1 Operating Regimes of a Gyrotron Backward-Wave Oscillator Driven by an External Signal Student ： Chih-Wei Liao Advisor ： Yi-Sheng Yeh [ NTHU ]

1

Operating Regimes of a Gyrotron Backward-Wave Oscillator Driven by an External Si

gnal

Student： Chih-Wei Liao Advisor： Yi-Sheng Yeh

[ NTHU ]

2

Stability Analysis of an Injection-Locking Gyro-BWO

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

0 .00 .10 .20 .30 .40 .5

r w(z

) (c

m)

(b ) m ag n e tic f ie ld

1 3 .4

1 3 .6

1 3 .8

Bz(

z) (

kG)

(c ) f ie ld p ro f ile

0 2 4 6 8 1 0 1 20 .00 .30 .50 .81 .0

| f(z

)|

z (c m )z 1 z 2

0 .3 3 cm 0 .2 6 8 cm 0 .3 3 cm

-4 -2 0 2 4kz (cm-1)

0

20

40

60

80

100

f (

GH

z)

s=1 TE11

B0=13.8 kG

Fig. (a) Profile of the interaction structure . (b) Magnetic field . (c) Normalized field profile versus z in a gyro-BWO. The oscillation frequency on free-running operation is 32.8525 GHz in the gyro-BWO. Parameters are Vb=100 kV, B0 =13.8 kG, Ib=5 A, α=1.1, and rc=0.09 cm.

＊ Y. S. Yeh, T. H. Chang, and Y. C. Yu, “Stability analysis of a gyrotron backward-wave oscillation with an external injection signal,” IEEE. Trams. Plasma Sci., vol. 34, no. 4, 2006.

(STUT and NTHU)

3

Amplifier Mode

0 .0 0 1 0 .0 1 0 .1 1P in (W )

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

Pou

t (W

)

I b= 4 .7 5 Af o= 3 0 .8 8 5 1 G H z

f = -0 .3 M H z

n o n lin ea rlin ea r

0 .0 0 1 0 .0 1 0 .1 1 1 0 1 0 0P in (W )

0 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

Pou

t (W

)

I b= 5 .0 Af o= 3 0 .8 9 4 6 G H z

f = -0 .3 M H z


- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5( -

-3 6 0

-3 1 5

-2 7 0

-2 2 5

-1 8 0

-1 3 5

(o )


I b= 4 .7 5 A P in= 0 .0 0 1 W

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5( -

-3 6 0

-3 1 5

-2 7 0

-2 2 5

-1 8 0

-1 3 5

(o )

n o n lin e a rlin e a r

I b= 5 .0 A P in= 0 .0 0 1 W

4

Oscillator Plane of a Uniform Structure Gyro-BWO Driven by an External Signal

A: amplifier mode regime

B: mode competing regime

C: phase-locking oscillation mode regime

0 .0 0 0 1 0 .0 1 1 1 0 0 1 0 0 0 0P in (W )

0

2

4

6

8

I b (A

)

B 0= 1 3 .8 k Gf = -0 .7 M H z

A BC

A

0 .0 0 1 0 .0 1 0 .1 1 1 0 1 0 0P in (W )

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

Pou

t (W

)f = -0 .7 M H z

I b= 4 .7 1 A 5 .0

5

1 e-0 0 5 0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1P in (k W )

0 .0 1

0 .1

1

1 0

1 0 0

Pou

t (W

)

I b= 2 .4 3 Af o= 3 2 .8 6 8 6 G H z

f = -0 .7 M H z

a m p lif ierm o d e

p h a se -lo ck in g o sc illa tio n

m o d e

cr itica l d r iv ep o w er

2. Non-uniform Structure

Fig. (a) Profile of the interaction structure. (b) Magnetic field versus z in a gyro-BWO. Ist=2.43 fo=30.8686 GHz. Parameters are Vb=100 kV, B0 =13.8 kG, α=1.1, and rc=0.09 cm.

