1

W-Band Harmonic Multiplying Gyrotron

Traveling Wave Amplifier

Student： ChiaWei HungAdvisor： Yi Sheng Yeh

2- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

2 0

4 0

6 0

1 0

3 0

5 0

f (G

Hz)

T E 0 3

T E 0 2

2

s= 1

s= 2T E 3 1

T E 0 1T E 2 1

T E 1 1

(a ) (b )

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

2 0

4 0

6 0

1 0

3 0

5 0

f (G

Hz)

T E 0 3

s= 2

T E 1 1

T E 2 1

T E 0 1

T E 3 11

T E 0 2

Harmonic Multiplying Gyro-TWA (TE02→TE03)

[ K. R. Chu, etc., Phys. Rev. Lett., vol. 78, no. 24, pp. 4461-4464, 1997.]

drive sectionharmonic interaction section

r2=1.45 cmr1=2.044 cm

wall loss

(1) (2)

drive stage harmonic interaction stage

3

Performance of Harmonic Multiplying Gyro-TWA

Operating current : 13 A

Velocity spread : 5 %

Drive frequency : 16.925 GHz

Output frequency : 33.85 GHz

Peak power : 140 kW at 33.85 GHz

Saturated gain : 40 dB

Saturated efficiency : 18 %

Bandwidth : 3.2 %

[ K. R. Chu, etc., Phys. Rev. Lett., vol. 78, no. 24, pp. 4461-4464, 1997.]

4

Third-Harmonic Frequency Multiplication of a Two-Stage Tapered Gyro-TWA

By modulating an axis-encircling electron beam at the fundamental harmonic cyclotron frequency in the input stage, a frequency-tripled signal induced by the third-harmonic interaction in output stage.

[ C. W. Baik, etc, IEEE Trans. Electron Devices, 2005. ]

5

Harmonic Multiplying Gyro-TWA with Lossy Section and Serverd Section

Suppressing the absolute instability (kz>0)

Suppressing the absolute instability (kz<0)

[Ref. Y. S. Yeh, Y. Y. Shin, Y. C. You, and L. K. Chen, Phys. Plasmas. Vol. 12, pp. 043108, 2005.]

(NTHU)

(UCD)

(STUT)

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

2 0

4 0

6 0

8 0

1 0

3 0

5 0

7 0

f (G

Hz)

s = 1

s = 2 T E 0 1

T E 3 1

T E 2 11

T E 4 1

T E 1 1

s= 3

r 1= 0 .5 2 5 2 cm

2

3

d riv e s tag e(a )

6

Harmonic Multiplying Gyro-TWA (TE02→TE03)

(a ) p h y s ica l co n f ig u ra tio n

1 .0 0

1 .4 0

1 .8 0

2 .2 0

r w (c

m)

(b ) p ro f ile o f w a ll re s is tiv ity

1 0 21 0 41 0 6

0 1 0 2 0 30 4 0 5 0

cu

z (cm )

(a )

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

2 0

4 0

6 0

1 0

3 0

5 0

f (G

Hz)

T E 03

s= 2

T E 1 1

T E 2 1

T E 0 1

T E 3 11

T E 0 2

1 1 0 1 0 0 1 0 0 0/(cu1 0 4)

0

3

6

9

1 2

1 5

1 8

I st

T E 01

T E 11

T E 21

T E 31

(1)

(1 )

(1 )

(1 )

[Ref. 陳良愷，”磁旋行波放大器 “私立南台科技大學光電研究所碩士論文， (2006)6]

1 1 0 1 0 0 1 0 0 0/ (cu1 0 4)

0

1

2

3

4

5

|f(z

)|

T E 0 1

T E 1 1

T E 2 1

T E 3 1

(1 )

(1 )

(1 )

(1 )

L

(1) (2)

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

2 0

4 0

6 0

1 0

3 0

5 0

f (G

Hz)

T E 0 3

T E 0 2

2

s= 1

s= 2T E 3 1

T E 0 1T E 21

T E 1 1

(b )

34

5

6

34

5

6

34

5

6

7

W-band Harmonic Multiplying Gyro-TWA(TE11→TE21)

