ω - kz
180 GHz second harmonic-multiplying gyrotron
traveling -wave amplifier
Y.S Yeh, C.H. Lai , C. H. Chen,T. Y. Lin
Department of Electro-Optical Engineering, Southern Taiwan University, Tainan 710, Taiwan
Abstract
研究方向
This study proposes a 180 GHz harmonic multiplying gyro-TWT operating at lower-order modes to avoid the
fundamental harmonic absolute instabilities. By amplifying a TE01 (s=1) drive wave, the second harmonic
component TE02 (s=2) of the beam current initiates a wave to be amplified. A nonlinear self-consistent code,
based on a slow time scale formulation, is developed to evaluate the performance of stable gyro-TWT amplifier.
The multi-stage gyro-TWT is predicted to yield a peak output power of ~330 kW at 180 GHz, a saturated gain of
~70 dB and a bandwidth of 5.0 GHz for a 100 kV, 15 A electron beam with an axial velocity spread Δvz/vz=5%.
Dispersion relation
The development of high-power microwave amplifiers in the Gband for commercial, industrial, and military applications is
attracting considerable interest. The highest average power of a
conventional linear beam slow wave device at 94 GHz is 1 kW.
Harmonic multiplying gyrotron traveling-wave amplifiers (gyroTWTs) provide the magnetic field reduction and frequency
multiplication [1]. Recently, the experimental result of a Ka-band
harmonic-multiplying gyro-TWT amplifier have shown that 75
kW of peak output power with a bandwidth of 1.06% and a gain
of more than 25 dB [2]. However, spurious oscillations may reduce
the amplification of the gyro-TWT operating at a high beam
current. This work proposes a G-band harmonic multiplying
gyro-TWT operating at lower-order modes to avoid the
fundamental harmonic absolute instabilities in the harmonic
interaction stage.
350
300
harmonic interaction stage
r1=0.1885 cm
TE04
TE03
s=3
5
250
f (GHz)
I. Introduction
200
TE02
s=2
150
100
4
TE01
s=1
50
0
-10 -8 -6 -4 -2 0 2 4
k z (cm-1)
6
8 10
Absolute instabilities
II. Computer Models of Nonlinear Simulation Code

i 1t m1
2
Bz  km1n1 f1 ( z ) J m1 (km1n1 r )e

 km2 2n2 f 2 ( z ) J m2 (km2n2 r )e i (2t m2 )
Field equation
Fundamental mode:

N
8
I
v
(
z
)

E
(rj , j , t j , z)
 d2
2
b
j
1
 2  k1z  f1 ( z)  i 2
Wj


dz
x
K
ω
v
(
z
)
f
( z)
j

1


zj
1
m1n1
m1n1 1
d
e
P  eE  v   Bext  B 
dt
c
Boundary conditions (amplification)
Fundamental mode:
ik z z
 ik z z
1
f1 ( z1 )  f1  e
 f1  e 1
f1 ' ( z1 )  ik z ( f1  e
ik z z
1
 f1  e
 ik z z
1
8 Ib
v j ( z )  E2 (rj , j , t j , z )
d
2
 2  k2 z  f 2 ( z )  i 2
Wj


dz
x
K
ω
v
(
z
)
f
( z)
j

1


2
zj
2
m2n2
m2n2
N

5
)
f1 ' ( z2 )  ik z f1 ( z2 )
Harmonic mode:
2
Relativistic equation of motion
IV. Performance of the Harmonic Multiplying Gyro-TWA
Harmonic mode:
f 2 ' ( z1 )  ik z f 2 ( z1 )
120
f 2 ' ( z2 )  ik z f 2 ( z2 )
L1
III. Absolute Instabilities
c u
rw (cm)
0.3
0.2
L3
L4
L5 L6 L7
L8
(a) physical configuration
drive stage
0.1
r1
harmonic interaction stage
tapered
section
sever
section
lossy
section
copper
section
0.0
10 6 (b) profile of wall resistivity
10 54
  
10

3
10  



1.0
0
This study proposes a G-band harmonic multiplying gyro-TWT
operating at lower-order modes to avoid the fundamental
harmonic absolute instabilities. The second harmonic
component TE21 (s=2) of the beam current initiates a wave to be
amplified by amplifying a TE11 (s=1) drive wave. The
parameters of the gyro-TWT are beam voltage Vb=100 kV,
magnetic field B0=36.56 kG, guiding center radius rc/rw=0.355 ,
and perpendicular-to-parallel velocity ratio α=1.2. For absolute
instabilities, the gyro-TWT is susceptible to the TE11 (s=1)
mode in the drive stage and the TE21 (s=2) and TE31 (s=3)
modes in the harmonic interaction stage. Shorting interaction
circuit and increasing wall losses are employed for preventing
high beam currents in the gyro-TWT.
L2
z1
2
4
6
8
z (cm)
10
12
r8

14
16
z2
Saturated Power (kW)
Fields of the circularly polarized TEmn mode
1cu=1.5101
4cu=1105
80
40
0
97
98
99
100
Frequency (GHz)
101
References
[1] K. R. Chu, etc. “Theory of the harmonic multiplying gyrotron traveling wave
amplifier,” Phys. Rev. Lett., vol. 78, pp. 4661-4664, 1997.
[2] J. Luo , etc. “Operation of a Ka-band harmonic-multiplying gyrotron travelingwave tube,” IEEE Trans. Plasmas Sci., vol. 57, no. 103, pp. 2768-2773, 2010.
Acknowledgments
The authors are also grateful to the National Center for High-Performance Computing
(NCHC) for providing computing facilities. This work was supported by the National
Science Council under Contract No. NSC 99-2221-E-218 -009.