE |0 fundamental mode, and in this case the TE 10i mode did not appear at
2.18 GHz. Either the TE 012 mode dominated due to this taper, or the fundamental TE 101
mode frequency shifted up to the frequency of the TE 102 mode.
Pulse shortening was observed in both the small orbit and large orbit gyrotron
experiments. Optical emission spectroscopy clearly demonstrated plasma formation in
the RCS gyrotron cavity. Whether plasma formation is a source or symptom o f the pulse
shortening problem is currently under investigation.
Several changes could be completed in future work to improve experimental
results. I f the anode aperture and annular e-beam emission surface area were increased
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
127
(producing a larger current annular e-beam), the increased e-beam current could produce
higher power microwaves, although gyrotron efficiency might suffer from increased a
spread and increased space charge effects. Sharpening the cusp further could lead to
improved current transport, less current scraping, and better experimental results. Power
could possibly be raised if mode competition were suppressed; using a slotted cavity as
opposed to a solid cavity might enhance the RCS gyrotron’s performance. The RCS
cavity is approximately the length o f
1 /2
guide wavelength; experiments utilizing a full
wavelength guide could possibly raise the cavity Q and might raise the microwave power.
When M ELBA’s lucite insulator stack is replaced with a ceramic insulating stack, and the
vacuum system is improved by the addition of a second cryo pump, baking out the
experiment to remove moisture and other impurities could also produce higher
microwave power with longer pulse lengths. If the magnetic fields and cavity dimensions
were altered, the experiment on the RCS gyrotron could easily be scaled to the millimeter
wave regime. Finally, injecting a horizontally polarized (TE 0 i) signal upstream in a
tapered cavity would be interesting as a proof-of-principle experiment for the Active
Circulator.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDICES
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
129
APPENDIX A
N E G A TIVE MASS IN S T A B IL IT Y D E R IVA TIO N
The following derivation follows from course notes from NE590 [LAU95].
Beginning with the following parameters and the equations of motion:
gamma
y = l /^ l - (32
cyclotron frequency
(A .l)
£2e = |e|B0 /m 0 Y0
(A.2)
Y
► X
Figure A .I. X -Y plane with gyro-orbit of a single electron about the magnetic field.
First we need to consider electron motion in the x-y plane. Consider an electron
at position r0 = r0r rotating about a magnetic field B = B0 z. The first order influence
o f the perturbed EM field on the displacement o f the electron from its cyclotron orbit
may be decomposed into:
r,= $ ? + Ti0
(A.3)
The rate of change of the unit vectors from time t to t + At can be solved for:
dr/dt = coo 0
(A 4 )
de/dt = -o )0?
(A.5)
Now consider the velocity vector for the electron,
v = d / dt(r0 + r j) = rofl)o0 + [(£ - tig) 0 )r + (T) +
)§] = v0 + v,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(A .6 )
130
Given Y=Y0+Yi and dY=Yi and d ji= jii and differentiating formula for gamma:
y 2 = - j- L - = > y 2 - y ¥ = i
(A.7)
Y i= Y o iV P l
(A.8)
Yi _ YpVpVie
(A 9)
results in:
Y0
c
Write the Lorentz force equation in terms of zero and first order quantities.
^ [m 0(Yo + Y i)(v0 + v j)] = e[(E 0 + E ,) + (v0 + v, )x(B 0 + B ,)]
(A. 10)
The 0^-order equation gives the results that v0 = vo0 with
v0 = r0 co0 = r0 £2ce. Now look at the first order equation and substitute the quantities
from (A.6 ) in for the first order terms. Solving for the radial and theta components yield:
i - (YoPotOo)2^ - “ oYo1! = —5— [E ir + v0 Blz]
(A. 11)
Ti-t-co04 =
(A. 12)
moYo
— ^ -3
E ie
moYo
Assume that the perturbed fields are of the form Ei=Eir<r,t)r + E i 0 (r,t)§. and
H l= zH lz(r,t). Look at modes that co-rotate with the electron beam. Ignore radial force
in the analysis, and consider a circularly polarized mode [E i 0 =EiQ(r=ro)exp(jo)t-jm6 )
where m=integer and 0 = 0 o+®ot]- For gyrotrons |co-mcoo|«0 ) (and assume m =l).
4 = j'(to - m(D0 )5 => |4 | = |co- mtD0 ||4 | «
co|4 |
(A. 13)
=>|4 | = |oJ-m o)0| |4 |« c o 2 |4|
Using the radial force equation (ignoring radial force and now ^ ), we find:
-(YoPo^o )2^ - “ oYJti = 0 =* £ = —^2
“ oPo
|5| ~
co-mooJ. .
- ~2 H =>
“ oPo
, ,
M » fi|
(A. 14)
(A -15)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
131
Substitute (A.14) into equation (A.12), and recall that (l-po^)=l/Yo^- This gives:
1
i
0 N)
1
o
I"
e
1
TI + COq
- Tj[ P o - 1]
3 C10
L Po J m0Yo
(A. 16)
q•• = --Po
! - 2 .—e
Yo mo
: 10
This shows a force applied in the positive theta ( 6 ) direction will result in
acceleration in the minus theta direction (the force is acting on a negative mass). I f the
radial force is not ignored, there is a threshold in the ECM (or negative mass) instability,
implying the beam must be sufficiently relativistic for the instability to occur (E>5keV).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
APPENDIX B
RECTANG ULAR VA C U U M W A V EG U ID E DISPERSION R E LA TIO N AND
ELEC TR O M A G N ETIC FIELD S D E R IV A TIO N
(propogation in x)
z
Figure B .l. Waveguide geometry.
This derivation follows that o f Griffiths [GRI89].
Starting with the general form o f the electromagnetic fields:
E (x,y,z,t) = E 0 (yIz)el(kx_(ol)
(B.l)
B(x,y 1z,t) = B0 (y,z)ei(kx- ax>
0 .2)
E 0 = Ex(x) + Ey(y) + Ez(z)
0 -3 )
B0 = Bx(x) + By(y) + Bz(z)
(B.4)
where
The wavenumber, k, is related to the wavelength, X, by:
X=2 rc/k
(B.5)
The fields must satisfy Maxwell's equations:
V -E = p /e 0 = 0
(B.6 a)
VB =0
(B.6 b)
VxE = -3 B /3 t
(B.6 c)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
133
VxB = (l/c 2 )3E /at + p 0J = (l/c 2 )ai/at
(B.6 d)
Placing (B .l) through (B.4) into Maxwell's equations (B.6 c • B.6 d), we obtain:
(i)3Ez/3y -3Ey/3z = i©Bx
(B.7a)
(ii)3Ex/az-3Ez/ax = i©By
(B.7b)
(iii)ikEy -3 E x/3y = i©Bz
(B.7c)
(iv)3Bz/3y-aBy/az = -icoEx / c2
(B.7d)
(v)3Bx/3z -ikBz = -i©Ey / c2
(B.7e)
(vi)ikBy - 3Bx/3y = -i©Bz / c2
(B.7f)
Solving equations in (B.7) for Ey, Ez, By, Bz in terms of Bx and Ex,
Ey = (© /c ) 2 - k
Ez =
(co/c)2 - k
3BV
k i§E,
p L + ( 0 ir
x.
2
2
3y
(B.8 a)
dz
—x
3BX
k - r -5- - © — dz
3y.
(B.8 b)
© aEx l
By =
Bz =
(to /c ) 2 - k
2
kl T
. ay
© aE x 1
(CO / c) 2 - k 2
(B.8 c)
c2 3z
(B .8 d)
c2 3 y .
Plug equations (B.8 a -B.8 d) into the remaining Maxwell's equations (B.6 a - B.6 b)
to decouple the equations for Ex and Bx:
0y2
_3_2
1- —
3-2
3z2
r® .\i2 —k
+ (—
' C>
K
a2
3y
3z
Ex = 0
(B9a)
Bx = 0
(B.9b)
c
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
134
For transverse electric (T E ) waves, Ex=0, and for transverse magnetic (T M )
waves, Bx=0. Solving for the TE case with the following boundary conditions at the
walls: Eparallel»^perpendicular* 0
Let Bx(y,z)=Y(y)Z(z)
(B.10)
such that:
j 2y
d^Z
Z —^ - + Y — £ + ( ( © / c) 2 - k 2) YZ = 0
dyz
dz
(B .l I)
Divide by yz, and note the y- and z-dependent terms must each be constant:
Z dz
((to / c) 2 - k2) - k 2 - k 2= 0
(B .l 3)
The general solutions to equations (B .l2a) and (B.12b) are:
Y = Asin(kyy) + Bcos(kyy)
(B.14)
Z = Csin(kzz) + Dcos(kzz)
(B.15)
Imposing the boundary conditions By(0)=By(a)=0, and hence also
dY/dy=dZ/dz=0, this results in A=C=0, and
ky = mrc/a
kz = nit / b
(m = 0,1,2,...)
(B.16)
(n = 0,1,2,...)
(B.17)
Bx = B0 c o s ( ^ ) c o s ( ^ )
a
b
(B. 18)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
135
The solution is called the TEmn mode, and one of the indices must be nonzero.
