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Potential Designs of High Power Degenerate Band Edge Oscillator (DBEO) for Hot Test at UNM and MIT
Mohamed Othman1, Alex Figotin2 , Filippo Capolino1
1March 03, 2017
1Department of Electrical Engineering and Computer Science, UCI
2Department of Mathematics, UCI
MURI Teleconference, March 2017
I. Degenerate band edge (DBE) in slow-wave structures (SWSs)
II. Degenerate band edge oscillator (DBEO)
III. A number of potential designs for experimental hot test
- Design 1. High power DBEO, compatible with UNM setup
• 12 ns e-beam pulse, ~160 MW pulsed output power
- Design 2. High power DBEO, compatible with MIT setup
• Long e-beam pulse, ~20 MW output power
IV. Conclusion
Outline
2
Degenerate band edge (DBE)
Waveguide structures can support a DBE, instead of only an RBE (regular
band edge). At DBE, we have four degenerate modes
4
DBE dispersion d dk k Periodic slow wave structure (SWS)
j t jkze e
z
Bloch waves
Angula
r F
requen
cy
d
/ d
Figotin, Vitebskiy, Phys. Rev. E, vol. 72,
no. 3, p. 036619, Sep. 2005.
Othman, Capolino, IEEE Microw. Wirel.
Compon. Lett., vol. 25, no. 11, 2015
Evan
esce
nt
d
3
First experimental demonstration of DBE
Othman, Pan, Atmatzakis, Christodoulou, Capolino, (under review), arxiv preprint, arXiv: 1611.03450 (2016) [Link]
Good agreement between full-
wave simulations (CST) and
measurements
Giant scaling of the group delay. The Q factor is proportional to the group
delay : ~Q
Degenerate band edge
Elliptical rings
Degenerate band edge
4
Four mode synchronous operation
4
0 0
2( , , )d d C ku k Ih k k
Dispersion relation for SWS with DBE and e-beam
0d
d
uk
Othman, Veysi, Figotin, Capolino, Phys. Plasmas, Vol. 23, No. 3,
033112, 2016.
Othman, Tamma, Capolino, IEEE Trans. Plasma Sci, Vol. 44,
No. 4, 2016.
Othman, Tamma, Capolino, IEEE Trans. Plasma Sci, Vol. 44,
No. 6, 2016.
0 : electron's average
velocity
u
Angu
lar
Fre
qu
ency d
/ d
Ev
anes
cen
t
Four EM modes e-beam coupling
Leads to enhanced power
transfer between the e-beam
and the DBE modes
Four mode synchronous interaction
5
Periodic slow wave structure (SWS)
d
e-beam
z
Degenerate Band Edge Oscillator (DBEO)
The starting oscillation current
Ist decreases with increasing
DBEO length, as
5, : number of unit cellsstI N
N
DBEO
Othman, Veysi, Figotin, Capolino, IEEE Trans Plasma
Sci, vol 44, no. 6, 918-929, 2016.