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

0 .0 00 .1 00 .2 00 .3 00 .4 00 .5 0

r w (

cm)

(b )

0 2 4 6 8 1 0 1 2

z (cm )

1 3 .4

1 3 .6

1 3 .8

B0

m ag n e tic f ie ld

0 .3 3 cm 0 .2 6 8 cm 0 .3 3 cm

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1P in (W )

0 .0 0 1

0 .0 1

0 .1

1

1 0

Pou

t (W

)

I b= 1 .8 Af o= 3 2 .8 5 7 0 G H z

f = -0 .7 M H z


1 e -0 0 5 0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1P in (k W )

0 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

Pou

t (W

)

f = -0 .7 M H z

I b= 2 .4 5 Af o= 3 2 .8 6 8 2 G H z


m o d eco m p etin g

p h a se -lo ck in g o sc illa tio n

m o d e

unstable mode

6

Phase-locking Oscillation mode (I)

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (W )

0 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0P

out (

W)

I b= 3 .1 Af o= 3 2 .8 5 2 9 G H z

f = -0 .7 M H z

0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

Pou

t (W

)

I b= 5 .0 Af o= 3 2 .8 5 2 5 G H z

f = -0 .7 M H z

- 8 - 4 0 4 8

( -

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

PinP

out (

dB)

I b= 3 .1 AQ = 1 3 5

A d le r 's cu rv en o n lin e a r c o d e

- 8 - 4 0 4 8

( -

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

PinP

out (

dB)


I b= 5 .0 AQ = 1 3 5

7

Phase-locking Oscillation mode (II)

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (W )

0 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0P

out (

W)

I b= 3 .1 Af o= 3 2 .8 5 2 9 G H z

f = -0 .7 M H z

0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

Pou

t (W

)

I b= 5 .0 Af o= 3 2 .8 5 2 5 G H z

f = -0 .7 M H z

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5( -

-9 0

-4 5

0

4 5

9 0

(o )

n o n lin ea rth eo rtic a l

I b= 5 .0 A P in= 1 k W

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5( -

-9 0

-4 5

0

4 5

9 0

(o )

lo ck in gth eo rtic a l

I b= 3 .1 A P in= 0 .1 W

80 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

Pou

t (W

)

I b= 5 .0 Af = -0 .7 M H z

Three Operating Regimes

Theory of Nonlinear Oscillations

amplifiermode

phase-locking oscillation mode

Hard-excitation region

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

0

4 0 0 0 0

8 0 0 0 0

1 2 0 0 0 0

1 6 0 0 0 0

2 0 0 0 0 0

Pou

t (W

)

I b= 5 .0 Af = -0 .7 M H z

amplifiermode

modecompeting

phase-locking oscillation

mode unstable mode

E

d Ed t

III

III

C 2

C 1

P

Ref.[20]

Ref.[20]

9

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (W )

0 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

Pou

t (W

) I b= 3 .1 Af o= 3 2 .8 5 2 9 G H z

f = -0 .7 M H z -3 -9

0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

Pou

t (W

)I b= 5 .0 Af o= 3 2 .8 5 2 5 G H z

f = -0 .7 M H z -3 -9

Amplitude-Frequency Response

-6 0 -4 0 -2 0 0 2 0 4 0 6 0f - f o (M H z)

0 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

Pou

t (kW

)

I b= 5 .0 Af o= 3 2 .8 5 2 5 G H z

2 0 0 W 1 k W1 0 W

1 0 k W

2 0 0 W

1 k W

1 0 W

-4 0 -3 0 -2 0 -1 0 0 1 0 2 0 3 0 4 0f - f o (M H z)

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

Pou

t (W

)

I b= 3 .1 Af o= 3 2 .8 5 2 9 G H z

1 W1 0 W

0 .1 W

0 .1 W

1 W

10

Oscillator Plane of a Non-uniform Structure Gyro-BWO Driven by an External Signal

0 .0 0 1 0 .1 1 0 1 0 0 0P in(W )

0

1

2

3

4

5

6

I b(A

)

B 0= 1 3 .8 k Gf = -3 .0 M H z

A

B

C

A

A: amplifier mode regime

B: mode competing regime

C: phase-locking oscillation mode regime

0 .0 0 0 1 0 .0 1 1 1 0 0 1 0 0 0 0P in (W )

0 .1

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

1 0 0 0 0 0

1 0 0 0 0 0 0

Pou

t (W

)

f = -3 .0 M H z

I b= 2 .4 5 A 3 .1 5 .0

11

IV. Summary (I) There are three different operating

regimes, amplifier regime , mode competing regime and phase-locking oscillation regime in a gyro-BWO driven by an external signal.

Only amplifier mode occur where the beam currents are below the free-running currents. The nonlinear results of the mode are consistent with the linear theoretical results.

In the phase-locking oscillation mode regime, the nonlinear results correspond to Alder’s curve.

There are three possible mode , amplifier mode , unstable mode and phase-locking oscillation mode in the mode competing regime.

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

0

4 0 0 0 0

8 0 0 0 0

1 2 0 0 0 0

1 6 0 0 0 0

2 0 0 0 0 0

Pou

t (W

)

I b= 5 .0 Af = -0 .7 M H z

0 .0 0 1 0 .0 1 0 .1P in (W )

0 .0 1

0 .1

1

1 0

Pou

t (W

)

I b= 4 .4 Af o= 3 0 .8 6 6 8 G H z

f = -0 .3 M H z


- 8 - 4 0 4 8

( -

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

PinP

out (

dB)


I b= 5 .0 AQ = 1 3 5

0 .0 0 0 1 0 .0 0 1 0 .0 1 0 .1 1 1 0P in (k W )

0

4 0 0 0 0

8 0 0 0 0

1 2 0 0 0 0

1 6 0 0 0 0

2 0 0 0 0 0

Pou

t (W

)I b= 5 .0 Af = -0 .7 M H z

modecompeting

regime

amplifierregime

phase-lockingoscillation

regime

amplifiermode

phase-lockingoscillation

modeunstable

mode

12

IV. Summary (II)

Due to nonlinear oscillation theory the solutions of the unstable mode are the steady-state solutions, but aren’t stable solutions.

In amplitude-frequency response of gyro-BWOs driven by an external signal, the phase-locking oscillation modes occur where the driven frequencies approach the free-running frequencies.

There are two competing modes, amplifier mode and phase-locking oscillation mode in the amplitude-frequency response where the gyro-BWOs are driven by low injected power signals with ∆f=0.

E

d Ed t

III

III

C 2

C 1

P

-4 0 -3 0 -2 0 -1 0 0 1 0 2 0 3 0 4 0f - f o (M H z)

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

Pou

t (W

)

I b= 3 .1 Af o= 3 2 .8 5 2 9 G H z

1 W1 0 W

0 .1 W

0 .1 W

1 W

13

V. References (I)[1] G. S. Nusinovich and O. Dumbrajs, “Theory of gyro-backward wave oscillators with tapered magnetic field and waveguide

cross section,” IEEE Trans. Plasma Sci., vol. 24, pp. 620-629, Jun. 1996.[2] S. Y. Park, V. L. Granatstein, and R. K. Parker, “A linear theory and design study for a gyrotron backward wave oscillator,”

Int. J. Electron., vol. 57, pp. 1109-1123, Jun.1984.[3] C. S. Kou, “Starting oscillation conditions for gyrotron backward wave oscillators,” Phys. Plasmas, vol. 1, pp. 3093–3099,

Sep. 1994.[4] A. K. Ganguly and S. Ahn, “Nonlinear analysis of the Gyro-BWO in three dimensions,” Int. J. Electron., vol. 67, pp. 261

–276, Feb. 1989.A. T. Lin, Phys. Rev. A 46, R4516 (1992).[5] A. T. Lin, “Mechanisms of efficiency enhancement in gyrotron backward- wave oscillators with tapered magnetic fields,

” Phys. Rev. A, Gen. Phys., vol. 46, pp. R4516–R4519, Oct. 1992.[6] M. T.Walter, R.M. Gilgenbach, P. R. Menge, and T. A. Spencer, “Effects of tapered tubes on long- pulse microwave emis

sion from intense e-beam gyrotron-backward-wave-oscillators,” IEEE Trans. Plasma Sci., vol. 22, pp. 578–583, Oct. 1994.