By convention the first index is associated with the larger dimension, i.e. a > b. Plugging
ky and kz into equation above, and solving for k, the dispersion relation is:
k=
(to )2
c
_(jm C ) 2 _^mt ) 2
a
(B.19)
b
If the frequency is:
® < c7W l ^
) 2
+ (% t
5
“ m"2 ®co
(B.20)
the wave number, k, is imaginary, and waves willnot travel, but be attenuated. Therefore,
©nut is called the cutoff frequency. For a rectangular waveguide, the lowest frequency
occurs for the TE jo mode for a > b:
(°10=c7t/a
(B.21)
The wave number can be simplified in terms of the cutoff frequency:
k = i y 0 ) 2 -co5in
(B.22)
The phase velocity can be found:
where o)mn= 2 ttfcThe wavelength along the axis o f the wave guide is referred to as the guide
wavelength, and for frequencies above cutoff, it may be written as:
‘V a r - T T n ?
ll- l^
(B '24)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
136
APPENDIX C
M A G IC 2D (1994.5 VERSIO N) IN P U T FILE FO R LARGE O RBIT
G YRO TR O N SIM U LA TIO N S
TITLE "ACTIVE CIRCULATOR IN RECTANGULAR WAVEGUIDE";
COMMENT "FOUR ROTATING BEAMLETS";
C This simulation runs for the large-orbit case where the beam alpha is
determined to be
approximately 1.0 and the cavity current is approximately 200A;
C
PARAMETERS;
C
parameters that can be changed without modifying the code;
DEFINE C 2.9979E+08;
DEFINE BEXZ 0.150;
DEFINE KVOLT 800.0;
C
DEFINE ALPHA AS PERV/PARV;
DEFINE ALPHA=1.0;
DEFINE G A M M A T=l+K V O LT/511;
DEFINE BETAT=(SQRT( 1- 1/(G AM M AT*G AM M AT)));
DEFINE BETAZ=BETAT/(SQRT(1+ALPHA* ALPHA));
DEFINE BETAP=SQRT(BETAT*BETAT-BETAZ*BETAZ);
DEFINE PARV=C*BETAZ;
DEFINE PERV=C*BETAP;
DEFINE PARP=GA M M A T * PAR V;
DEFINE PERP=GAMMAT*PERV;
DEFINE F=2.8E9*BEXZ* 10/GAMMAT;
DEFINE RL=PERV/(6.28*F);
DEFINE RHO=7.246E-3;
C
J=RHO*V, where V=BETAT*C and J=200A/cmA2(four beamlets);
C
SPACE;
C
This creates my spatial grid, and needed space parameters;
DEFINE X M IN 1.0E-08;
DEFINE Y M IN 1.0E-08;
DEFINE XM A X5.4E-2;
DEFINE Y M A X 7.2E-2;
DEFINE R1 2.2E-2;
DEFINE R22.4E-2;
DEFINE M A XX 110;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
137
DEFINE
DEFINE
DEFINE
DEFINE
DEFINE
M IN X 2;
M A XY 146;
M IN Y 2;
M ID X =(M A X X -M IN X )/2;
M ID Y =(M A X Y -M IN Y )/2;
D X =X M A X /(M A X X -M IN X );
D Y =Y M A X /(M A X Y -M IN Y );
SYSTEM CARTESIAN;
X I GRID UNIFORM M A X X M IN X X M IN DX;
X2GRID UNIFORM M A X Y M IN Y Y M IN DY;
C
TIME;
C
This defines all the temporal parts o f the simulation. The courant condition
stipulates that nothing in the simulation can travel faster than light due to
computer error. The other variable allows me to tell the simulation to take data at
a specific time;
DEFINE COURANT 0.9;
DEFINE DT=COURANT/(C* SQRT(1.0/(D X *D X )+ l .0/(D Y *D Y)));;
DEFINE TIMEOFSIM 30.0E-09;
DEFINE ND T=TIM EO FSIM /D T;
DEFINE DATAT 1.0E-9;
DEFINE ITAK EDA T=DA TAT/DT;
DIAGNOSE COURANT 1 0 0;
C
GEOMETRY;
C
This creates my metallic RCS cavity (infinite in z);
CONDUCTOR BOT A LIG N M IN X M IN Y M A X X M IN Y ;
CONDUCTOR TOP A N TI-A LIG N M IN X M A X Y M A X X M AXY;
CONDUCTOR RT A N TI-A LIG N M A X X M IN Y M A X X M A XY;
CONDUCTOR LT A LIG N M IN X M IN Y M IN X M A XY;
C
FIELDS;
C
This section deals with the EM fields;
FIELDS ALL CENTERED N D T DT;
C
Specifies the type o f algorithm used to advance the EM field. Here, we use
a centered-difference method. It is the simplest model;
BEXTERNAL 0 0 BEXZ;
C
Applys the DC external magnetic field;
C
ADD TEST ANTENNA;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
138
C
Tests the system, not used during simulation runs,places an antenna located
at the center of the cavity that creates a EM signal;
C
C
FUNCTION "TIM E(T)=SIN(6.26*2.1E9*T)H;
ANTENNA TIM E NULL NULL E 1 M ID X M ID X M ID Y M ID Y;
C
PARTICLES;
C
This deals with the macro-particle attributes in general;
CURRENTS LCC NO NO 0 1;
KINEMATICS ELECTRON 1 YES NO YES EM 1 1;
C
SPLIT TRANSVERSE M OTION EQUALLY TO X& Y;
DEFINE PX=0.5*PERP;
DEFINE PY=0.5*PERP;
DEFINE B Y l=M ID Y-5;
DEFINE BY2=MIDY+5;
DEFINE IRL=RL/DX;
DEFINE
DEFINE
DEFINE
DEFINE
DEFINE
DEFINE
BX 1=M ID X +IR L-5;
BX2=M IDX+IRL+5;
C X 1=M ID X -IR L-5;
CX2=M IDX-IRL+5;
D X l=M ID X-5;
D X2-M ID X+5;
DEFINE
DEFINE
DEFINE
DEFINE
DEFINE
CY 1=M ID Y+IR L-5;
CY2=M ID Y+IRL+5;
D Y 1=M ID Y-IR L-5;
DY2=M IDY-IRL+5;
NEGPERP=-1*PERP;
C Populate the initial particles distribution in the simulation;
POPULATE DENSITY ELECTRON 1 BX1 BX2 BY1 BY2
RHOO.5 0.5 0.0 PERP PARP;
POPULATE DENSITY ELECTRON 1 C X I CX2 BY1 BY2
RHO 0.5 0.5 0.0 NEGPERP PARP;
POPULATE DENSITY ELECTRON 1 DX1 DX2 CY1 CY2
RHO 0.5 0.5 NEGPERP 0.0 PARP;
POPULATE DENSITY ELECTRON 1 DX1 DX2 DY1 DY2
RHO 0.5 0.5 PERP 0.0 PARP;
C Take the initial charge distribution and solve Poisson’s eqn. for space charge;
POISSON FISH 4 BOT 0.0 TOP 0.0 RT 0.0 LT 0.0;
C Apply the fields calculated to the simulation;
PRESET E l POISSON FISH;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
139
PRESET E2 POISSON FISH;
C
DIAGNOSTICS;
OUTPUT SYSTEM;
DISPLAY REAL 0.0 X M A X 0.0YM A X ;
C
This shows the grid and computational space & metal boundries;
TIM E R PTIME PERIODIC 0 N D TITA K ED A T;
TIM E R TONCE DISCRETE 0 ;
DEFINE KDUMP 10;
C This is the number of time steps that are "lumped"together in the trajectory
plot;
TRAJECTORY KDUMP PTIME 1 ELECTRON 0.0 X M A X 0.0 YM AX;
VECTOR TONCE FIELD E l E2;
C
This gives a vector plot of the initial (space charge) field;
OBSERVE FIELD E l M ID X 5 M ID X 5 FFT 5 W INDO W FREQUENCY 1E9
10E9;
OBSERVE FIELD E2 M ID X 5 M ID X 5 FFT 5 W INDO W FREQUENCY 1E9
10E9;
OBSERVE FIELD E l 5 M ID Y 5 M ID Y FFT 5 W INDO W FREQUENCY 1E9
10E9;
OBSERVE FIELD E2 5 M ID Y 5 M ID Y FFT 5 W INDO W FREQUENCY 1E9
10E9;
OBSERVE FIELD E l M ID X M ID Y M ID X M ID Y
FFT 5 W INDOW FREQUENCY 1E9 10E9;
OBSERVE FIELD E2 M ID X M ID Y M ID X M ID Y
FFT 5W INDOW FREQUENCY 1E9 10E9;
STATISTICS PTIME;
START;
STOP;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
140
APPENDIX D
SAMPLE EGUN IN PU T F IL E FO R SM ALL O R B IT G YRO TR O N
SIM U LA TIO N S
Small orbit gyro (RCS), ANNULAR BEAM, 2.25cm cathode PROFILE ,750
KV, 12 cycles, 0.15 mesh/step, 15rays, SPC=1.0, mag=1.0
RLIM Z L IM POTN
POT(POTN)
LSTPOT M I MAGSEG
370
1400 4
0.0,7.50E05,0.0,0.0
2
3
-1
* Insert magnetic field values (Bz) here
Listed below describes the geometry and potential of the simulation space:
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
0
1
2
10
18
19
20
21
23
25
27
28
29
30
31
31
32
33
35
35
36
1 37
1 38
1 42
1 45
1 46
4 47
4 48
167
167
167
167
167
167
168
168
169
170
172
174
175
177
179
181
182
183
184
185
185
185
185
0 .0
185
185
185
185
185
2 .0
2 .0
2 .0
2 .0
2 .0
0 .2
2 .0
0 .6
0.5
0 .0 1
0 .1
0.5
0 .2
0.3
0 .1
0.9
0.4
0.15
0 .1
2 .0
2 .0
2 .0
2 .0
2 .0
2 .0
2 .0
2 .0
■0.5
-0.5
-0.5
-0.5
-0.3
-0 .1
-0 .8
-0 . 2
-0.3
-0 .0 1
-0 .1
-0.9
-0 . 2
-0.7
-0.7
2 .0
-0 . 8
-0 .1
-0 .1
-0.7
-0 .1
-0 .0 1
-0 .0 1
-0 .0 1
-0 .0 1
-0 .0 1
-0 . 2
-0.7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
141
184
183
181
179
178
177
176
175
174
172
150
135
120
110
108
107
106
105
104
102
98
94
90
86
85
84
83
82
80
78
75
72
69
66
62
60
56
52
47
41
4 125 35
4 127 26
4 128 23
-0 . 6
-0.3
-0 .1
i
©
49
50
51
52
53
53
53
53
53
54
61
65
70
73
74
74
75
76
78
80
85
90
94
97
4 98
4 99
4 100
4 10 1
4 102
4 104
4 106
4 108
4 110
4 112
4 114
4 115
4 117
4 119
4 121
4 123
-0 . 6
-0.4
-0 . 2
-0.99
-0.99
2 .0
-0 .8
2 .0
2 .0
-0.5
-0.3
2 .0
-0 .1
-0 .1
2 .0
-0.5
-0.85
2 .0
-0 .1
-0 .1
-0 .1
-0 .1
-0.3
-0.7
-0 . 6
2 .0
-0 . 2
-0 . 8
-0.607
-0.429
-0.203
-0.147
-0.836
-0.626
-0 .2 1 1
-0.166
-0.346
-0.300
-0.926
