Second Harmonic TE21 Gyrotron Backward Wave

Oscillator

報 告 人：吳 庭 旭 指 導 教 授：葉 義 生 老師

南台科技大學 電機所

Introduction to Gyro-BWO The gyrotron backward-wave oscillator (gyro-BWO) is a

promising source of coherent millimeter wave radiation based on the electron cyclotron maser instability on a backward waveguide mode.

The gyro-BWO is a nonresonant structure, so that the frequency can be tuned over a wide range by changing the magnetic field or the beam voltage.

The magnetic field is proportional to the relativistic electron cyclotron frequency, so the magnetic field of a gyrotron operating at the cyclotron harmonic is nearly 1/s of that of a gyrotron operating at the fundamental cyclotron.

Basic Mechanism of Gyrotron

X axis

Y axis Z axis

Boundary conditions (gyro-BWO)Fields of the circularly polarized TEmn mode

Field equation

The relativistic equation of motion

Computer Models of Nonlinear Simulation Code

N

j zj

jjjjj

mnmn

bz zfzv

ztrzW

ωKxI

izfkdzd

12

22

2

)()(),,,()(8

)(Ev

)()(' 11 zfikzf z

)()(' 22 zfikzf z

BBvceEeP

dtd

0

)(2 )()( mtimnmmnz erkJzfkB

Saturated Behavior

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

0

2

4

6

8

10

12

f

L = 5 .0 cm6 .07 .2

10 .012 .0

gyro-BWOTE21(2)

Z1 Z2

(b)

(a)

Ref [5]

Start-Oscillation Conditions of Various Transverse Modes

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

0

20

40

60

80

10 0

12 0f

(GH

z)

s= 1s= 2

T E 2 1T E 1 1

s= 3T E 0 11

3

2

T E 3 1

gyro-BWOTE21(2)

beam mode

waveguide mode

operating point

Start-Oscillation Conditions of Various Transverse Modes

-1 0 -8 -6 -4 -2 0 2 4 6 8 10k z (cm -1)

0

20

40

60

80

10 0

12 0

f (G

Hz) s= 1

T E 1 1

s= 3

T E 3 1

B 0= 7 .0 k GB 0= 8 .5 k G

(2)21TE(1)11TE(3)31TE

6 .5 7 .0 7 .5 8 .0 8 .5 9 .0 9 .5B 0 (k G )

0

4

8

12

16

20

24

I st (A

)

TE21(2)

TE11(1)

TE31(3)

13.7A

(b)

(a)

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

0

20

40

60

80

10 0

12 0

f (G

Hz)

s= 3T E 3 1

V b= 70 k VV b= 14 0 k V

(2)21TE(3)31TE

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0V b (k V )

02 04 06 08 0

1 0 01 2 01 4 0

I st (A

)

TE31(3)

TE21(2)

13.7A

(b)

(a)

Start-Oscillation Conditions of Various Axial Modes

6 .5 7 .0 7 .5 8 .0 8 .5 9 .0 9 .5B 0 (k G )

0

10

20

30

40

50

60

I st (A

)

3 2= 1

13.7A

(a)

| f(z

)|| f

(z)|

| f(z

)|

(a ) = 1

(b ) = 2

0 1 2 3 4 5 6 7z (cm )

(c ) = 3

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0V b (k V )

0

20

40

60

80

I st (A

)

32

= 1

14.1A

(b)

Start-Oscillation Conditions of Various Axial Modes

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0V b (k V )

trans

it an

gle(

radi

an)

3 4

3 5

3 6

3 7

f (G

Hz)= 3

= 2

= 1

987654320

(b)

)/)(( 0c0 zzz vLsvkω

6 .5 7 .0 7 .5 8 .0 8 .5 9 .0 9 .5B 0 (k G )

trans

it an

gle(

radi

an)

3 4

3 5

3 6

3 7

3 8

3 9

f (G

Hz)

987654320

= 3

= 2

= 1

(a)

The electron transit angle provides the total phase variation of the backward wave as experienced by the electrons in the interaction space. The electron transit angle is defined as

Performance of the Gyro-BWOs

6 .5 7 .0 7 .5 8 .0 8 .5 9 .0 9 .5B 0 (k G )

0

50

10 0

15 0

20 0

Pou

t (kW

)

3 4

3 5

3 6

3 7

3 8

f (G

Hz)

1 2 A

1 5 A

6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0V b (k V )

0

50

10 0

15 0

20 0

P out (k

W)

3 4 .2

34 .4

34 .6

34 .8

35 .0

35 .2

35 .4

f (G

Hz)1 5 A

12 A

(b)(a)

Conclusions The simulated results show that the field amplitude increases with

the interaction length until the length reaches the relaxation length in the gyro-BWO.

The electron transit angle of each axial mode has unique value, almost independent of the magnetic field and beam voltage, unless the oscillation frequency closes to the waveguide cutoff.

The gyro-BWO is predicted to yield a peak output power of 137 kW with an efficiency of 9.5 % at a beam voltage of 120 kV, beam current is 12 A and electron beam with an axial velocity spread .

TE21(2)

%8/ zz vv

References1. G. S. Kou, S. H. Chen, L. R. Barnett, H. Y. Chen, and K. R. Chu, “Experimental

study of an injection-locked gyrotron backward-wave oscillator,” Phys. Rev. Lett., vol. 70, no. 7, pp. 924-927, 1993.

2. T. H. Chang, K. F. Pao, C. T. Fan, S. H. Chen, and K. R. Chu, “Study of axial modes in the gyrotron backward-wave oscillator,” in Proc. Third IEEE International Vacuum Electronics Conference, 2002, pp. 123-124.

3. A. T. Lin, K. R. Chu, C. C. Lin, C. S. Kou, D. B. Mcdermott, and N. C. Luhmann, Jr., “Marginal stability design criterion for gyro-TWT, and comparison of fundamental with second harmonc operation,” Int. J. Electron., vol. 72, no. 5, pp. 813-885, 1992.

4. Y. S. Yeh, C. L. Hung, C. W. Su, T. S. Wu, Y. Y. Shin, and Y. T. Lo, “W-band second-harmonic gyrotron traveling wave amplifier with distributed-loss and severed structures,” Int. J. Infrared and Millimeter Waves, vol. 25, no. 1, 2004.

5. S. H. Chen, K. R. Chu, and T. H. Chang, “Saturated behavior of the gyrotron backward-wave oscillator,” Phys. Rev. Lett., vol. 85, no. 12, pp. 2633-2636, 2000.

6. S. H. Chen, T. H. Chang, K. F. Pao, C. T. Fan, and K. R. Chu, “Linear and time-dependent behavior of the gyrotron backward-wave oscillator,” Phys. Rev. Lett., vol. 89, no. 26, pp. 268303-1-268303-4, 2002.

7. 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. Plasma Sci., vol. 27, no. 2, pp. 391-404, 1999.

8. S. H. Chen, K. R. Chu, and T. H. Chang, “Saturated behavior of the gyrotron backward-wave oscillator,” Phys. Rev. Lett., vol. 85, no. 12, pp. 2633-2636, 2000.