[7] C. S. Kou, C. H. Chen, and T. J. Wu, “Mechanisms of efficiency enhancement by a tapered waveguide in gyrotron backward wave oscillators,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 57, pp. 7162–7168, Jun. 1998.

[8] M. T. Walter, R. M. Gilgenbach, J. W. Luginsland, J. M. Hochman, J. I. Rintamaki, R. L. Jaynes, Y. Y. Lau, and T. A. Spencer, “Effects of plasma tapering on gyrotron backward-wave oscillators,” IEEE Trans. Plasma Sci., vol. 24, pp. 636–647, Jun. 1996. [11] R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE, vol. 61, pp. 1380–1385, Oct. 1973.

[9] R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE, vol. 61, pp. 1380–1385, Oct. 1973.[10] H. Guo, D. J. Hoppe, J. Rodgers, R. M. Perez, J. P. Tate, B. L. Conroy, V. L. Granatstein, A. M. Bhanji,

P. E. Latham, G. S. Nusinovich, M. L. Naiman, and S. H. Chen, “Phase-locking of a second harmonic gyrotron oscillator using a quasioptical circulator to separate injection and output signals,” IEEE Trans. Plasma Sci., vol. 23, pp. 822–832, Oct. 1995.

14

V. References (II)[11] C. S. Kou, S. H. Chen, L. R. Barnett, H. Y. Chen, and K. R. Chu, “Experimental study of an injection-locked gyrotron bac

kward-wave oscillator,” Phys. Rev. Lett., vol. 70, pp. 924–927, Feb. 1993.[12] T. H. Chang, S. H. Chen, F. H. Cheng, C. S. Kou, and K. R. Chu, “Experimental study of an injection

locked Gyro-BWO,” in Proc. 24th IRMMW, 1999, pp. M–A2.[13] A. Grudiev and K. Schunemann, “Numerical analysis of an injection-locked gyrotron backward-wave

oscillator with tapered sections,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 68, pp. 016501-1–016501-10, Jul. 2003.

[14] A. W. Fliflet and W. M. Manheimer, “Nonlinear theory of phase locked gyrotron oscillators driven by an external signal,” Phys. Rev. A, vol. 39, pp. 3422–3443, Apr. 1989.

[15] W. M. Manheimer, B. Levush, and T. M. Antonsen, Jr., “Equilibrium and stability of free-running, phase- locked, and mode-locked quasioptical gyrotrons,” IEEE Trans. Plasma Sci., vol. 18, pp. 350–368, Jun. 1990.

[16] R. A. York and T. Itoh, “Injection- and phase-locking techniques for beam control,” IEEE Trans. Microwave Theory Tech., vol. 46, pp. 1920–1929, Nov. 1998.

[17] K. R. Chu, H. Y. Chen, C. L. Hung, T. H. Chang, L. R. Barnett, S. H. Chen, T. T. Yang, and D. Dialetis, “Theory and experiment of ultrahigh gain gyrotron traveling-wave amplifier,” IEEE Trans. Plasma. Sci., vol. 27, no. 2, pp. 391–404, Apr. 1999.

[18] 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, no. 21, pp. 4760–4763, Nov. 1998.

[19] C. S. Kou, “Backward traveling wave amplification in the gyrotron ” Phys. Plasmas, vol. 4, no. 11, pp. 4140-4143, 1997.[20] A. H. McCurdy, A. K. Ganguly, C. M. Armstrong, “Operation of a driven single-mode electron cyclotron master,” Phys. R

ev. A, vol. 40, no. 3, pp. 1402-1417, 1989.[21] Y. S. Yeh, T. H. Chang, and Y. C. Yu, “Stability analysis of a gyrotron backward-wave oscillation with an external injectio

n signal,” IEEE. Trams. Plasma Sci., vol. 34, no. 4, pp.1523-1528, Aug. 2006.

Documents

1 Operating Regimes of a Gyrotron Backward-Wave Oscillator Driven by an External Signal Student ： Chih-Wei Liao Advisor ： Yi-Sheng Yeh [ NTHU ]