-0 . 8 8 6
-0 . 8 8 6
0.926
- 0 .1
-0 .1
-0.4
-0.439
-0.518
-0.596
-0.718
-0.769
-0.949
-0.166
- 0 .2 1 1
-0.626
-0.836
-0.429
-0.607
-0.361
-0.542
-0.413
-0.661
-0.581
-0.990
-0.307
-0.565
-0.238
-0.458
-0.234
-0.419
-0.399
-0.919
-0.330
-0.856
-0.162
-0.488
i
o
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
-0.319
-0.137
-0.559
2 .0
-0.677
2 .0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142
4
4
4
4
4
4
4
4
4
4
4
4
128
129
129
129
129
130
130
130
130
130
130
130
0
131 0
369 0
370 0
370 100
370 412
150 412
90 412
8 8 412
85 412
84 413
84 414
84 435
84 436
84 437
85 438
90 438
92 438
93 438
93 439
93 440
93 900
93 1398
93 1399
93 1400
92 1400
85 1400
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
0
0
0
0
21
19
17
15
12
11
9
7
5
2
1
0
1 1400
01400
0 500
0 168
-0.214
-0.901
-0.621
-0.372
-0.057
-0.968
-0.813
-0.689
-0.597
-0.515
-0.504
-0.500
2 .0
2 .0
2 .0
2 .0
-0.631
2 .0
2 .0
2 .0
2 .0
2 .0
2 .0
0 .0
2 .0
0 .0
2 .0
0 .0
0 .0 0 1
0 .0
0 .0 0 1
2 .0
0 .0 0 1
0.55
0.55
0.55
0.55
0.55
2 .0
2 .0
2 .0
2 .0
0.18
0.18
0.18
0.18
0.18
2 .0
2 .0
2 .0
0.98
0.98
0.98
0.98
0.98
0.98
0.98
2 .0
2 .0
2 .0
2 .0
2 .0
-0 .0 0 1
-0 .0 0 1
-0 .0 0 1
-0 . 0 0 1
2 .0
2 .0
2 .0
2 .0
2 .0
0 .0
2 .0
0 .0
2 .0
0 .0
2 .0
0 .0
0 .0
0 .0
0 .0
2 .0
0 .0
2 .0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
143
U N IT
M AXRAY STEP NS SPC MASS ZEND VIO N SAVE
0.00054 15
0.15 12
1.0
0.0
1400 -1.E8 0
START A V AVR RC ZC
DENS
'GENERAL' 0 1.0 36.0 186.0 5000.0
SURFACE M AGMLT MAGORD
1
1.0
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
144
APPENDIX E
ANODE APERTURE SCHEMATICS AND CATHODE TIP DESIGN
10
cm-
aperture diameter=9.2 cm
11.5 cm
Figure E .l. Anode aperture for small orbit gyrotron measurements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
145
10 cm-
r=2.4 cm
11.5 cm
r= 2 . 0 cm
slotted aperture with 3 vanes
Figure E.2. Slotted anode aperture for large orbit gyrotron measurements.
cathode stalk
aluminum cathode tip
Figure E.3. Cathode stalk with aluminum cathode tip. Both the cathode stalk and the tip
were coated with Glyptal insulating enamel to prevent emission except from a
bare aluminum ring on the tip with a radius of 2.25 + 0.25 cm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
146
10 cm-
1.5 cm
r=2.25 cm
1 mm pinhole
aperture
Figure E.4. Anode aperture for ebeam a (vperp/V||) measurements. Eight pinholes were
used to radiation darken a beam pattern on a glass plate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
147
APPENDIX F
LIBRA (4.0) 500 MHz FREQUENCY FILTER DESIGNS
Figure F .l. Four filter design using Libra 4.0. The design uses 3 Wilkinson power
dividers to split an input signal four ways. A combination of microstrip
coupled lines create the 500 M Hz filters. The first output at the top right
measures signals from 2.0 to 2.5 GHz. The second signal measures response
from 2.5 to 3.0 GHz. The third signal on the right measures responses in the
frequency range of 3.0 to 3.5 GHz, and the bottom right signal measures
responses from 3.5 to 4.0 GHz.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
148
- 2 0 .0
24.0
-2 8 .0
Frequency
1.0
GH2/0IV
Figure F.2. Theoretical response to the filters designed using Libra 4.0. The vertical scale
is the transmitted power (S21) response in dB.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
C H
I
S g j
i o g
tr- ■ ■- ....................
i &a
S
MAC
•MARKER
5 5 C I0 0 Q
d 9 /
HF.F
0
dS
64
P?
I
j. .
start
i
ooc. coo ca c
km*
H
<
1-
J
\J
!
i \
'
l U -L il
STOP 6 0 0 a . OCO OOO MHx
Figure F.3. Actual response of Filter A (2.0-2.5 GHz) design. The vertical scale, 5
dB/div, is the transmitted power response (S21).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
CHX
S2 l
lo g
MAC
3 dB /"
R EF O dB
I* —1B« 5 0 2
dB
s s o 7 io < r c i r8 MHzj
• '■ " 1
»
C2
M ARKER
S 5 C I0 C 0
GHz
V rfw iT .iV iT i. v t T f l l- W IT r T - m if iT I I T . T W ~
S TA R T
1 OGO. 0 0 0
• ••
OOO M H *
jlj
STOP B OOO. 0 0 0
.
OOO MMx
Figure F.4. Actual response of Filter B (2.5-3.0 GHz) design. Transmitted power (S21) is
5 dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
151
CHI
S2 t
lo g
MAG
S
da/
REP O
da
1 * - 1 9 . 0 4 .3 d B
027.~$oo i
CM
15553
C2
500134
GHz
p?
'S T A R T
1 OOO. OOO OOO MM*
STO P 6
OOO. 0 0 0
OOO MHst
Figure F.5. Actual response of Filter C (3.0-3.5 GHz) design. The vertical scale is 5
dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
152
lo g
02
MAC
9 d8/
MARKER
.6 0 3 0 0 0 1 9 9
REF O dS
Xj - 1 C .
0 3 2 da
S O Q .io O
1Q Q M h 3
COO. 0 0 0
OOO MHz
GHz
p?
STA R T
1 0 0 0 . OOO 0 0 0 MHz
STO P 6
Figure F.6 . Actual response of Filter D (3.5-4.0 GHz) design. The vertical scale is 5
dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
153
APPENDIX G
C A V IT Y CO LD TESTS, W H IT E TA N K AND CO UPLER C A LIB R A TIO N
Cold tests were shown for the uniform cavity (cavity A) as well as the tapered
cavities in the experiemental configuration chapter. The following figures show the
cavity cold test frequency response over more narrow frequency ranges. The different
modes are clearly visible. Following these cold tests, the frequency spectrum is shown
for the large microwave chamber at the end of the experiment where the S-band
waveguides were placed, for an S-Band 30 dB coupler used in measurements, and for a 4
GHz low pass filter.
2 1 P 6 1997 10 3 1 3 1
OH
S
,,
b|MAQ
)d »
KEF-tOdB
).:1302 dB
2.141 7 >0006011*
■0
l„>1141 dB
24 40 OH*
r
.
2.141 700006 G1 Ez
2.:-l404 dB
2I3IOHZ
I
A
START 1J00 000 000OHz
STOP 2.100000 000OH*
Figure G. 1. Uniform cavity response between 1.5 and 2.5 GHz. The T E io i mode
appeared at 2.15 GHz. Measurement is of the SI 1 parameter at 3 dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
154
27 M 1 M 7 1 12»«
5dB/
11
IJStODbOQOOHB
TJieJle
ZD lG H s
>325d l
3.339 GHz
1 .:1 6 J > d l
I 2JM G HI
START 2.600 000 000 QKX
sto p
jjo o o o o o o o a m
Figure G.2. Uniform cavity response between 2.6 and 3.6 GHz. TheTEon mode
appeared at 2.84 GHz and the TE i 11 had a resonance at 3.34 GHz. The
vertical scale is 5 dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
155
27 P m 1997 ll:)73«
I . -5-107 <■
MFOdB
11
Ptm
Cm
MARKER 1
3.6598 GHz
10d
START JJOO 000 000 O llt
STOP 4jOOOOOOaOOK>
Figure G.3. Uniform cavity response between 3.5 and 4.5 GHz. TheTE 2 0 l mode
appeared at 4.02 GHz. The vertical scale is 3 dfi/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
156
O il
S
4 _:-J2.74l M
21
Flm
1
2.1 CH»
Cor
3.6 G
STAJIT 1.500000 000 GHl
TTOf JJOOOOOOOOGHl
Figure G.4. The frequency spectrum for the microwave chamber. The scale is 3 dB/div
with a reference line at -35 dB (indicated by the arrow to the left).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
157
•60
2
2.5
3
4
3.5
frequency (GHz)
4.5
5
5.5
6
Figure G.5. Frequency spectrum for the 30 dB S-Band directional coupler. Vertical scale
is the transmitted power (S21) at 10 dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
158
10.0
.0
0
40 .0
5 0 .0
Frequency
0 .5
G Hz/DiV
Figure G.6 . Frequency spectrum for a 4 GHz low pass filter. Vertical scale is from the
transmitted power at 10 dB/div.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
159
APPENDIX H
T IM E SEQUENCING AND FA RADAY CAGE W IR IN G
Systron-Donner 101 Pulse Generators
O O O
o
r
-+
t
0
o
1
External in
External in
Bank
Trigger
O O O
0
SCR
Trigger
Trigger Generator (MELBA only)
5V input
300V output
?
<j
?’ BB
level
O
slope
300V output
‘i
■— ► D D
laiiitiui
U1UIUIUI
tUMfcja
input
5V input
IllU tiy
ujujtaca
input
level
O
input
slope
LUEIIflH
level
O
slope
QC
+
ext.
-+
initial
per.
