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Theoretic and experimental investigation of gyro-BWO
1. Theoretic and Experimental
Investigation of Gyrotron Backward-
wave Oscillator with High Efficiency and
Broad-Band Capabilities
Student : Pei-Che Chang
Advisor : Kwo-Ray Chu Prof.
January 20, 2015
2. Outline
Efficiency Enhancement of the Gyro-BWO :
Tapered Waveguide – A Review
Efficiency Enhancement of the Gyro-BWO :
High Order Axial Mode Competition – A Review
A Broadband Gyro-BWO Scheme : Simulation
95kV Gyro-BWO Design : Experiment
Conclusion
3. Efficiency Enhancement of the Gyro-BWO :
Tapered Waveguide – A Review (1)
11Operation Mode : TE
Cyclotron Harmonic : Fundamental
0.3 cm
Cutoff frequency (at = 0
wref
w
R
r
0
.3 cm) 29.28 GHz
Beam current ( ) 2 A
Beam voltage ( ) 80 kV
Magnetic field ( ) 15 kG
Guiding c
b
b
I
V
B
0
enter position ( ) 0.35
Velocity ratio ( / ) 1.4
Velocity spread ( / ) 0 %
c w
z
z z
r r
v v
v v
α ⊥=
∆
Simulation parameters of the Gyro-BWODispersion relation
-20 -10 0 10 20
0
20
40
60
80
100
120
TE11 (operating mode)
S = 1
Frequency(GHz)
kz (cm-1)
2 2 2 2 2
waveguide mode ( - - 0)z mnk c k cω =
beam mode ( 0)e
z z
s
k vω
γ
Ω
− − =
Simulation structure
2r
C. S. Kou, C. H. Chen, and T. J. Wu, Phys. Rev. E. 57, 7162 (1998).
4. 1.25 1.30 1.35 1.40 1.45 1.50
32
33
34
35
36
37
frequency(GHz)
B0
/ Bg
tapered waveguide
uniform waveguide
The frequency of the intersection point
between the beam mode and waveguide mode
resonance mismatch , slope ,
electrons inertially bunched deeper in the phase space.
↑ ↑ ⇒
Efficiency Enhancement of the Gyro-BWO :
Tapered Waveguide – A Review (2)
Under the tapered structure the oscillation
frequency will up-shift.
The equation of the initial resonance
mismatch, is given by
,e
z z
s
k vω
γ
Ω
∆ ≡ + −
The initial resonance mismatch determines
the initial slop of the spatial evolution of the
electron phase trajectory.
5. Uniform structure
The larger the resonance mismatch, the steeper the slope.
Electron can be inertially bunched deeper and even longer in the phase space.
(initial resonance mismatch) , where ( ) ( / 2)
d
t s s m m s
dz
ω φ ψ π
Λ
∆ = Λ = − + − + − − Φ
taper structure
2 0.3 , 2br cm I A= =
2 0.24 , 2br cm I A= =
Z (cm)
Fieldamplitudeandenergydepositionrate
(normalizedscale)
Efficiency Enhancement of the Gyro-BWO :
Tapered Waveguide – A Review (3)
6. for HOAMs, , beam energy reabsorption
interaction strength
at same interaction length, , .stl I
Θ ↑ ↑
⇒ ↓
⇒ ↑ ↑
For uniform structure
For taper structure
for HOAMs, , through deeper
eff st
f
L I
↑
⇒ ↑⇒ ↓
Efficiency Enhancement of the Gyro-BWO :
High Order Axial Mode Competition – A Review
0 1 2 3 4 5 6
0.00
0.02
0.04
0.06
0.08
0.10
z (cm)
Fieldamplitude
Leff
0.0
0.1
0.2
0.3
0.4
wallradius(cm)
l=1, Ist = 1.14 A, f = 33.632 GHz
B0 = 15.2 kG
0 1 2 3 4 5 6
0.00
0.02
0.04
0.06
0.08
0.10
z (cm)
Fieldamplitude
0.0
0.1
0.2
0.3
0.4
Leff
wallradius(cm)
l=2, Ist = 1.08 A, f = 34.786 GHz
1. Fast-growing and well-established mode
is subsequently suppressed by a
later-starting mode with a more favorable field profile.
2. HOMs, , , .
3. HOMs, , interaction strength , .
4. HOM
eff st
st
f L I
I
↑ ↑ ↓
Θ ↑ ↓ ↑
s, , , .z stf k I↑ ↑ ↑
Axial mode competition criteria for our design
K. F. Pao, et.al, Phys. Plasmas 14, 093301 (2007).
7. Unlike the standing-wave mode in a gyro-monotron,
there is no resonant mode in a
cold gyro-BWO circuit (basically a waveguide).
So the hot gyro-BWO field profile is determined
entirely by beam-wave interactions.
This allows a magnetic field taper to change the hot field profile
and consequently achieve the optimal efficiency at a broad range
of beam current and magnetic field.
In our doctoral thesis, this effect is exploited to
achieve a gyro-BWO with above 30% 3dB bandwidth tunability.
A Broadband Gyro-BWO Scheme : Simulation
Basic Idea:
8. 11Operation Mode : TE
Cyclotron Harmonic : Fundamental
0.3 cm
Cutoff frequency (at = 0
wref
w
R
r
0
.3 cm) 29.28 GHz
Beam current ( ) 3~8 A
Beam voltage ( ) 75 kV
Magnetic field ( ) 13~18 kG
Guiding c
b
b
I
V
B
0
enter position ( ) 0.35
Velocity ratio ( / ) 1.2
Velocity spread ( / ) 5 %
c w
z
z z
r r
v v
v v
α ⊥=
∆
Simulation parameters of the Gyro-BWO
Interaction structure for our design
A Broadband Gyro-BWO Scheme (1)
9. -10 -5 0 5 10 15
31.6
31.8
32.0
32.2
32.4
32.6
∆B/B (%)
Frequency(GHz)
8 A
7 A
6 A
5 A
4 A
3 A
B0 = 14 kG
Predicted efficiency, frequency as a function of ∆B/B.
P.S.
NTU taper coil has the max
current restriction ~ 20 A
so the corresponding taper magnetic field
percentage must less than 6%
when doing the experiment.
A Broadband Gyro-BWO Scheme (2)
-10 -5 0 5 10 15
0
5
10
15
20
25
30
35
40
8 A
7 A6 A5 A
4 A
∆B/B (%)
Efficiency(%)
3 A
0 2 4 6 8
13.2
13.4
13.6
13.8
14.0
14.2
For example :
∆B/B = (14.07-13.93)/14 = 0.1 = 1%
∆B
z (cm)
B-field(kG)
the total length of the interaction section
8.4 cm
10. -8 -6 -4 -2 0 2 4 6 8
0
10
20
30
40
∆B/B (%)
Efficiency(%)
-8 -6 -4 -2 0 2 4 6 8
0
2
4
6
8
Power
Power(kW)
I(A)
∆B/B (%)
Current
50
100
150
200
Corresponding beam current and output power as a function of ∆B/B
13.0 13.5 14.0 14.5 15.0 15.5 16.0
0
5
10
15
20
25
30
35
40
Frequency(GHz)
Efficiency(%)
30
32
34
36
38
l = 3
l = 2
B (kG)
l = 1
Interaction efficiency (line) and
oscillation frequency (dash) vs magnetic field
for different axial mode l = 1, 2, 3,
beam current = 5A
Different HOAMs efficiency vs B
In different current we can tune the taper B-field to achieve almost the same high efficiency.
A Broadband Gyro-BWO Scheme (3)
-10 -5 0 5 10 15
0
5
10
15
20
25
30
35
40
8 A
7 A6 A5 A
4 A
∆B/B (%)
Efficiency(%)
3 A
11. Fieldprofiled(line)andenergydepositionrate(dashline)
(relativescale)
B0 = 14 kG
Start-oscillation currents vs B
for the first three axial modes
Compare the first three axial modes
1. , , , .
2. , , interaction strength , .
two competing trends result in crossing
of the v.s. of two axial modes.
eff st
st
st
l f L I
l I
I B
↑ ↑ ↑ ↓
↑ Θ ↑ ↓ ↑
A Broadband Gyro-BWO Scheme (4)
(b) l = 1, Ist = 1.71 A, 0.81πΘ = , f = 32.46 GHz
0 1 2 3 4 5 6 7 8
-1.0
-0.5
0.0
0.5
1.0
energy deposition rate
field amplitude
Leff
(c) l = 2, Ist = 1.35 A, 3.29πΘ = , f = 33.22 GHz
0 1 2 3 4 5 6 7 8
-1.0
-0.5
0.0
0.5
1.0
energy deposition rate
field amplitudeLeff
(d) l = 3, Ist = 3.84 A, 5.05πΘ = , f = 33.77 GHz
0 1 2 3 4 5 6 7 8
-1.0
-0.5
0.0
0.5
1.0
energy deposition rate
field amplitude
Leff
Z (cm)
13 14 15 16
0
1
2
3
4
5
l = 2
l = 1
Ist(A)
B (kG)
0 1 2 3 4 5 6 7 8
0.0
0.1
0.2
0.3
0.4
12. 0 500 1000 1500 2000 2500 3000
0
10
20
30
40
50
60
70
80
90
100
TE(1)
1,1,2
TE(1)
1,1,1
Power(kW)
Time (ns)
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 500 ns
Normalizedamplitude
Frequency (GHz)
33.261
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 600 ns
33.360Normalizedamplitude
Frequency (GHz)
32.485
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 550 ns33.277
Normalizedamplitude
Frequency (GHz)
32.452
400 600 800
0
20
40
TE(1)
1,1,2
TE(1)
1,1,1
Power(kW)
Time (ns)
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 650 ns
Normalizedamplitude
Frequency (GHz)
32.485
Zoom in
2l = 2l =
2l =
1l =
1l =
1l =
0 500 1000 1500 2000 2500 3000
0
10
20
30
0
1
2
3
4
5
Etabwd(%)
Time (ns)
Ib(A)
Corresponding backward wave
efficiency and beam current
versus time
75kV, 14 kG, 4A
Power versus time
Time-dependent
spectrum 1l =
2l =
FFT spectrum of output power for different time
The latest-starting, lowest-order l = 1 mode eventually dominates.
A Broadband Gyro-BWO Scheme (5)
13. 30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 500 ns
Normalizedamplitude
Frequency (GHz)
32.776
13 14 15 16
0
1
2
3
4
B (kG)
Ist(A)
l = 1
l = 2
A Broadband Gyro-BWO Scheme (6)
0 500 1000 1500 2000
0
50
100
150
Ib(A)
Pfwd(kW)
0
2
4
6
Time (ns)
Corresponding backward wave
power and beam current versus
time
14 kG, 95 kV, 5A FFT spectrum of output power for different time
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 31.843 580 ns
Normalizedamplitude
Frequency (GHz)
32.794
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 31.843 600 ns
Normalizedamplitude
Frequency (GHz)
32.811
30 32 34 36 38 40
0.0
0.2
0.4
0.6
0.8
1.0 31.843 650 ns
Normalizedamplitude
Frequency (GHz)
2l =
1l =
1l = 1l =
2l =
2l =
Time-dependent
spectrum
The latest-starting, lowest-order l = 1 mode eventually dominates.
400 600 800
0
20
40
60
80
Ib(A)
Pfwd(kW)
0
2
4
6
Time (ns)
1l =2l =
Zoom in
14. A Broadband Gyro-BWO Scheme (7)
0 2 4 6 8 10
0
2
4
6
8
10
Velocityspread(%)
I (A)
Optimized bandwidth
(BW) versus current
with and without
taper.
1 2 3 4 5 6 7 8 9 10
0
10
20
30
40
50
60
without taper
with taper
I (A)
BW(%)
1dB BW
1 2 3 4 5 6 7 8 9 10
0
10
20
30
40
50
60
3dB BW
without taper
with taper
I (A)
BW(%)
Base on E-gun simulation
Spread versus current. Without taper map With taper map
75kV
15. A Broadband Gyro-BWO Scheme: Q-discussion (8)
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
35
Power(kW)
Efficiency(%)
14 kG
0
50
100
150
I (A)
0 2 4 6 8 10
0
200
400
600
800
1000
Qtotal
Qohm
Qd
14 kG
I (A)
Qd/Qohm/Qtotal
1 2 3 4 5 6 7 8 9 10
0
5
10
15
20
25
30
35
Power(kW)
Efficiency(%)
14 kG
0
50
100
150
200
250
I (A)
0 2 4 6 8 10
0
200
400
600
800
1000
Qtotal
Qohm
Qd
14 kG
I (A)
Qd/Qohm/Qtotal
75kV Without taper With taper
Without taper
14 kG, 4.5 A
Max efficiency
Qohm = 600.
With taper
14 kG, 3~8 A
Max efficiency
Qohm ~ 600.
What makes Qohm has such a modulation capability ? Field amplitude !
16. A Broadband Gyro-BWO Scheme: Q-discussion (9)
0 2 4 6 8 10
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0 dash_without taper
line_with taper
energy deposition rate
field profile
structure
z (cm)
normalizedamplitude
0 2 4 6 8 10
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
energy deposition rate
normalizedamplitude
dash_without taper
line_with taper
field profile
structure
z (cm)
14 kG, 5 A 14 kG, 8 A
17. Kou’s SC Magnet
95 kV Gyro-BWO Design : Experiment
Conditioning and test of Kou’s SC Magnet in NTU
95 kV−
18. 95 kV Gyro-BWO Design : MIG Simulation
2
(adiabatic invariant).
( 0, )z
p
J
B r z
⊥
=
=
EGUN drawing of the over all MIG,
electron trajectories,
adiabatic and equi-potential v.s. z.
95 kV
13.8 kG
α and spread v.s. B and Voltage,
corresponding to our experiment parameters.
19. 95 kV Gyro-BWO Design : Experiment
Interaction structure
to drift section to collector
Squeezed to elliptical cross-section
Output port :
Coupler (WR-28) with flange
Welding and air leakage test
11TE○
01TE□
back-ward wave
First step:
Connect all section (OFHC) with
flanges (SS304).
Using Au/Cu 35/65.
Second step:
Connect interaction section (OFHC) to
Coupler section (OFHC) and WR-28 section
(OFHC).
Using Palcusil #10.
After welding each step, it should be tested
by helium leak detector (~10-9 torr).
20. 95 kV Gyro-BWO Design : Experiment
Cold test
Short
Load
port 1
port 2
port 1
port 2
30 32 34 36 38 40
-40
-30
-20
-10
0
S11(dB)
Frequency (GHz)
30 32 34 36 38 40
-40
-30
-20
-10
0
S21(dB)
Frequency (GHz)
30 32 34 36 38 40
-40
-30
-20
-10
0
S11(dB)
Frequency (GHz)
30 32 34 36 38 40
-40
-30
-20
-10
0
S21(dB)
Frequency (GHz)
01 11
11 01
(port 1) ( )
( ) (port 2)
TE elliptical TE LHCP reflection
TE RHCP elliptical TE
⇒ ⇒ ⇒
⇒ ⇒ ⇒
□ ○
○ □
01 11(port 1) ( ) no wave (port 2)TE elliptical TE LHCP load⇒ ⇒ ⇒ ⇒□ ○
load
Through
21. 95 kV Gyro-BWO Design : Experiment
External diagnostic circuits
30 dB
20 dB attenuator
frequency
meter
3 dB
level set
attenuator
spectrum
analyzer
crystal
detector
oscilloscope
Narrow
band-pass
filter
22. 32 33 34 35 36
0
20
40
60
80
Power(kW)
freq (GHz)
without taper
with +taper
with -taper
4 A, 95kV
12 13 14 15 16 17
31
32
33
34
35
36 4 A, 95kV
Freq(GHz)
B-field (kG)
without taper
with +taper
with -taper
95 kV Gyro-BWO Design : Experiment
95 kV, 4A, tune B-field
All three set of data points are gun coil optimized.
We can see the efficiency enhancement clearly by adding the + taper.
Data is taken by G. D. Li and Y. N. Lin, and I am grateful to them for many years helpful cooperation.
23. Conclusion
Both of tapered waveguide and tapered B-field can enhance the
efficiency of gyro-BWO.
Because these effect increase the initial frequency mismatch result in
better bunch in phase space.
Asymmetry of field profiles plays a dominant role in mode competition.
A mode with a favorable field profile will suppress another mode with
a less favorable field profile.
Simulation with and without taper B-field reveal that broad bandwidth and
high-efficiency tunability.
A preliminary results reveals the capability of single mode operation with a
peak efficiency of 12 % and tunable bandwidth of 2 GHz (without taper)
tunable bandwidth of 4 GHz (with taper) at a test Ib = 4 A. Which 3dB
bandwidth can increase from 6% to 7.5%.
