Journal of the Korean Physical Society, Vol. 62, No. 6, March 2013, pp. 949∼953
Time-dependent Nonlinear Theory and Numerical Simulation of Folded
Waveguide Traveling Wave Tubes
Wei Feng Peng, Zhong Hai Ya n g and Yu Lu Hu
∗
National Key Laboratory of Science and Technology on Vacuum Electronics,
University of Electronic Science and Technology of China, Chengdu 610054, China
Zan Cao
China Electronics Standardization Institute, Beijing 100007, China
Yin-Fu Hu,Jin-JunFeng and Xian-Ping Wu
Vacuum Electronics National Lab, Beijing Vacuum Elec tronics Research Institute, Beijing 100015, China
(Received 17 December 2012, in final form 27 February 2013)
In this paper, a time-dependent nonlinear theory including the generalized time-dependent ra-
diofrequency (RF) field equations is presented to simulate the beam and wave interaction (BWI) of
folded waveguide (FWG) traveling wave tubes (TWTs). The analytical RF fields in FWG TWTs
are replaced by digitized RF field profiles obtained from electromagnetic simulations. A W-band
FWG TWT is studied by using a self-consistent one-dimensional code based on the theory. The
numerical results show good predictions when compared with the experimental tests.
PACS numbers: 84.40.Fe, 13.40.Ks
Keywords: Traveling wave tube, Folded waveguide, Time-dependent, Nonlinear
DOI: 10.3938/jkps.62.949
I. INTRODUCTION
Because of their outstanding characteristics, such as
high power, high frequency and good heat dissipation,
folded waveguide (FWG) TWTs are becoming more and
more important in millimeter and terahertz devices [1,2].
For improving the performances of FWG TWTs, three-
dimensional (3D) particle-in-cell (PIC) software such as
CST [3] or MAGIC [4,5] is applied to model their beam
and wave interaction (BWI) phenomena in the time do-
main, but huge computing resources are required for
practical simulations. As an alternate faster way, non-
linear BWI theories [6–11] have been developed for helix
and coupled cavity (CC) TWTs over the past decades,
but none of them is particularly for FWG TWTs [12].
In this paper, the generalized time-dependent RF field
equations are presented. With the digitized RF field pro-
files from the electromagnetic simulation software (such
as HFSS [13]), the certified time-dependent nonlinear
BWI theory can be expanded to simulate the FWG
TWTs. A one-dimensional (1-D) code based on this time-
dependent theory is constructed to simulate the BWI
performances of the FWG TWT whose slow wave struc-
ture (SWS) is shown in Fig. 1 [14]. The consistency be-
∗
E-mail: yuluhu@uestc.edu.cn
tween simulated and experimental results validates this
time-dependent BWI theory model.
This paper is organized as follows. In Sec. II, a time-
dependent nonlinear BWI theory for FWG TWTs
is constructed including the RF field equations, the
spacecharge (SC) field equations and the electron mo-
tion equations. In Sec. III, the W-band FWG TWT is
simulated and compared with experimental results. The
conclusion of this paper is in Sec. IV.
II. NONLINEAR TIME-DEPENDENT
THEORY
The RF fields in a SWS can be represented in the form
of the product of a complex amplitude f
n
(z,t), the RF
field profiles e
n
(x)andh
n
(x) and an exponential phase
factor as
E
rf
(x, t)=
[f
n
(z,t)e
−iω
n
t
e
n
(x)/S
n
(z)+c.c](1)
H
rf
(x, t)=
[f
n
(z,t)e
−iω
n
t
e
n
(x)/S
n
(z)+c.c], (2)
where e
n
(x)andh
n
(x) are the solutions of Maxwell’s
equations without a beam loaded, ω
n
is the angular fre-
quency, and the normalized function S
n
(z)in one period
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