It.
out
O
O
ext.
delay
Q
mag scope
trig g e r^ -
scope:
trigger
-+
®
initial delay
per.
r ©
gate
out
O
ext.
-+
initial
delay
per.
o
t
mag remote
out
scope timer
Figure H. 1. Schematic for pulse and delay generators to set the timing for magnet banks
and MELBA triggering.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
160
MONITORED SIGNAL PATHS:
I)
voltage monitor: voltage monitor, resistive divider, RG-59 cable, lOx
attenuator, SO O splitter, oscilloscope (DSA602) terminated (SO O).
II) Diode current: B-dot loop, RG-59 cable, 50 O terminator, RC integrator (x=
20
pis), oscilloscope terminated (1 MO).
III) Aperture Current: Rogowski coil, RG-59 cable, 50 O terminator, RC
integrator (t= 20 ^is), oscilloscope terminated (1 M O ).
IV ) Cavity entrance current: Rogowski coil, RG-59 cable, 50 O terminator, RC
integrator (x= 20 ^s), oscilloscope terminated (1 M O).
V)
Exit plate current: graphite paddle, Pearson coil (0.1 V/A), RG-59 cable, lOx
attenuator, oscilloscope (DSA602) terminated (50 O).
V I) Diode Magnetic field signal: shunt resistor (r= 0.0477 O), RG-59 cable,
oscilloscope terminated (1 MO).
V II) Solenoidal field signal: Pearson coil ( 0.01V/A), RG-59 cable, oscilloscope
terminated (1 MO).
V III) Vertically polarized S-Band microwave signal: S-Band waveguide, 30 dB
S-Band directional coupler (used in some measurements), RG-214/U type E15402
coaxial cable, 0-60 dB coaxial attenuators, 4 GHz low pass filter, diode crystal detector,
RG-59 cable, 50 O terminator, oscilloscope (DSA602) terminated (1 MO).
IX ) Horizontally polarized S-Band microwave signal: S-Band waveguide, 30
dB S-Band directional coupler (used in some measurements), RG-214/U type E l 5402
coaxial cable, 0-60 dB coaxial attenuators, 4 GHz low pass filter, diode crystal detector,
RG-59 cable, 50 O terminator, oscilloscope (DSA602) terminated (1 MO).
X ) Frequency filtered microwave signal: S-Band waveguide, 0 -20 dB S-Band
variable attenuator, RG-214/U type E l 5402 coaxial cable, 0-30 dB coaxial attenuators, 4
GHz low pass filter, 4 channel microstrip detector system (shown in appendix F), diode
crystal detector, RG-59 cable, 50 O terminator, oscilloscope (DSA602) terminated (1
M O ).
X I) Mixer and dual mixer signal path: S-Band waveguide, 0 -20 dB S-Band
variable attenuator, RG-214/U type E15402 coaxial cable (this brings the microwave
signal into the screen room), see the following diagrams for path of rf signal input:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
161
2-4 GHz UTE isolator
CT3040-OT SN R8638
HP 83SO B sweep
osciUator HP83590A RF
plug-in 2-20GHz
Mixer ¥ LO
Mitech Mixer
DB0218LW2
S/N 395312,
DSA602
RF
4 GHz LP filter
microwave line from
experiment ------ £
I variable attenuationl
Figure H.2. Single mixer signal path inside Faraday cage.
HP 8350 B sweep
osciUator HP83590A RF
plug-in 2-20GHz
General Radio microwave
oscillator (1.74.1 GHz)
Type 1360-B serial 628
2-4 GHz UTE isolator
CT3040-OT SN R8638
14 GHz FXR isolator
model N157FSN 111
Mitech Mixer
DB0218LW2
T7¥—
attenuation
HP 5361B pulse/cw
micorwave counter
2-20GHz________
LO
Mixer
3 dB splitter
Mixer
minicurcuit 15542
zem-4300MH
0-9704
RF
S/N 395312
DSA602
3 dB splitter
RF
4 GHz LP filter
variable attenuationl
microwave line from
experiment
Figure H.3. Dual mixer signal paths inside Faraday cage.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
162
APPENDIX I
TAPERED CAVITIES USED IN LARGE ORBIT EXPERIMENTS
a=7.2 cm
^
b=5.4cm
z= 2 1 cm
b=4.8 ci
/
r=2 . 6 cm
a=7.2 cm
Figure 1.1. Cavity B. This cavity was tapered in the vertical direction to attempt to
suppress the horizontal TEoi mode.
a=7.2 cm
b=5.4 cm
z=
b=5.4 cm
21
cm
r=2 . 6 cm
f
►
a=5.6 cm
Figure 1.2. Cavity C. This cavity was tapered in the horizontal direction to attempt to
suppress the fundamental TE io mode.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
163
APPENDIX J
SAM PLE M A G IC 3D M (SEPTEM BER 1997 VERSIO N) IN P U T F IL E
FOR LARG E O R B IT G YRO TRO N S IM U LA TIO N S
The following input file was built with the assistance o f Larry Ludeking and
David Smithe [GOP97].
TERM INATE ERROR;
GRAPHICS SCREEN;
! GRAPHICS PAUSE;
! Identification--------------HEADER ORGANIZATION "U of M , PLASMA BAY";
HEADER AUTHOR "Jonathan Hochman";
HEADER DEVICE "RCS GYROTRON";
HEADER REMARKS "ANNULAR BEAM IN M ODIFIED S-BAND WAVEGUIDE";
!!! Switches. l=on and 0=off.
IEM ISSION = 1;
GUIDE.BFIELDS = 1;
CHECK.BFIELDS = 0 ;
ALGORITHM = 1 ;! EIGENMODE
ALGORITHM = 2 ;! BIASED
!!! Basic control parameters.
PHSVEL = 4;
! Exit port phase velocity factor.
TIM EO FSIM = 100E-9;
! Simulation duration in seconds.
KCREATE = 5;
! Kcreation rate/time scaling.
! Do not use a value less than 5 without
! testing the stability. This number may be increased.
! to 10 or 20. Or any integer.
current_max = 200 amps; ! Supplied gun current in amps.
BEAMJVOLTAGE = 800;
! Kilovolts.
Beam_Spread = 0.05;
! Beam energy spread fraction. Provides some thermalization.
Bexz= 1.8 kilogauss; ! Static axial bfield
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
164
! MAX_BEAMLETS = 2 ;
M A X BEAMLETS = 5 ;
! MAX_BEAMLETS = 3 ;
!
!
!
IF (ALG 0RITHM .EQ .2) T H E N ;
HEADER REMARKS "port phase velocity = 'phsvel:f4.2"';
HEADER REMARKS H'max_beamlets’ BEAMLETS, BAXIAL='bexz:f5.3' Tesla";
ELSE;
HEADER REMARKS "Eigenmode scan.";
E N D IF ;
!!!
!!! Assign space parameters---------------!!! Cavity dimensions.
X C A V ITY = 7.2 C M ;
Y C A V ITY = 5.4 C M ;
ZC A V ITY = 21. C M ;
DZSTRIP = 1 M M ; ! We W O NT BOTHER TO RESOLVE THIS.
D Y STR IP =1 C M ;
DXSTRIP = 7.2C M ;
! Grid resolution parameters.
D X= 4M M ;
DY = 4M M ;
DZ = 8 M M ;
DZSTRIP = M AX(DZ,D ZSTR IP);
!!! Make waveguide at end of cavity same size as cavity.
ZLENGTH = D Z + ZC AVITY + DZSTRIP + Z C A V IT Y ;
!!! Construct metal box, then hollow it out.
XLO = -D X -X C A V IT Y /2;
X H I = +D X +X C A V IT Y /2;
YLO = -D Y -Y C A V IT Y /2;
Y H I = +D Y +Y C A V IT Y /2;
ZLO = 0.0; Z H I = ZLO + ZLENG TH;
VOLUM E METALBOX CONFORMAL XLO ,YLO ,ZLO X H I,Y H I,Z H I;
VOLUM E EMITTORPLATE CONFORMAL XLO ,YLO ,ZLO X H I,Y H I,D Z ;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
165
M ARK M ETALBOX X I SIZE D X ;
M ARK METALBOX X2 SIZE D Y ;
M ARK M ETALBOX X3 SIZE D Z ;
!!! Construct cavity volume.
XLO .C A VITY = -XCA V1TY/2;
X H I.C A V ITY = + X C A V IT Y /2;
X M D .C A V ITY = 0.5*(X LO .C A V ITY +X H I.C A V ITY );
YLO.CAV1TY = -Y C A V IT Y /2;
Y H I.C A V ITY = + Y C A V IT Y /2;
Y M D .C A VITY = 0.5*(Y LO .C A V ITY +Y H I.C A V ITY );
ZLO .C A VITY = D Z ;
ZH I.C A V ITY = ZLO .CAVITY + Z C A V IT Y ;
ZM D .C A VITY = 0.5 * (ZLO .CAVITY+ZHI .C A V IT Y );
ZMD1 .C A VITY = ZLO .CAVITY + 0.8*Z C A V IT Y ;
VOLUME C A V ITY CONFORMAL XLO .CA VITY,YLO .C AVITY,ZLO .CA VITY
X H I.C A V IT Y ,Y H I.C A V IT Y ,Z H I.C A V IT Y ;
AREA C A VITY.ZM D CONFORMAL XLO .C A VITY,YLO .C A VITY,ZM D .C A VITY
X H I.C A V ITY ,Y H I.C A V IT Y ,Z M D .C A V IT Y ;
AREA C A V ITY .E X IT CONFORMAL XLO .C A VITY,YLO .C A VITY,ZH I.C A VITY
X H I.C A V IT Y ,Y H I.C A V IT Y ,Z H I.C A V IT Y ;
LINE XLIN E.C A V ITY CONFORMAL
XLO .C A VITY, YM D .C A V ITY ,ZM D 1.CAVITY
X H I.C A VITY, Y M D .C A V ITY ,ZM D 1.C A V IT Y ;
LINE YLIN E.C A V ITY CONFORMAL
XM D .C A VITY, YLO .CA VITY,ZM D 1.CAVITY
XM D .C A VITY, YH I.C A VITY,ZM D 1.C A V IT Y ;
M ARK C A V ITY X I SIZE D X ;
MARK C A V ITY X2 SIZE D Y ;
M ARK C A V ITY X3 SIZE DZ ;
!!! Construct C A V ITY APERATURE volume.
