Embed Size (px)
Citation preview
TE0,2,1 mode S =2, Vb = 30 kV, alpha = 2.57, velocity spread = 0% Rc / Rw = 0.3268, Rw = 0.3571 cm
L
rw
2 3 4 5 6 7 8 9 100
1x105
2x105
3x105
4x105
5x105
L / rwbe
am e
ffic
ienc
y (%
)
0
10
20
30
40
QP
b (
kW)
Rw = 0.3571 cm
Vb = 30 kV, alpha = 2.57, Bz0 = 17.4 kG
-20 -10 0 10 200
20
40
60
80
100
120
140
160 TE13TE32
TE61
TE02 (operating mode)TE22
TE51TE12
TE31
TE01TE21
S = 2
freq
uenc
y (G
Hz)
kz (cm-1)
S = 1
TE11
(1) Do QPVSB runs with the ideal cavity parameters you used to run for Larry's TE02, s=2 design Previous parameters: Rw = 0.3571 cm, L/ Rw = 6, Rc / Rw = 0.3268 Vb = 30 kV, alpha = 2.57, delta = -10 ~ 20 Operation mode TE021 S=2
-10 -5 0 5 10 15 200.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105 TE(2)022
TE(2)025
TE(2)023
TE(2)024 TE(1)
115
TE(2)022
TE(1)214
TE(1)213
TE(1)212
delta
QP
(kW
)
TE(2)021
16.8 17.2 17.6 18.00.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
TE(1)115
TE(2)025
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(1)214
TE(1)213
QP
(kW
)
B (kG)
TE(2)021TE(1)
212
(2) Let Vb =30 kV, Rc= 1.26 mm, alpha= 2.0, dVz/Vz = 5%, ismain =2, immain=0, inmain =2, ilmain=1, dmin=-10, dmax= 20
Rw = 0.3571 cm, L/ Rw = 6, Rc / Rw = 0.3528, velocity spread = 5% Vb = 30 kV, alpha = 2.0, delta = -10 ~ 20 Operation mode TE021 S=2
-10 -5 0 5 10 15 200.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105 TE(2)022
TE(1)215
TE(2)023
TE(2)024
TE(1)115
TE(2)022 TE(1)
214
TE(1)213 TE(1)
212
delta
QP
(kW
)
TE(2)021
16.8 17.2 17.6 18.00.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
TE(1)115
TE(1)215
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(1)214
TE(1)213
QP
(kW
)
B (kG)
TE(2)021TE(1)
212
Electron-wave resonance lines for the S=1 ~ S=3 Rw = 0.3571 cm, Vb = 30 kV, alpha = 2.0, Bz0 = 17.5 kG Operation mode TE021 S=2
-20 -10 0 10 20
20406080
100120140160180 TE14TE33TE91
TE52TE03TE23TE81
TE42
TE71TE13TE32TE61TE02TE22
TE51TE12TE41
S = 3
S = 2S = 1
TE31
TE01TE21
TE11
kz (cm-1)
freq
uenc
y (G
Hz)
(1) Do QPVSB runs with the ideal cavity parameters you used to run for Larry's TE02, s=2 design Previous parameters: Rw = 0.3571 cm, L/ Rw = 6, Rc / Rw = 0.3268, velocity spread = 0% Vb = 30 kV, alpha = 2.57, delta = -10 ~ 20 Operation mode TE021 S=2
16.8 17.2 17.6 18.00.0
5.0x105
1.0x106
1.5x106
2.0x106
TE(1)115TE(1)
214
TE(1)213
TE(1)212
TE(2)226
TE(2)225
TE(2)224
TE(2)224
TE(2)223
TE(2)223
TE(2)222TE(2)
222
TE(2)221 TE(2)
516
TE(2)515