(a ) p h ysica l co n f ig u ra tio n

0 .0

0 .1

0 .2

r w (c

m)

(b ) p ro f ile o f w a ll re s is tiv ity

110 21 0 41 0 6

0 5 1 0z (cm )

cu

r 1 r 5

se rv e re d sec tio n

lo ssy sectio n

L L L L L

tap e red sec tio n co p p er

sec tio nd rive s tag e

harm o n ic in te rac tio n s tag e

z 1 z 2

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

5 0

1 0 0

1 5 0

2 0 0

2 5

7 5

1 2 5

1 7 5

f (G

Hz)

s = 1

s= 2T E 0 1

T E 3 1

T E 2 1

T E 4 1

T E 1 1

s= 3

r 1= 0 .1 7 9 5 c md riv e s ta g e

1

(a )

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

5 0

1 0 0

1 5 0

2 0 0

2 5

7 5

1 2 5

1 7 5

f (G

Hz)

T E 0 1

T E 4 1

s = 1

s = 2

s = 3

h a rm o n ic in te rac tio n s ta g er 5= 0 .1 4 9 2 c m

T E 1 1

T E 2 1

T E 3 1

2

(b )

L1=1.5cm

L2=1 cm

L3=5.5 cm

L4=1.5 cm

L5=4.0 cm

ρ1 = 2 × 101ρcu

ρ4 = 1× 105ρcu

r1 =0.1795 cm

r4 =0.1792 cm

(1) (2)

8

Analysis of Absolute Instability in the Harmonic Interaction Stage (Ⅰ)

(a ) p h y s ic a l co n f ig u ra tio n

0 .0

0 .1

0 .2

r w (c

m)

(b ) p ro f ile o f w a ll res is tiv ity

11 0 21 0 41 0 6

0 5 10z (cm )

cu

r 1 r 5

se rv e red sec tio n

lo ssy sec tio n

L L L L L

tap e re d sec tio n co p p e r

sec tio nd riv e s tag e

h a rm o nic in te rac tio n s tag e

z 1 z 2

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

5 0

1 0 0

1 5 0

2 0 0

2 5

7 5

1 2 5

1 7 5

f (G

Hz)

T E 0 1

T E 4 1

s = 1

s= 2

s = 3

h a rm o n ic in te ra c tio n s tag er 5= 0 .1 4 9 2 cm

T E 1 1

T E 21

T E 3 1

2

(b )

0 5 1 0z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

f

0 .0

0 .1

0 .2

r w (c

m)

r w

0 5 1 0z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

f

0 .0

0 .1

0 .2

r w (c

m)

f = 1 00 G H z

r w

0 5 1 0z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

f

0 .0

0 .1

0 .2

r w (c

m)

r w(a )

(b )

(c )

0 5 1 0z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

f

0 .0

0 .1

0 .2

r w (c

m)

r w(d )

f = 1 0 0 G H z

f = 10 0 G H z

f = 1 0 0 G H z

I = 1 5 A

I = 9 A

I = 1 3 A

I = 5 .5 A

0 5 1 0z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

f

T E 2 1 m o d e ab so lu te in s tab ilityI s t= 8 Af = 1 0 0 G H z L 5= 4 cm

(2 )

0 5 10z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

f

T E 2 1 m o d e ab s o lu te in s tab ili tyI st= 8 Af = 10 0 G H z L 5= 4 cm

(2 )

0 5 1 0z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

f

T E 2 1 m o d e a b s o lu te in s tab ilityI st= 8 Af = 1 0 0 G H z L 5= 4 cm

(2 )

0 5 10z (cm )

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

f

T E 2 1 m o d e ab s o lu te in s tab ilityI st= 7 .4 2 Af = 10 0 G H z L 5= 4 cm

(2 )

(1 .1cu)

(8cu)

(6c u)

(1c u)

(a )

(b )

(c )

(d )

9

Analysis of Absolute Instability in the Harmonic Interaction Stage (Ⅱ)

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (cm -1 )