XLO.APER = -X C A V IT Y /2;
XHI.APER = + X C A V IT Y /2;
YLO.APER = -YCA VITY/2+DYSTR IP;
YHI.APER = +YC A VITY /2-D Y STR IP;
ZLO.APER = ZH I.C A V ITY ;
ZHI.APER = ZLO.APER + D Z ;
VOLUM E APERATURE CONFORMAL XLO.APER,YLO.APER,ZLO.APER
XHI.APER,YHI.APER,ZHI.APER;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
166
M ARK APERATURE X I SIZE D X ;
M ARK APERATURE X2 SIZE D Y ;
M ARK APERATURE X3 SIZE D Z ;
!!! Construct EX IT WAVE GUIDE volume.
XLO.GUIDE = -X C A V IT Y /2;
XH I.G UIDE = +XCAVITY/2 ;
YLO.GUIDE = -Y C A V IT Y /2;
YH I.G UIDE = + Y C A V IT Y /2;
ZLO.GUIDE = ZH I.APER;
ZH I.G U ID E = ZLO.GUIDE + ZC A VITY ;
VOLUME GUIDE CONFORMAL XLO.GUIDE,YLO.GUIDE,ZLO.GUIDE
X H I.G U ID E,YH I.G U ID E,ZH I.G U ID E;
AREA G UIDE.EXIT CONFORMAL XLO.GUIDE,YLO.GUIDE,ZHI.GUIDE
X H I.G U ID E,YH I.G U ID E,ZH I.G U ID E;
M ARK GUIDE X I S IZ E D X ;
M ARK GUIDE X2 SIZE D Y ;
M ARK GUIDE X3 SIZE D Z ;
Generate grid and conductor and vacuum region.
A U TO G R ID ;
CONDUCTOR M ETA LBO X;
CONDUCTOR EMITTORPLATE;
VO ID C A V IT Y ;
IF (ALGORITHM .NE. 1) T H E N ;! EIGENMODE
V O ID APERATURE;
V O ID G U ID E ;
E N D IF ;
! Field algoritm.Time properties------------IF (ALGORITHM.EQ. 1) T H E N ;! EIGENMODE
! EIGENMODE SCAN FROM 2GHZ SCAN_TO 6 G H Z ;
EIGENMODE SCAN_LIST 4 2.18GHZ 2.5GHZ 2.83GHZ 3.56GHZ ;
IEM ISSION = 0 ;
GUIDE.BFIELDS = 0 ;
Area C A V IT Y .X Y CONFORMAL SYS$X1M N,SYS$X2MN,ZM D.CAVITY
SYS$X1M X,SYS$X2M X,ZM D.CAVITY;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
167
Area C A VITY.XZ CONFORMAL SYS$X1M N,SYS$X2M D,-DZ+ZL0.CAVITY
SYS$X 1M X,S Y S $X2M D ,+D Z+ZH I.C A VITY;
Area C A VITY.YZ CONFORMAL SYS$X1M D,SYS$X2M N,-DZ+ZL0.CAVITY
SYS$X 1MD,S YS $X 2M X ,+D Z+ZH I.C A V ITY ;
CONTOUR FIELD E l C A V IT Y .X Y TSYSSEIGENMODE;
CONTOUR FIELD E l C A V ITY .X Z TSYS$EIGENMODE;
CONTOUR FIELD E l C A V ITY .Y Z TSYSSEIGENMODE;
CONTOUR FIELD E2 C A V IT Y .X Y TSYSSEIGENMODE;
CONTOUR FIELD
CONTOUR FIELD
CONTOUR FIELD
CONTOUR FIELD
CONTOUR FIELD
E2 C A V ITY .X Z TSYSSEIGENMODE;
E2 C A V ITY .Y Z TSYSSEIGENMODE;
B3 C A V IT Y .X Y TSYSSEIGENMODE;
B3 C A V ITY .X Z TSYSSEIGENMODE;
B3 C A V ITY .Y Z TSYSSEIGENMODE;
ELSE IF (ALGORITHM.EQ.2) T H E N ;
! Use reduced time step with Gyro emission
M AXW ELL BIASED .5 .5 0 4 ;
! and highcurrent density. This tends to
DT= SYSSDTIME/KCREATE ;
! stabilize the omega_p dt instability.
OBSERVE INTERVAL KC R EA TE;
! Adjust time history recording interval.
TIME_STEP DT;
! Time step adjustment.
DURATION TIMEOFSIM ;
! time of simulation
PORT GUIDE.EXIT NEG A TIVE
! where kz=ko*sqrt(l-(fc/f)**2)
PHASE_VELOCITY PHSVEL;
! omegaO/Vphase=omegaO/C*sqrt(l-(fc/f)**2)
! so, Vphase=C/sqrt(l-(fc/f)**2)
TIM ER TONCE DISCRETE 0;
! discrete timer for time 0
E N D IF ;
D IS P L A Y J D ;
VIEW _3D CO NDUCTOR;
V IE W 3 D CONDUCTOR NO_WIRES;
! Large Orbit Gyrotron;
! below is the method for confining the gyro beam and is
! used for magnetic dumping fields. Twists the beam to the
! guide wall.
IF (GUIDE.BFIELDS.EQ. 1) T H E N ;
ZS = ZLO.GUIDE + 2 c m ;
Z M = Z S + 1C M ;
ZF = ZS + 5 C M ;
ZFE = ZF + 3C M ;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
168
ZM ID = 0.5*(ZS+ZF);
Bexy = 0.10 TE S LA ;
FUNCTION FBY(X,Y,Z)= T H E T A (Z -Z S )*B e xy*M IN (l(Z -Z S )/(Z M ZS))*THETA(ZF-Z);
FUNCTION FBZ(X,Y,Z)= Bexz;
! fct above calcs By and here Bz
PRESET B2ST FUNCTION FBY;
! Set static b fields.
PRESET B3ST FUNCTION FBZ;
! set the static fields,
areadumpxl conformal sys$xlmd,sys$x2 mn,zlo.guide
sys$xlmd,sys$x2mx,ZFE;
area dumpx2 conformal sys$xlmn,sys$x2 md,zlo.guide
sys$xlmx,sys$x2md,ZFE;
area dumpx3 conformal sys$xlmn,sys$x2mn,zmid
sys$xlmx,sys$x2 m x,zm id;
IF (CHECK.BFIELDS.EQ. 1) THEN ;
! contour field blst dumpxl TONCE shade
! use these contours
! contour field blst dumpx2 TONCE shade
! contour field blst dumpx3 TONCE shade
contour field b2st dumpxl TONCE shade
! are correct
contour field b2st dumpx2 TONCE shade
! to check to make
contour field b2st dumpx3 TONCE shade
contour field b3st dumpxl TONCE shade
contour field b3st dumpx2 TONCE shade ! sure initial fields
contour field b3st dumpx2 TONCE shade
E N D IF ;
E N D IF ;
IF (IEM ISSIO N.EQ .l) T H E N ;
!!! a few beamlets are used to distribute the beam energy, i.e.
!!! approximate thermalization.
!!!
speedC= 2.998e8;
R E A LJ;
!speed o f light
Real Melbakvolt;
Delta_Beam = Beam_Spread * Beam_VoItage / MAX_BEAMLETS ;
DO 1=1 ,M AX_BEAM LETS;
DELTAVOLT = Delta_Beam *(I-(M AX_BEAM LETS+l)/2);
melbakvolt= Beam_voltage + D E LTA V O LT;
! MELBA operating keV
gammat= (1+melbakvolt/511);
! Gamma based on MELBA
betat= (l-(l/gam m at)**2)**(0.5);
! Total Beta
alpha= 1.0;
! Beam alpha (Vperp/Vparallel)
betaz= (betat* *2/( 1+((alpha)* *2 )))* *(0.5); ! Betaz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
169
betap= (((betat)**2)-((betaz)**2))*'|,(0.5); ! Beta perp
parv= speedC*betaz;
! parallel velocity
PARAMETER parp'I - gammat*parv;
! parallel momentum
perv= speedC*betap;
! perpendicular velocity
PARAMETER perp'I - gammat*perv;
! perpendicular momentum
PARAMETER FE= 2.8e9*Bexz* 10/gammat;
! cyclotron frequency
PARAMETER TPERIODT = 1/FE ;
rl=perv/(2pi*FE);
! larmor radius
J=current_max/MAX_BEAMLETS;
! Beam current Amps
rho=J/(betat*speedC);
! Beam density
EN D D O ;
TPERIOD = 0 ;
DO 1=1,MAX_BEAMLETS ;
TPERIOD = TPERIOD + TPERIODT ;
ENDDO;
TPERIOD=TPERIOD/MAX_BEAMLETS;
NDT= TIMEOFSIM/DT;
DATAT=2E-9;
ITAKEDAT= DATAT/DT;
TIM ER PTIM E PERIODIC 0 N D TITA K ED A T;
! particles(beam)----------TRISE=TPERIOD;
CURRENT_BEAMLET = CURRENT M A X /M A X BEAM LETS;
FUNCTION GJ(t)=CURRENT_BEAMLET*MIN(T/TRISE, 1.0);
DO 1=1 ,M AX_BEAM LETS;
EMISSION GYRO GJ Bexz parpT perpT 0.0
0,0,0
MODEL GYROT
TIM IN G KCREATE;
EM IT GYROT EM ITTO RPLATE;
ENDDO;
TIM ER PTIME0 PERIODIC 0 9999999 10;
ISTATS = KCREATE * 50;
TIM ER PSTATS PERIODIC 0 9999999 ISTATS ;
STATISTICS ISTA TS;
! Output---------------------OBSERVE FIELDJNTEG RAL J.DA C A V ITY .ZM D FILTER STEP TP E R IO D ;
OBSERVE FIELDJNTEG RAL J.DA C A V ITY .E X IT FILTER STEP TP E R IO D ;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
170
OBSERVE CREATED ALL ELECTRON CURRENT ;
OBSERVE DESTROYED ALL ELECTRON CURRENT FILTER STEP TPERIOD;
OBSERVE FIELDJNTEGRAL E.DL X LIN E.C A V ITY FFT M AGNITUDE W INDOW
FREQ 1E9 6E9;
OBSERVE FIELDJNTEGRAL E.DL YLIN E.C A V ITY FFT M AGNITUDE W INDOW
FREQ 1E9 6E9;
OBSERVE FIELDJ>OWER S.DA C A VITY.ZM D FILTER LO_PASS TPERIO D;
OBSERVE FIELD_POWER S.DA C A V ITY .E X IT FILTER LO_PASS TPERIO D;
OBSERVE FIELD_POWER S.DA G UIDE.EXIT FILTER LO_PASS TPERIO D;
TIM ER CHARM PERIODIC REAL lOnanosec 1.0 lOnanosec;
RANGE PARTICLE CURRENT ELECTRON X3 CHARM;
RANGE PARTICLE POWER ELECTRON X3 CHARM;
TIM ER phas_TIME PERIODIC REAL lOnanosec 1. lOnanosec ;
FUNCTION PT(X 1,X2,X3,P1 ,P2) = SQRT(P1*P1+P2*P2);
PHASESPACE AXES X3,KE PHAS_TIME;
PHASESPACE AXES X I,X 2 PHAS_TIME;
PHASESPACE AXES X I,X 3 PH A S TIM E;
PHASESPACE AXES X2,X3 PHAS_TIME;
PHASESPACE AXES X2,X3 PHAS TIM E;
!!! trajectories of a few tagged particles.