Although DBE (cold structure) has
zero group velocity, interaction with
beam dramatically decreases the group delay
- What is left from the DBE is
the four mode interaction
- Starting oscillation time reduces
significantly by increasing the
beam current
DB
EO
sta
rtin
g
tim
e [n
s]
6
Two designs of DBEO for hot test
Design 1. High pulsed power, fast rise time
DBEO compatible with UNM setup with a
short e-beam pulse
Design 2. High power, high efficiency DBEO
compatible with MIT setup with a long e-beam
pulse
Parameter Values Parameter Values
Beam current ~5 kA annular beam Beam current ~80 A solid beam
Beam voltage 500 kV Beam voltage 490 kV
Cathode radius 10 mm Cathode radius 2 mm
Magnetic field 1.5 T Magnetic field 0.15 T
e-beam pulse width ~12 ns e-beam pulse width >1 μs
Rise time 10 ns Rise time 75 ns
Output power > 120 MW Output power ~20 MW
SWS length 290 mm SWS length 350 mm
SWS radius 25 mm SWS radius 35 mm
Output waveguide Horn antenna Output waveguide 2×WR284 waveguides
Frequency ~3.8 GHz Frequency ~3.8 GHz
7
SWS with DBE and strong axial field
‒ A unit cell consisting of circular waveguide loaded with two irises
‒ The iris is formed by two complementary split rings
‒ There is misalignment angle between the split rings
• DBE frequency ~ 3.8 GHz
• Mode distribution has a strong Ez component synchronous to the e-beam
PIC simulations are done using CST Particle Studio 2016
y
z
Ez
8
Dispersion of the DBE mode for various
misalignment angles
1. Plan for hot test at UNM
UNM parameter
setupValue
Beam current Up to 6 kA
Beam voltage Up to 600 kV
Cathode outer
radius10 mm annular
Magnetic field Up to 1.5 T
Beam pulse 12 ns
Maximum SWS
length350 mm (9 solenoids)
Maximum radius 25 mm max
Output waveguideHorn antenna and
windowe-
bea
m p
uls
e sh
ape
Benford, Swegle, Schamiloglu, High power microwaves,
CRC Press, 2015
Photo courtesy of
UNM
E. Schamiloglu,
S. Yurt
UNM set up
‒ All critical parameters are
accommodated in our design
9
Optimized DBEO for UNM experimental setup
TM mode
SWS length 290 mm
Total length
including horn450 mm
horn radius 75 mm
Waveguide
radius25 mm
Magnetic field Up to 1.5 T
Beam voltage 500 kV
Beam current Up to 5 kA
Window (output port)
Circular horn
290 mm
cathode
150 mm
450 mm
50 mm
Simulation parameters
N =16 unit cells240 mm
10
PIC simulation resultse-
bea
m p
uls
e sh
ape
Round trip time ~ 3 ns
UNM SINUS-6 e-beam pulse
Round trip RF signal path
e-
Outp
ut
RF
pow
er [
MW
]
11
e-b
eam
cu
rren
t [A
]
Tunability of the DBEO
A coaxial extraction scheme may
be used to aid the extraction of
power (similar to UNM* design)
Misalignment angle between rings can
be used to tune the output power
• During cold test we will show the tunability of the response
Tunability range of output
power
Beam collection tube
*Kevin Shipman, Experimental Plan for Testing the UNM Metamaterial Slow Wave Structure for High Power Microwave Generation, MURI Teleseminar August 5, 2016.
12
Beam tunnel
Distribution of Ez in the DBEO
Field profile shows some hot spots
of fields between the rings‒ Breakdown investigating (in
progress)
Output radiation pattern‒ Horn antenna design slightly
improves power extraction
Particle energies at t = 8 ns
Distribution of Ez in the DBEO
Aperture field distribution
Field hot spot 13
No
rmal
ized
Ou
tpu
t
spec
tru
m
DBEO design summary
UNM requirement
checkParameter
Values used in UCI
PIC simulations
Pass (current can be
adjusted)Beam current 5 kA
Pass Beam voltage 500 kV
Pass Cathode radius 10 mm
Pass (goes up to 1.6 T
or a bit higher)Magnetic field 1.5 T
Pass (can be
shortened)Rise time 10 ns
Pass (maximum has to
be less that the
9 solenoid lengths)
SWS length 290 mm
PassTotal length
including horn450 mm
Pass (needs
characterization)horn radius 75 mm
Pass (very critical for
solenoid)