0

5 0

1 0 0

1 5 0

2 0 0

2 5

7 5

1 2 5

1 7 5

f (G

Hz)

T E 0 1

T E 4 1

s= 1

s = 2

s= 3

h a rm o n ic in te ra c tio n s ta g er 5= 0 .1 4 9 2 c m

T E 1 1

T E 2 1

T E 3 1

2

(b )(a ) p h y s ica l co n f ig u ra tio n

0 .0

0 .1

0 .2

r w (c

m)

(b ) p ro f ile o f w a ll re s is tiv ity

11 0 21 0 41 0 6

0 5 1 0z (cm )

cu

r 1 r 5

serve red sec tio n

lo ssy se c tio n

L L L L L

tap e re d sec tio n co p p e r

sec tio nd rive s tag e

harm o n ic in te rac tio n s tag e

z 1 z 2

0 1 2 3 4 5

(cu)

0

5

1 0

1 5

2 0

I st (A

)

T E 2 1

L 5= 4 cm

(2 )

7.42A7.42A

0 5 1 0L 5 (c m )

0

5

1 0

1 5

I st (A

)

T E 2 1(2 )

c u

10

Performance of W-band Harmonic Multiplying Gyro-TWA

0 5 1 0z (c m )

-6 0

-2 0

2 0

6 0

1 0 0

Gai

n (d

B)

Pfw

d (kW

)

(b )

1 0 -6

1 0 -4

1 0 -2

1

1 0 2

1 0 -8

P f w d

G ain

T E 2 1(2 )

Operating current : 7.42A

Velocity spread : 8 %

Operating voltage : 60 kV

Drive frequency : 50 GHz

Input power : 96 W

Output frequency : 100 GHz

Peak power : 30 kW

Efficiency : 7%

Saturated gain : 20 dB

(a ) p h y sic a l c o n f ig u ra tio n

0 .0

0 .1

0 .2

r w (c

m)

(b ) p ro f ile o f w all re s is tiv ity

11 0 21 0 41 0 6

0 5 1 0z (cm )

cu

r 1 r 5

se rv ere d sec tion

lo ssy sec tion

L L L L L

tape re d sec tio n cop p e r

se ctiond riv e stag e

harm o n ic in te rac tio n stage

z 1 z 2

0 5 1 0z (cm )

-6 0

-2 0

2 0

6 0

1 0 0

Gai

n (d

B)

Pfw

d (kW

)(b )

1 0 -6

1 0 -4

1 0 -2

1

1 0 2

1 0 -8

P f w d

G ain

T E 2 1(2 )

0 1 2 3 4z (cm )

0 .1

0 .1 5

0 .2

r w (c

m)

P fwd (

W)

(a )

1 0 -2

1

1 0 2

P f w dr w

1 0 -1

1 0 1

1 0 3

P d= 96 Wf = 5 0 G H z2 f = 10 0 G H z

T E 1 1(1 )

11

A Ka-band and W-band harmonic multiplying gyro-TWTs with distributed wall losses and attenuating severs are proposed to improve the stability of the amplification and the performance of an amplifier.

Due to absolute instabilities in the harmonic multiplying gyro-TWA (TE02TE03) , the harmonic multiplying gyro-TWA operates at TE11 TE21 modes.

Conclusions(Ⅰ)

(a ) p h y sica l co n f ig u ra tio n

0 .00 .20 .40 .60 .81 .0

r w (c

m)

(b ) p ro f ile o f w a ll re s is tiv ity

11 0 21 0 41 0 6

0 5 1 0 1 5 2 0z (c m )

cu

r 1 r 5

se rv e red sec tio n

lo ssy sec tio n

L L L L L

tap ere d se ctio n

c o p p erse c tio n

d riv e s tag e h a rm o n ic in te rac tio n s tag e

z 1 z 2

(1) (2)

(1) (2)

- 8 - 4 0 4 8- 6 - 2 2 6 1 0- 1 0k z (c m -1 )

0

2 0

4 0

6 0

8 0

1 0

3 0

5 0

7 0

f (G

Hz)

T E 0 14

T E 4 1

5

s = 1

s= 2

s= 36

h a rm o n ic in te ra c tio n s tag e r 5= 0 .4 4 1 0 c m

(b )

T E 1 1

T E 2 1

T E 3 1

12

Conclusions(Ⅱ)

Ka-band harmonic multiplying gyro-TWT is predicted to yield a peakpower of 230 kW, corresponding to a saturated gain of 40 dB at an interaction efficiency of 30% where Ib=13 A and Δvz /vz=8%.