TIM ER TRAJ TIM E PERIODIC REAL lOnanosec 1. lOnanosec INTEGRATE
TPERIOD;
TAG_FRACTION=0.0005;
TAGGING T AG_FRACTION;
PHASESPACE AXES X2,X3 TRAJ_TIME T A G ;
I
particle p lo t** * * * ** * * *
! pick these three numbers for best looks—
ZAXIS_ANGLE=40_DEGREES;
ZAXIS_SC ALE= 1.;
!
Yaxis
--*
Xaxis
Zaxis_Angle(/
/
Zaxis/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
171
SINZAX=SIN(ZAXIS_ANGLE);
COSZAX=COS(ZAXIS_ANGLE);
FUNCTION X A X I S_PROJECTION(X 1,X2,X3)=X1-ZAXIS_SCALE*C0SZAX*X3;
FUNCTION YAXIS_PROJECTION(Xl,X2,X3)=X2-ZAXIS_SCALE*SINZAX*X3;
PHASESPACE AXES XAXIS_PROJECTION,YAXIS_PROJECTION TRAJ_TIME
TAG;
I *********************************************
E N D IF ;
DUMP TYPE ALL;
START;
STOP;
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
172
APPENDIX K
SAMPLE MAGIC3DM RESULTS FOR LARGE ORBIT GYROTRON
SIMULATIONS
These are preliminary results which may require further work.
(a)
8.2SE5 .
7,3 ^ -------- ------0.0
|
S
Z2.1<m
)
4.36E-I
(b)
3.1 E-2
0.0
-3.1
-4 .0
0.0
X (n)
4.0E-2
Figure K .l. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a Bfield of 1.7 kG. (a) The energy per particle as a function of distance from
the five beamlets emitted. The beamlets are emitted at 800 keV with a 5
% energy spread, (b) An X -Y perspective of the e-beam looking down the
waveguide (this shows the horizontal reflecting strips).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
173
(b)
4.36E -I
Z <n>
(C)
4 .3 6 E - I
e
2 .1 8 .
0 .0 . TTTTTm
-4 .0
0.0
X Cm)
2.1 8
2.18
0.0
4.0E-2
4.36E-I
0.0
.
-3.1 0.0 3.1 E-2
Y Cm)
.
-3.1 0.0 3.1 E-2
Y Cm)
Figure K.2. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a Bfieldof 1.7kG. (a) The X -Z perspective of the e-beam, (b) TheY-Z
perspective of the e-beam, (c) This Y-Z perspective tags a small fraction of
those particles in (b) to give a better picture of the electron trajectories.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
174
Figure K.3. Phasespace plots for the large orbit gyrotron simulations at 100 ns for a Bfield of 1.7 kG. (a) The energy per particle as a function of distance from
the five beamlets emitted. The beamlets are emitted at 800 keV with a 5
% energy spread, (b) A X -Y perspective of the beam (looking down the
waveguide (this shows the horizontal reflecting strips).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
175
Z <m>
4.36E-I -
2.18 .
0.0
0.0
-4.0
0.0
X (m)
4.0E-2
-3.1 0.0 3.1 E-2
Y (m)
.
-3.1 0.0 3.1 E-2
Y <m>
Figure K.4. Phasespace plots for the large orbit gyrotron simulations at 100 ns for a Bfield o f 1.7 kG. (a) The X -Z perspective of the e-beam, (b) TheY-Z
perspective of the e-beam, (c) The Y-Z perspective with a small fraction of
the particles in (b). From (b) and (c) scraping is observed and could lead to
the possible formation of plasma.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
176
(a)
0.0E2
-
0.8
..
<
- 1.6 ..
-2 .4 .
0.0
0 .7 5
1.5
2 .2 5
Z (M)
3.0
3.75
4.5E-1
1.5
2 .2 5
Z (M)
3.0
3.75
4.5E-1
(b)
2 .0 E 8
5o
»
1.0 . .
0 .5 . .
0.0 .
0.0
0 .7 5
Figure K.5. Range plots for the large orbit gyrotron at a B-field of 1.7 kG at 100 ns in the
simulation, (a) shows the e-beam current as a function of distance, (b)
shows the e-beam power as a function o f distance. The horizontal strips are
at 2 1 cm.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
177
(a)
0.0E2
-0 .5
-
1.0
1.5
-
2.0
0 .0
0 .0 2
0 .0 4
Tin*
(M d
T in *
Cm c )
0 .0 6
0 .0 6
0 .1 E -6
0 .0 6
0 .0 8
O .tE -6
(b)
4.0E6
3.2 . .
2 .4 . .
O
O
»
0.8
0.0
0 .0
0 .0 2
0 .0 4
Figure K.6 . Large orbit gyrotron simulation results at a B-field of 1.7 kG. (a) The
current exiting the RCS cavity as a function o f time [field integral J*dA],
(prior to the beam dump), (b) Field power (S*dA) at the RCS cavity exit as
a function o f time. The decrease in power could show pulse shortening.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
178
(a)
1.5E4
0.0
0.02
0.04
Tin*
(tec)
0.06
0.08
0.1 E-6
(b)
4.0E5
5
3
0.0
.4
Frequency
(GHz)
Figure K.7. Large orbit gyrotron simulation results at a B-field of 1.7 kG. (a) The
integral E«dL of a horizontal line near the exit to the RCS cavity [from
coordinates (-3.6,0,17.8) to (3.6,0,17.8) in cm], (b) the FFT o f (a)
showing resonances at 2.16 GHz, 2.88 GHz (small), 3.48 GHz (small), and
4.27 GHz. These correspond to the TEi0, TE 0 i, TEn, and TE 20 modes
respectively.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
179
(a)
2.0E5 .
■
1.0
I
0.0
-
1.0
-
2.0
g
—
n —
■r
Ik ^
0.0
0.02
0.04
0.06
Tin*
0.08
0.1E-6
Caec)
(b)
I.0E7
z
o
Fr*qu#rtcy
(GH*)
Figure K.8 . Large orbit gyrotron simulation results at a B-field of 1.7 kG. (a) The
integral E*dL of a vertical line near the exit to the RCS cavity [from
coordinates (0, -2.7,17.8) to (0,2.7,17.8) in cm], (b) the FFT of (a)
showing a resonance at 2.16 GHz. This corresponds to the TE | 0 mode.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
180
(b)
3.1 E-2
^*Vy Jpk*
»>e. * <1
s o.o
4.0E-2
Figure K.9. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a Bfield o f 2.4 kG. (a) The energy per particle as a function o f distance from
the five beamlets emitted. The beamlets are emitted at 800 keV with a 5
% energy spread, (b) A X -Y perspective o f the beam.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
181
(c)
4 .3 6 E -I
4.3 6 E -I
Z (m)
(a)
S
2 .1 8 .
0.0
- 4 .0
0 .0
X (it)
4 .0 E -2
2 .1 8 . U
0.0 .
-3 .1 0 .0 3.1 E -2
Y (it)
-3.1 0 .0 3.1 E -2
Y (it)
Figure K. 10. Phasespace plots for the large orbit gyrotron simulations at 10 ns for a Bfield of 2.4 kG. (a) The X -Z perspective of the e-beam, (b) The Y-Z
perspective of the e-beam, (c) This Y-Z perspective with a small fraction
of electrons from(b).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
182
(a)
1.5E6
x <no
Figure K. 11. Phasespace plots for the large orbit gyrotron simulations at 100 ns for a Bfield of 2.4 kG. (a) The energy per particle as a function o f distance from
the five beamlets emitted. The beamlets are emitted at 800 keV with a 5 %
energy spread, (b) A X -Y perspective o f the e-beam.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
183
(b)
2 Cm)
4.36E-1
(c)
4.36E-1
4.36E-1
S 2.18
IM
•S 2.18 . U
0.0
0.0
-4 .0
0.0
X Cm)
4.0E-2
-3.1 0.0 3.1 E-2
Y Cm)
-3.1 0.0 3.1 E-2
Y Cm)
Figure K.12. Phasespace plots for the large orbit gyrotron simulations at 100 ns for a Bfield o f 2.4 kG. (a) The X-Z perspective of the e-beam, (b) The Y -Z
perspective of the e-beam, (c) The Y-Z perspective with a small fraction
of the particles in (b).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
184
(a)
0.0E2
-0.75
<
-2.25
-3.0
0.0
0.75
1.5
2.25
3.0
3.75
4.5E-1
2.25
3.0
3.75
4.5E-1
Z (M)
(b)
2.0E8
1.6
...
0.8
..
I)
0.4 .