Waveguide
radius25 mm
Depending on
measurement setupFrequency 3.8 GHz
RF transient signal
Peak output RF power up to 160 MW after 11 ns
Peak power efficiency ~ 15.5%
Frequency ~3.8 GHz
RF signal spectrum
14
Fabrication and test at UNM
Target
1. Cold test. S-parameters. Dispersion synthesis.
2. Hot test: Optimum number of cells and antenna fabrication
Beam diagnostics (Rogowski Coil)
Frequency diagnostics (waveguide detector)
Power diagnostics (calorimeter)
Output radiation pattern diagnostics (grid)
Breakdown test (PMT)
RF radiation
15
2. Plan for hot test at MIT
• Our DBEO is redesigned to be compatible with MIT setup,
dimensions and beam parameters
• Can also be adapted in rectangular waveguide geometry
Photo taken from MIT teleseminar talks
courtesy of MIT
Hummelt et al, “Design and Test of a
Metamaterial Based High Power Microwave
Generator” MURI teleseminar, MIT, March
2016
Lu et al, “Stage II of Metamaterial Based
Backward Wave Oscillator Experiment at
MIT”, MURI teleseminar, MIT, Sep. 2016
E-beame-beam
WR284 waveguidesMIT Parameter Values
Beam current 84 A solid beam
Beam voltage 490 kV
Cathode radius 2 mm
Magnetic field Up to 0.15 T
Max. SWS length 357.6 mm
Output
waveguide
2×WR284
waveguides
Frequency 2~4 GHz
MIT set up
16
Optimized DBEO for MIT experimental setup
Beam current 80 DC
Beam voltage 490 kV
Cathode radius 2 mm
Magnetic field 0.15 T
Rise time <500 ns17
Port 2 Port 1
Simulation parameters
Output signal in the fundamental TE10 mode
Dimensions
fits MIT
vacuum
setup
Port
2
Distribution of Ez in the DBEO
Field hot spots
TE10 mode
Evolution of Ez field in the DBOE in time
18
Magnetic field variation
Target design
19
from
po
rt1
Magnetic field variation
TE10 mode dominates output power for magnetic field higher than 700 G
Target design
swirling of trajectories occur for Bz<0.07 T
Electron’s trajectories and energies
from
po
rt1
20
PIC simulation summary
Peak power efficiency Psat / (V0I0) ~ 50%
Output RF power ~ 20 MW after 120 ns
Frequency: 3.8 GHz
MIT requirement
checkParameter
Values used in UCI
PIC simulations
Pass (can be
adjusted)Beam current 80 A solid beam
pass Beam voltage 490 kV
pass Cathode radius 2 mm
Pass (can be
lowered)Magnetic field 0.15 T
pass Rise time 75 ns
passMaximum SWS
length357.6 mm
pass Maximum radius 148.3 mm
pass Output waveguide WR284
Pass Frequency 3.8 GHz
Fast rise time
cathodeOutput ports WR284 waveguides
350 mm
70 mm
148 mm
Beam outputtunnel
Port
1P
ort
2
Port 1Port 2
Time [ns]
Outp
ut
pow
er [
MW
]
3.8 GHz
21
Fabrication and hot test at MIT
1. Cold test. S-parameters. Dispersion synthesis.
2. Hot test: Optimum number of cells and antenna
fabrication
Beam diagnostics
Frequency diagnostics (filters to measure power)
Power diagnostics (waveguide attenuator/detector)
Breakdown test
Photo taken from MIT teleseminar talks
courtesy of MIT
Hummelt et al, “Design and Test of a
Metamaterial Based High Power Microwave
Generator” MURI teleseminar, MIT, March
2016
MIT V/I curve at the collector
22
Conclusion
• Degenerate band edge oscillator (DBEO) theory based on four mode
interaction with an e-beam was employed to design efficient high power
microwaves sources
• PIC simulations of metallic SWS with DBE show strong e-beam and EM waves
interaction. High efficiency oscillations are reported
• DBE is found in many SWS geometries, and other special points in the dispersion
can also be engineered and utilized for oscillator and amplifier design
• Both UNM and MIT hot test considerations are accounted for: all the data and
parameters are designed to be compatible with the respective experimental setup
- Design 1. Short pulse-beam, output power 160 MW → UNM setup
- Design 2. Long pulse e-beam, output power 20 MW → MIT setup
• Future work: - Finalize designs, investigate tolerances
- Cold test of the DBE waveguide
- Output extraction optimization. 23
Thank you
24
Auxiliary slides
25
Interaction impedance
Interaction impedance
2
22Re( )
zp
p
zp r
EZ
k P
: component of the Floquet harmonic of the mode
: Bloch wavenumber, : Floquet harmonic
: Power flow
zp
zp
r
E z
k p
P
Fundamental harmonic, p = 0
p = 1
p = +1
Four harmonics of propagating modes
are engaged at the DBE
x
y
z
DBE frequency26
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