TE(2)515
TE(2)514
TE(2)513
TE(2)512
TE(2)025
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(2)021
TE(3)426
TE(3)425
TE(3)236
TE(3)236
TE(3)235TE(3)
235 TE(3)234
TE(3)234
TE(3)233
TE(3)233
TE(3)232
TE(3)232TE(3)
231TE(3)
036
TE(3)035
TE(3)035
TE(3)034
TE(3)034 TE(3)
033
TE(3)033
TE(3)032 TE(3)
032TE(3)031
TE(3)526
TE(3)525TE(3)
524
TE(3)523
TE(3)523
TE(3)522
TE(3)521
B (kG)
QP
(kW
)
17.0 17.2 17.4 17.6 17.8 18.00.0
2.0x105
4.0x105
6.0x105
8.0x105
1.0x106
TE(1)115
TE(1)214 TE(1)
213
TE(2)226TE(2)
225
TE(2)224
TE(2)223
TE(2)222
TE(2)516
TE(2)514
TE(2)513
TE(2)025
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(2)021
TE(3)426
TE(3)235
TE(3)234
TE(3)233
TE(3)232
TE(3)036TE(3)
035
TE(3)034
TE(3)034
TE(3)033
TE(3)033
TE(3)032
TE(3)032
TE(3)031
TE(3)526
TE(3)525 TE(3)
524
TE(3)522
TE(3)522
TE(3)523
TE(3)521
B (kG)
QP
(kW
)
16.8 17.2 17.6 18.00
1x105
2x105
3x105
4x105
5x105
TE(2)223
TE(2)223
TE(2)222
TE(2)222
TE(2)221
TE(2)515TE(2)
514
TE(2)022
TE(2)426
TE(3)526
TE(3)523
TE(3)036
TE(3)035
TE(3)035
TE(3)034TE(3)
034 TE(3)033
TE(3)033
TE(3)032
TE(1)115TE(1)
214 TE(1)213
TE(1)212
TE(2)425
TE(2)516
TE(2)515
TE(2)513
TE(3)031
TE(2)512
TE(2)025
TE(2)024TE(2)
023TE(2)
022
TE(3)032
TE(3)524
TE(3)523
TE(3)522
TE(3)525
TE(3)521
TE(2)021
B (kG)
QP
(kW
)
16.8 17.2 17.6 18.00.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
TE(1)115
TE(2)025
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(1)214
TE(1)213
QP
(kW
)
B (kG)
TE(2)021TE(1)
212
(2) Let Vb =30 kV, Rc= 1.26 mm, alpha= 2.0, dVz/Vz = 5%, ismain =2, immain=0, inmain =2, ilmain=1, dmin=-10, dmax= 20
Rw = 0.3571 cm, L/ Rw = 6, Rc / Rw = 0.3528, velocity spread = 5% Vb = 30 kV, alpha = 2.0, delta = -10 ~ 20 Operation mode TE021 S=2
16.4 16.8 17.2 17.6 18.00.0
5.0x105
1.0x106
1.5x106
2.0x106
TE(1)115
TE(1)215
TE(1)214
TE(1)213TE(1)
212
TE(2)416
TE(2)126
TE(2)516
TE(2)515
TE(2)515
TE(2)514
TE(2)513
TE(2)512
TE(2)026
TE(2)025
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(2)021
TE(3)424
TE(3)036TE(3)
035
TE(3)035
TE(3)034TE(3)
034 TE(3)033
TE(3)033
TE(3)032
TE(3)032TE(3)
031
TE(3)526
TE(3)525
TE(3)524
TE(3)523
TE(3)523
TE(3)522
TE(3)521
B (kG)
QP
(kW
)
17.0 17.2 17.4 17.6 17.8 18.00.0
2.0x105
4.0x105
6.0x105
8.0x105
1.0x106
TE(1)115 TE(1)
215
TE(1)214
TE(1)213
TE(2)514
TE(2)513
TE(2)026
TE(2)025TE(2)
024
TE(2)023
TE(2)022
TE(2)022
TE(3)036 TE(3)
034TE(3)033TE(3)
032TE(3)
031 TE(3)526
TE(3)525
TE(3)524TE(3)
523
TE(3)522
TE(3)522
TE(3)521
TE(2)021
B (kG)
QP
(kW
)
16.5 17.0 17.5 18.00
1x105
2x105
3x105
4x105
5x105
TE(1)115
TE(1)215
TE(1)214
TE(1)213
TE(1)212
TE(2)416
TE(2)126
TE(2)516
TE(2)515
TE(2)515
TE(2)514
TE(2)513
TE(2)512
TE(2)026
TE(2)025
TE(2)024
TE(2)023
TE(2)022TE(2)
022
TE(3)032
TE(3)524
TE(3)523 TE(3)
523
TE(3)522
TE(3)522
TE(3)521
TE(2)021
B (kG)
QP
(kW
)
16.8 17.2 17.6 18.00.0
2.0x104
4.0x104
6.0x104
8.0x104
1.0x105
TE(1)115
TE(1)215
TE(2)024
TE(2)023
TE(2)022
TE(2)022
TE(1)214
TE(1)213
QP
(kW
)
B (kG)
TE(2)021TE(1)
212
Structure (all dimension in cm)
0 1 2 3 40.0
0.1
0.2
0.3
0.4
0.5
3.9855 cm
0.4077r1 = 0.35 0.3571
12.3
0.13550.3
0.15
Rw
(cm
)
Z (cm)
0.1
Parameters Table.1. (cavity dimensions shown above)
Vb = 35kV, alpha = 2.0, dVz/Vz = 6 %, Rc/Rw = 0.3192, and / 1Cu in all structure section.
Operation mode: (2)021TE
Use the stationary self-consistent code(parameters as in Table.1) to estimate the start oscillation current vs
B(uniform) for each competition mode.
8 10 12 14 16 18 20 220
10
20
30
40
50
TE(2)5,1
TE(2)2,2
TE(1)1,1
TE(1)2,1
TE(2)0,2
B (kG)
I st (
A)
16 17 18 19 200
2
4
6
8
10
TE(2)5,1
TE(2)2,2
TE(1)1,1
TE(1)2,1
TE(2)0,2
B (kG)
I st (
A)
The corresponding hot f and hot Q vs B (Hot Q defined in Sec. III-B of S. H. Kao, C. C. Chiu, P. C. Chang, K.
L. Wu, and K. R. Chu, “Harmonic Mode Competition in a THz Gyrotron Backward-Wave Oscillator,” Phys.
Plasmas 19, 103103 (2012).)
17.5 18.0 18.5 19.0 19.5 20.090
92
94
96
98
100
102
104
B (kG)
= 3
= 2
= 1
0
1000
2000
3000
4000
5000TE(2)
0,2
Hot
f (G
Hz)
Hot
Q
10 12 14 16 18 2020
25
30
35
40
45
50
Hot
f (G
Hz)
20
40
60
80
100
120
TE(1)1,1
B (kG)
Hot
Q
15 16 17 18 19 2040
42
44
46
48
50
TE(1)2,1
B (kG)
Hot
f (G
Hz)
Hot
Q
0
100
200
300
400
17 18 19 2088
90
92
94
96
98
100
0
1000
2000
3000
4000
5000
TE(2)2,2
Hot
Q
Hot
f (G
Hz)
B (kG)
16 17 18 19 2085
90
95
100
0
500
1000
1500
2000
2500
3000
TE(2)5,1
Hot
Q
B (kG)
Hot
f (G
Hz)
Change r1 to see the trend of the Ist vs B
r1 = 0.35 cm
15 16 17 18 19 200
2
4
6
8
10
TE(2)5,1
TE(2)2,2
TE(1)1,1
TE(1)2,1
TE(2)0,2
B (kG)
I st (
A)
r1 = 0.3 cm
15 16 17 18 19 200
2
4
6
8
10
TE(2)5,1
TE(1)1,1
TE(1)2,1
TE(2)0,2
B (kG)
I st (
A)
r1 = 0.25 cm
15 16 17 18 19 200
2
4
6
8
10
TE(2)5,1
TE(1)1,1
TE(1)2,1
TE(2)0,2
B (kG)
I st (
A)
Using stationary self-consistent code to determined efficiency and forward wave power
choose r1 = 0.35 cm, B = 17.78 kG (the magnetic field corresponding to the lowest Ist)
other parameters are the same as in Table.1.
0 2 4 6 8 10 1293.90
93.92
93.94
93.96
93.98
94.00
94.02
94.04
94.06 TE(2)0,2
Ib (A)
F
requ
ency
(G
Hz)
0 1 2 3 4 5 6 7 8 9 10 11 120
5
10
15
20
25
30
35
40
TE(2)0,2
backward wave power
Ib (A)
pow
er (
kW)
forward wave power
TE(2)
02 Ist
0.93 A 1.51 ATE(1)
21 Ist TE(1)
11 Ist
2.76 A
0 1 2 3 4 5 6 7 8 9 10 11 120
1
2
3
4
5
6
7
8
9
10
11TE(2)
0,2
TE(2)
02 Ist
0.93 A 1.51 ATE(1)
21 Ist TE(1)
11 Ist
backward wave efficiency
forward wave efficiency
Effi
cien
cy (
%)
Ib (A)
2.76 A
choose r1 = 0.35 cm, Ib = 5A, tune B-field, other parameters are the same as in Table.1.
17.6 17.8 18.0 18.2 18.4 18.6
93.8
94.0
94.2
94.4
94.6
94.8
95.0
95.2
95.4
95.6
Fre
quen
cy (
GH
z)
B (kG)
17.4 17.6 17.8 18.0 18.2 18.4 18.60
10
20
30
40
50
60
70
backward wave power
forward wave power
pow
er (
kW)
B (kG)
17.4 17.6 17.8 18.0 18.2 18.4 18.60
5
10
15
20
25
30
35
40
backward wave efficiency
forward wave efficiency
Effi
cien
cy (
%)
B (kG)
Using stationary self-consistent code to determined efficiency and forward wave power
choose r1 = 0.3 cm, B = 17.78 kG (the magnetic field corresponding to the lowest Ist)
other parameters are the same as in Table.1.
0 2 4 6 8 10 1293.94
93.96
93.98
94.00
94.02
94.04
94.06
94.08TE(2)
0,2
Ib (A)
F
requ
ency
(G
Hz)
0 1 2 3 4 5 6 7 8 9 10 11 120
5
10
15
20
25
30
35
40
TE(2)0,2
backward wave power~0
Ib (A)
pow
er (
kW)
forward wave power
TE(2)
02 Ist
1.25 A 1.78 ATE(1)
21 Ist TE(1)
11 Ist
2.75 A
0 1 2 3 4 5 6 7 8 9 10 11 120
1
2
3
4
5
6
7
8
9
10
11TE(2)
0,2
TE(2)
02 Ist
1.25 A 1.78 ATE(1)
21 Ist TE(1)
11 Ist
backward wave efficiency~0
forward wave efficiency
Effi
cien
cy (
%)
Ib (A)
2.75 A
choose r1 = 0.3 cm, Ib = 5A, tune B-field, other parameters are the same as in Table.1.
17.4 17.6 17.8 18.0 18.2 18.4 18.6
93.8
94.0
94.2
94.4
94.6
94.8
95.0TE(2)
0,2
Fre
quen
cy (
GH
z)
B (kG)
17.4 17.6 17.8 18.0 18.2 18.4 18.60
10
20
30
40
50
60
70TE(2)
0,2
backward wave power
forward wave power
pow
er (
kW)
B (kG)
17.4 17.6 17.8 18.0 18.2 18.4 18.60
5
10
15
20
25
30
35
40TE(2)
0,2
backward wave efficiency
forward wave efficiency
Effi
cien
cy (
%)
B (kG)
Mode Competition Criteria
Ref.: S. H. Kao, C. C. Chiu, P. C. Chang, K. L. Wu, and K. R. Chu, “Harmonic Mode Competition in a
THz Gyrotron Backward-Wave Oscillator,” Phys. Plasmas 19, 103103 (2012).
The mode competition processes examined in the above reference (Sec. IV-C) consistently follow three
criteria:
(1) The presence of the s = 2 mode enhances the Ist of the competing modes. For example, in Fig. 4(d-f), the s
= 2 mode enhances the linear Ist of the lowest-kz, s = 1 mode by a factor of 2.63, 2.14, and 1.63, respectively. As
can be seen from the figures, the enhancement factor is larger for a higher-amplitude s = 2 mode. As shown in [30],
the enhancement factor can be as large as 15 if the competing mode is a high-kz, s = 1 mode. Clearly, this criterion
also applies to an early-starting mode of any cyclotron harmonic number.
(2) The early-starting s = 2 mode is eventually suppressed by an s = 1 mode because of the unfavorable
evolution of the s = 2 coupling coefficient. This is a criterion that gives a lower-s mode a dominant advantage over
a higher-s mode.
(3) Among the s = 1 modes, the one with the lowest kz (instead of the lowest Ist) has a competitive advantage.
This criterion plays an insignificant role in an s = 1 gyrotron because one can always tune the magnetic field to
favor a low-kz (e.g. 1 ) mode. However, it governs the competition among the s = 1 modes when the magnetic
field is tuned in favor of an s>1 mode as in the present case. For the reason discussed at the end of Sec. IV-A, this
criterion can be generalized to the competition between any two modes, with the same or different cyclotron
harmonic numbers.
In multiple-mode competitions, more than one criterion may be at work. In this case, all three criteria could
work in favor of one mode (e.g. an early-starting, low-kz, s = 1 mode) or two criteria play opposing roles [e.g. an
early-starting, low-kz, s = 2 mode competing with a low-kz, s = 1 mode with a higher Ist, as in Fig. 4(d-f)]. One
criterion does not necessarily override an opposing one. The outcome of the competition depends on the relative
weight of the criteria, which in turn depends on the relative magnitude of kz, the separation of Ist of the modes
involved, as well as the peak Ib value. Hence, a clearer picture lies in the details in the Ist versus B chart.
Although criteria (1) and (3) do not bias a particular cyclotron harmonic number, criterion (2) is inherently in
favor of a lower-s mode. Thus, overall, a higher-s mode is much more likely to be suppressed by a lower-s mode,
as in Fig. 4(d-f) and [13, 14, 16, 19, 20, 30, 31].
Analysis of the case inTable I
(r1 = 0.35 cm, Vb=35 kV, α=2, Δvz/vz=6%, Rc/Rw=0.3192, uniform B-field, etc.)
1. At B = 17.78 kG, as Ib rises to 0.93 A, the TE02 (s=2) mode will be the first mode excited. It will remain in
single-mode operation until Ib=1.51 A (Pout ~3 kW, η~5.7%) which is the linear Ist of the TE21 (s=1) mode.
As Ib rises further to Ib=2.76 A, it hits the linear Ist of the TE11 (s=1) mode. We have assumed α=2 for all Ib.
2. In the competition between the early-starting, low-kz,TE02 (s=2) mode and the two, higher-kz, s=1 modes,
Criteria (1) and (3) favor the TE02 (s=2) mode, while Criterion (2) favors the s=1 modes. By Criteria (1) and
(3), it is likely that the TE02 (s=2) mode can survive up to Ib~2.5 A (Pout~7.5 kW, η~8.7%) before it is
eventually suppressed by the TE21 (s=1) mode. By Criterion (3), the highest-kz, TE11 (s=1) is less
competitive than the TE21 (s=1) mode.
3. If Criteria (1) and (3) dominate over Criterion (2) at still higher Ib (e.g. 5A), the TE02 (s=2) mode may
remain in single mode operation with significantly higher Pout (e.g. Pout ~18 kW and η~10.3% at Ib~5 A).
4. From cases studied in the above reference, it is unlikely that the TE02 (s=2) mode can operate at a more
optimal B-field (e.g. 17.6 kG) by suppressing the early-starting TE21 (s=1) mode.
Scenario 2 is reasonable, but Scenario 3 may be too optimistic. Unfortunately, no one here knows how
to run our time-dependent, multi-mode code to verify Scenarios 2 and 3. It will take ~2 months to get one
data point anyway.