0.0
0.75
1.5
Z (M)
Figure K.13. Range plots for the large orbit gyrotron at a B-field o f 2.4 kG at 100 ns in
the simulation, (a) The e-beam current as a function o f distance, (b) The
e-beam power as a function o f distance.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
185
(a)
0.0E2 _
-0.4 ..
-0.8 ..
I-,,..
-
1 .6 . .
0.0
0.02
0.04
Tin*
(aac)
Tin*
(ate)
0.06
0.08
0.1E-6
0.06
0.08
0.1E-6
(b)
2.4E6
2.0
n
o
a
0.8
0 .4
0.0
0.0
0.02
0.04
Figure K. 14. Large orbit gyrotron simulation results at a B-field of 2.4 kG. (a) The
current exiting the RCS cavity as a function o f time [field integral J*dA],
(prior to the e-beam dump), (b) Field power (S*dA) at the RCS cavity exit
as a function of time. The initial power in (b) appears to be generated due
to some o f the e-beam.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
186
(a)
0.0
0.02
0.04
0.06
Tin*
0.08
0.1 E-6
(sec)
(b)
I.2E7
1.0 ..
0.8
..
i
o
0.4 ..
0.2 ..
0.0
0.8
1.6
2.4
3.2
Frequency
4.0
(GHz)
4.8
5.6
6.4
Figure K. 15. Large orbit gyrotron simulation results at a B-field of 2.4 kG. (a) The
integral E*dL o f a horizontal line near the exit to the RCS cavity [from
coordinates (-3.6,0,17.8) to (3.6,0,17.8) in cm], (b) the FFT o f (a)
showing a resonance at 2.88 GHz. This corresponds to the TE qi mode.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
187
(a)
0.0
0.02
0.04
Tin*
(i* c)
0.06
0.08
0.1 E-6
(b)
lJ
0.8
1.6
2.4
I
3.2
F rc q u tn c y
4.0
4.8
5.6
6.4
(GHz)
Figure K. 16. Large orbit gyrotron simulation results at a B-field of 2.4 kG. (a) The
integral E*dL of a vertical line near the exit to the RCS cavity [from
coordinates (0, -2.7,17.8) to (0,2 .7 ,1 7 .8 ) in cm], (b) the FFT o f (a)
showing resonances at 2.25 GHz and 2.88 GHz. These correspond to the
TEio and TEoi modes respectively. From (a) it appears that the
fundamental TE 10 mode grows initially, but mode competition from the
orthogonal TE0i mode allows the TE0i mode to grow and beat out the
fundamental mode.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
B IB LIO G R A PH Y
188
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
189
B IB LIO G R A P H Y
ABR77
E. A. Abramyan, B. A. Altercorp, and G. D. Kuleshov, “Microsecond
Intensive Electron Beams,” in Proc. o f the 2nd Int. Topical Conference on
High Power Electron and Ion Beam Research and Technology, Vol. 2, pp.
755 - 760, 1977.
AGE96
F. J. Agee, S. E. Calico, K. J. Hendricks, M . Haworth, T. Spencer, D.
Ralph, E. Blankenship, M . C. Clark, and R. W. Lemke, “Pulse shortening
in the magnetically insulated line oscillator (M ILO ),” Proceedings of SPDE
Conference, Intense Microwave Pulses IV , Vol. 2843, pp. 144 - 152,1996.
BAI87
J. M. Baird, “Gyrotron Theory,” in High-Power Microwave Sources. V. L.
Granatstein and I. AlexefF, Editors, Artech House, Norwood, MA, 1987.
BAL89
C. A. Balanis, Advanced Engineering Electromagnetics, John Wiley &
Sons, Inc., 1989.
BAR81
L. R. Barnett, Y. Y. Lau, K. R. Chu, and V. L. Granatstein, “An
experimental wideband gyrotron traveling-wave amplifier,” IEEE Trans.
Electron Devices, vol. ED-28, pp.872-878,1981.
BAR82
L. R. Barnett, Y. Y. Lau, K. R. Chu, C. R. Kyler, and V. L. Granatstein,
“A Wideband Fundamental Mode Millimeter Gyrotron TW A
Experiment,” in IED M Tech. Dig., pp. 375- 378, 1982.
BEK89
G. Bekefi, A. DiRienzo, C. Leibovitch, and B. G. Danly, “A 35 GHz
cyclotron autoresonance maser amplifier,” Appl. Phys. Lett. 54 (14),
1302-1304,1989.
BEN92
G. Benford, and J. Swegle, High Power Microwaves. Artech House, 1992.
BEN97
J. Benford, and G. Benford, “Survey of Pulse Shortening in High Power
Microwave Sources,” IEEE Trans, on Plasma Science, vol. 25, no. 2, April
1997.
BLA90
W. M. Black, S. H. Gold, A. W. Fliflet, D. A. Kirkpatrick, W. M.
Manheimer, R. C. Lee, V. L. Granatstein, D. L. Hardesty, A. K. Kinkhead,
and M. Sucy, “Megavolt, multikiloamp Ka band gyrotron oscillator
experiment,” Phys. Fluids B 2 (1), pp. 193-198,1990.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
190
BRA94
G. F. Brand, “Mode Competition in a High Harmonic Tunable Gyrotron,”
Int. Journal of Infrared and Millimeter Waves, vol 15 (1), January 1994.
CHE84
F. F. Chen, Introduction to Plasma Physics and Controlled Fusion. Plenum
Press, New York, 1984.
CH091
J. J. Choi, “Bragg Resonator Cyclotron Resonance Maser Experiments
Driven by a Microsecond, Intense Electron Beam Accelerator,” Ph. D.
Dissertation, The University of Michigan, 1991.
CH092
J. J. Choi, R. M. Gilgenbach, T. A. Spencer, P. R. Menge, and C. H.
Ching, “Measurement of long-pulse relativistic electron beam
perpendicular-to-parallel velocity ratio by Cerenckov emission and
radiation darkening on a glass plate,” Rev. Sci. Instrum. 63 (2), February
1992.
CHU78
K. R. Chu, and J. L. Hirshfield, “Comparative study of the axial and
azimuthal bunching mechanisms in electromagnetic cyclotron
instabilities,” Phys. Fluids 21(3), pp. 461-466,1978.
CHU80
K. R. Chu, A. T. Drobot, H. H. Szu, and P. Sprangle, “Theory and
Simulation of the Gyrotron Traveling Wave Amplifier Operating at
Cyclotron Harmonics,” IEEE Trans, on Microwave Theory and
Techniques, vol. M TT-25, No. 4, April 1980.
CUN89
M. Cuneo, “Characterization of the Time-evolution of a microsecond
Electron Beam Diode with Anode Effects,” Ph. D. Dissertation, The
University o f Michigan, 1989.
DES89
W. W. Destler, K. Irwin, W. Lawson, J. Rodgers, Z. Segalov, E. P.
Scannell, and S. T. Spang, “Intense beam fundamental mode large-orbit
gyrotron studies,” J. Appl. Phys. 66(9), pp. 4089-4094, 1989.
ELL92
W. Ellis Jr., E. Johnson, E. Lodi, and D. Schwalbe, Maple V Flight
Manual. Brooks/Cole Publishing Company, Belmont, CA, 1992.
FER84
A. M. Ferendeci, “Theory of High-Harmonic Rectangular Gyrotron for
TEmn Modes,” IEEE Trans, on Electron Devices, vol. ED-31, No. 9, pp.
1212 -1218, 1984.
GAL96
D. Gallagher, J. Richards, F. Scafuri, and C. Armstrong, “High Power
Peniotron Development,” Proceedings o f Vacuum Electronics Annual
Review, 1996.
GAP59
A. V. Gaponov, Adendum, Izvestiya VUZ, Radiofizika, 2,837,1959.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
191
GAP67
A. V.Gaponov, M. I. Petelin, and V. K. Yulpatov, Radiophys. Quant.
Electron. 10, 794-813,1967.
GAP94
A. V. Gaponov-Grekhov, and V. L. Granatstein, Applications o f High
Power Microwaves. Artech House (1994).
GIL80
R. M . Gilgenbach, M. E. Read, K. E. Hackett, R. Lucey, B. Hui, V. L.
Granatstein, K. R. Chu, A. C. England, C. M. Loring, 0 . C. Eldridge, A.
C. Howe, A. G. Kulchar, E. Lazarus, M . Murakami, and J. B. Wilgen,
“Heating at the Electron Cyclotron Frequency in ISX-B Tokamak,” Phys.
Rev. Lett., vol. 44, pp. 647-650,1980.
GIL85
R. M . Gilgenbach, L. D. Horton, R. F. Lucey, Jr., S. Bidwell, M . Cuneo, J.
M iller, and L. Smutek, “Microsecond Electron Beam Diode Closure
Experiments,” invited paper in Digest of Technical Papers of the Fifth
IEEE Pulsed Power Conference, pp. 126-132, June, 1985.
GIL94
R. M . Gilgenbach, NE575 course notes, 1994.
GIL98
R. M . Gilgenbach, J. M. Hochman, R. L. Jaynes, W. E. Cohen, J. I.
Rintamaki, C. Peters, D. E. Vollers, Y. Y. Lau, and T. A. Spencer,
“Optical Spectroscopy of Plasma in High Power Microwave Pulse
Shortening Experiments Driven by a |is e-BEAM,” submitted to IEEE
Transactions on Plasma Science.
GOL87
S. H. Gold, A. W. Fliflet, W . M. Manheimer, R. B. McCowan, W. M.
Black, R. C. Lee, V. L. Granatstein, A. K. Kinkead, D. L. Hardesty, and
M. Sucy, “High peak power K,-band gyrotron oscillator experiment,”
Phys. Fluids 30 (7), pp. 2226-2238,1987.
GOP94
B. Goplen, L. Ludeking, D. Smithe, G. Warren, MAGIC User’s Manual.
prepared for the AFOSR by Mission Research Corporation, 1994.
GOP97
B. Goplen, L. Ludeking, D. Smithe, G. Warren, MAGIC User’s Manual.
prepared for the AFOSR by Mission Research Corporation, August, 1997.