W-band harmonic multiplying gyro-TWT is predicted to yield a power of 30 kW, corresponding to a saturated gain of 20 dB at an interaction efficiency of 7% where Ib= 7.42 A and Δvz /vz=8%.

0 5 1 0z (cm )

-6 0

-2 0

2 0

6 0

1 0 0

Gai

n (d

B)

Pfw

d (kW

)

(b )

1 0 -6

1 0 -4

1 0 -2

1

1 0 2

1 0 -8

P f w d

G a in

T E 2 1(2 )

0 1 2 3 4z (c m )

0 .1

0 .1 5

0 .2

r w (c

m)

P fwd (

W)

(a )

1 0 -2

1

1 0 2

P f w dr w

1 0 -1

1 0 1

1 0 3

P d= 96 Wf = 5 0 G H z2 f = 10 0 G H z

T E 1 1(1 )

13

References (Ⅰ)

1. K. R. Chu, G. Guo and V. L. Granatstein, “Theory of the harmonic multiplying gyrotron traveling wave amplifier,” Phys. Rev. Lett., vol. 78, no. 24, pp. 4461-4464, 1997.

2. V. L. Granatstein, and I. Alexeff, High-power Microwave Source, Artech House, 1985.

3. J. Rodgers, H. Guo, G. S. Nusinovich, V. L. Granatstein, “Experimental study of phase deviation and pushing in a frequency doubling,” IEEE Trans. Electron Devices, vol. 48, no. 10, pp. 2434-2441, 2001.

4. K. R. Chu, G. Guo and V. L. Granatstein, “Theory of the harmonic multiplying gyrotron traveling wave amplifier,” Phys. Rev. Lett., vol. 78, no. 24, pp. 4461-4464, 1997.

5 .A. T. Lin, C. C. Lin, “Amplification mechanism in the output section of the harmonic multiplying grotron traveling-wave amplifier,” IEEE Trans. Plasma Sci., vol. 30, no. 3, pp. 931-937, 2002.

6. 朱國瑞 , 張存續 , 陳仕宏 , 電子迴旋脈射－原理與應用 , 物理雙月刊 , 2006.

14

References (Ⅱ)

7. C. W. Baik, S. G. Jeon, D. H. Kim, N. Sato, K. Yokoo, and G. S. Park, IEEE Trans. Electron Devices 52, 829 (2005)

8. S. Y. Park, V. L. Granatstein, and R. K. Parker, “A Linear theory and design study for a gyrotron backward-wave oscillator,” Int. J. Electronics, vol. 57, pp. 1109-1123, 1984.

9. Y. Y. Lau, K. R. Chu, L. R. Barnett, and V. L. Granatstein, “Gyrotron Traveling Wave Amplifier : I. Analysis of Oscillation,” Int. J. Infrared Millimeter Waves, vol. 2, pp. 373-393, 1981.

10. K. R. Chu, H. Y. Chen, C. L. Hung, T. H. Chang, L. R. Barnett, S. H. Chen, and T. T. Yang, “Ultra high gain gyrotron traveling wave amplifier, “Phys. Rev. Lett., vol. 81, pp. 4760-4763, 1998.

11. K. R. Chu, H. Y. Chen, C. L. Hung, T. H. Chang, L. R. Barnett, S. H. Chen, T. T. Yang, and D. J. Dialetis, “Theory and experiment of ultrahigh-gain gyrotron traveling wave amplifier,” IEEE Trans. Microwave Theory Tech., vol. 27, no. 2, pp. 391-404, 1999.

12. 陳良愷，”磁旋行波放大器 “私立南台科技大學光電研究所碩士論文， (2006)6.