GRA87
V. L. Granatstein, “Gyrotron Experimental Studies,” in High-Power
Microwave Sources. V. L. Granatstein and I. Alexeff, Editors, Artech
House, Norwood, MA, 1987.
GRA96
C. Grabowski, J. M. Gahl, E. Schamiloglu, and C. B. Fledderman, “Pulse
Shortening in High-Power Backward Wave Oscillators,” Proceedings of
SPIE Conference, Intense Microwave Pulses IV , Vol. 2843,1996.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
192
GRI89
D. J. Griffiths, Introduction to Electrodynamics. Prentice-Hall, Englewood
Cliffs, NJ, 1989.
HAR61
R. F. Harrington, Time-Harmonic Electromagnetic Fields. Chapter 4,
1961.
HEN97
K. Hendricks, M . Haworth, R. Lemke, M. Sena, D. Ralph, K. Allen, T.
Englert, D. Shiffler, T. Spencer, M. Arman, K. Hackett, S. Calico, D.
Coleman, C. Clark, and R. Gallagoes, “Success on elimination of pulse
shortening of GW-class, 300 nsec HPM sources,” IEEE Conferece
abstracts and paper, IEEE International Conference on Plasma Science,
May, 1997.
HER79
W. B. Hermannsfeldt, “Electron Trajectory Program,” SLA C -226,1979.
HIR64
J. L. Hirshfield, and J. M. Wachtel, “Electron Cyclotron Maser,” Phys.
Rev. Lett. 12 (19), pp. 533-536,1964.
HIR77
J. L. Hirshfield, and V. L. Granatstein, “The Electron Cyclotron Maser An Historical Survey,” IEEE Trans, on Microwave Theory and
Techniques, vol. M TT-25, no. 6 , pp. 522-527,1977.
HOC96
J. M. Hochman, R. M. Gilgenbach, R. L. Jaynes, J. I. Rintamaki, Y. Y.
Lau, J. W. Luginsland, J. S. Lash, and T. A. Spencer, “Rectangular crosssection high power gyrotron,” Proceedings of SPIE conference, Intense
Microwave Pulses IV , Vol. 2843,1996.
HOC98
J. M. Hochman, R. M. Gilgenbach, R. L. Jaynes, J. I. Rintamaki, Y. Y.
Lau, W. E. Cohen, C. Peters, and T. A. Spencer, “Polarization Control of
Microwave Emission from High Power Rectangular Cross Section
Gyrotron Devices,” submitted to IEEE Transactions on Plasma Science,
August 1997.
JAY97
R. L. Jaynes, R. M . Gilgenbach, J. M . Hochman, J. I. Rintamaki, W. E.
Cohen, C. Peters, Y. Y. Lau, and T. A. Spencer, “Microwave and electronbeam diagnostics of a rectangular cross-section gyrotron,” Proceedings of
SPIE Conference, San Diego, CA, 1997.
KIS95
R. A. Kishek, and Y. Y. Lau, Phys. Rev. Lett. 25,1218,1995.
KIS98
R. A. Kishek, and Y. Y. Lau, Phys. Rev. Lett. 80,193,1998.
LAU82
Y. Y. Lau, “Simple Macroscopic Theory of Cyclotron Maser
Instabilities,” IEEE Trans, on Electron Devices, Vol. ED-29, No. 2, pp.
320-335,1982.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
193
LAU83
Y. Y. Lau, and Larry R. Barnett, “A Note on Gyrotron Traveling-Wave
Amplifiers Using Rectangular Waveguides,” IEEE Trans, on Electron
Devices, vol. ED-30, No. 8 , pp. 908-912, 1983.
LAU84
Y. Y. Lau, Larry R. Barnett, and J. Mark Baird, “An Active CirculatorGyrotron Traveling-Wave Amplifier,” IEEE Trans on Electron Devices,
vol. ED-31, No. 3, pp. 337 - 347,1984.
LAU95
Y. Y. Lau, University o f Michigan, NE590 course notes, 1995.
LAU97
Y. Y. Lau, personal communication, March, 1997.
LAW85
W. Lawson, W. W. Destler, C. D. Striffler, “High-Power Microwave
Generation from a Large-Orbit Gyrotron in Vane and Hole-and-Slot
Conducting Wall Geometries,” IEEE Trans, on Plasma Science, Vol. PS13, No. 6 , pp. 444-453, 1985.
LAW92
W. Lawson, J. P. Calame, B. P. Hogan, M . Skopee, C. D. Striffler, and V.
L. Granatstein, “Performance Characteristics of a High-Power X-Band
Two-Cavity Gyroklystron,” IEEE Trans, on Plasma Science, Vol. 20, No.
3, pp. 216-223, 1992.
LEV87
B. Levush, and A. T. Drobot, “Generation of High-Power Microwaves,
Millimeter and Submillimeter Waves: Introduction and Overview,” in
High-Power Microwave Sources. V. L. Granatstein and I. Alexeff,
Editors, Artech House, Norwood, MA, 1987.
LOZ93
O. T. Loza, P. S. Strelkov, and S. N. Voronkov, “Plasma in a High-Power
Relativistic Generator Retarding Structure,” Plasma Phys. Rpts., vol 20,
1994.
LUC 8 8
R. F. Lucey, Jr., “Long-Pulse Relativistic Electron Beam Generation and
Propagation in Gases and in U V Laser Ionized Channels,” Ph. D.
Dissertation, The University of Michigan, 1988.
MAT94
H. W. Matthews, W. Lawson, J. P. Calame, M . K. E. Flaherty, B. Hogan,
J. Cheng, and P. E. Latham, “Experimental Studies of Stability and
Amplification in a Two-Cavity Second Harmonic Gyroklystron,” IEEE
Trans, on Plasma Science, Vol. 22, no. 5, pp. 825-833,1994.
MEN93
P. R. Menge, “Experimental Excitation and Reduction of the Beam
Breakup Instability in Long-Pulse Electron Beam Transport,” Ph. D.
Dissertation, The University of Michigan, 1993.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
194
M IL96
R. B. M iller, “Pulse Shortening in high-peak-power Reltron tubes,”
Proceedings o f SPIE conference, Intense Microwave Pulses IV , Vol. 2843,
pp. 2 - 13,1996.
MUS92
S. Musyoki, K. Sakamoto, A. Watanabe, N. Sato, K. Yokoo, S. Ono, S.
Kawasaki, M . Takahashi, H. Shimizu, S. Ohtani, E. Tanabe, and M. Shiho,
“Design of a High Power 2.7S GHz Relativistic Peniotron Oscillator,”
Japan Atomic Energy Res. Inst., Ibaraki, Japan, 1992.
PAR74
R. K. Parker, R. E. Anderson, and C. V. Duncan, “Plasma Induced Field
Emission and the Characteristics of High Current Flow,” Journal of
Applied Physics 45 ( 6 ), 2463, June 1974.
PAS87
J. A. Pasour, “Free-Electron Lasers,” in High-Power Microwave Sources,
V. L. Granatstein and I. Alexeff. Editors, Artech House, Norwood, MA,
1987.
POZ90
D. M. Pozar, Microwave Engineering. Addison-Wesley, 1990.
PSI83
Pulse Sciences Report, “Electron Beam Accelerator,” PSI-P-83-105, July
1984.
RAD93
D. J. Radack, K. Ramaswamy, W. W. Destler, and J. Rodgers, “A
fundamental mode, high-power, large-orbit gyrotron using a rectangular
interaction region,” J. Appl. Phys., 73 (12), pp. 8139- 8145,1993.
RHE74
M. J. Rhee and W. W. Destler, “Relativistic Electron Dynamics in a
Cusped Magnetic Field,” Phys. Fluids 17 (8 ), 1574, August 1974.
SCH59
J. Schneider, “Stimulated Emission of Radiation by Relativistic Electrons
in a Magnetic Field,” Phys. Rev. Lett., 2, pp. 504-505,1959.
SH087
M. M. Shoucri, “Dispersion Relation for a Large-Orbit Gyrotron,” Plasma
Physics and Controlled Fusion, Vol. 29, pp. 105-113,1987.
SLA50
J. C. Slater, Microwave Electronics. D. Van Nostrand Company, Inc.,
New York, N Y , 1950.
SPE91
T. A. Spencer, “High Current, Long-Pulse, Gyrotron-Backward-Wave
Oscillator Experiments,” Ph. D. Dissertation, The University of Michigan,
1991.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
195
SPR77
P. Sprangle, and A. T. Drobot, “The Linear and Self-Consistent Nonlinear
Theory of the Electron Cyclotron Maser Instability,” IEEE Trans, on
Microwave Theory and Techniques, Vol. MTT-25, NO. 6 , pp. 528-544,
1977.
TW I58
R. Q. Twiss, “Radiation Transfer and the Possibility of Negative
Absorption in Radio Astronomy,” Australian J. Phys., I I , pp 564-579,
1958.
UHM77
H. Uhm, and R. C. Davidson, “Intense microwave generation by negativemass instability, “ J. App. Phys., 49(2), pp. 593-598,1978.
UHM78
H. Uhm, R. C. Davidson, and K. R. Chu, “Cyclotron maser instability for
general magnetic harmonic number,” Phys. Fluids 21(10), pp. 1877-1886,
1978.
WAL95
M. T. Walter, “Effects of Tapering on High Current, Long Pulse Gyrotron
Backward Wave Oscillator Experiments,” Ph. D. Dissertation, The
University of Michigan, 1995.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IMAGE EVALUATION
TEST TARGET (Q A -3 )
<o
t u
%■
%
rp y
1 2.8
■ 10
u
u „
bUh
150mm
A P P L IE D A IM 4 G E . Inc
1653 East Main Street
- = •• R o ch e ster, NY 14 6 0 9 USA
-= = r — P h o n e: 716/4 8 2 -0 3 0 0
- = ~ - ^ Fax: 716/2 8 8 -5 9 8 9
0 1993. Applied Image. Inc.. All Rights Reserved
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
M
<• v , 4?
% U
y.«
1.0 |£ I£
1112'2
|f |£ in
l.l
lltii
1.25 1
III'-4 I
f t
Документ
Категория
Без категории
Просмотров
0
Размер файла
7 359 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа