Particle simulation of a ka-band gyrotron traveling wave amplifierShou-Xi Xu, Pu-Kun Liu, Shi-Chang Zhang, Chao-Hai Du, Qian-Zhong Xue, Zhi-Hui Geng, and Yi-Nong Su

Citation: Physics of Plasmas (1994-present) 18, 083501 (2011); doi: 10.1063/1.3620402 View online: http://dx.doi.org/10.1063/1.3620402 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/18/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Stability analysis of a two-stage tapered gyrotron traveling-wave tube amplifier with distributed losses Phys. Plasmas 19, 113111 (2012); 10.1063/1.4768436 Low-order-mode harmonic multiplying gyrotron traveling-wave amplifier in W band Phys. Plasmas 19, 093103 (2012); 10.1063/1.4751465 Effect of a backward wave on the stability of an ultrahigh gain gyrotron traveling-wave amplifier Phys. Plasmas 15, 123107 (2008); 10.1063/1.3041161 Theory and experiment of a 94 GHz gyrotron traveling-wave amplifier Phys. Plasmas 11, 2935 (2004); 10.1063/1.1690764 Backward traveling wave amplification in the gyrotron Phys. Plasmas 4, 4140 (1997); 10.1063/1.872534

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Particle simulation of a ka-band gyrotron traveling wave amplifier

Shou-Xi Xu, Pu-Kun Liu, Shi-Chang Zhang, Chao-Hai Du, Qian-Zhong Xue, Zhi-Hui Geng,and Yi-Nong SuKey Laboratory of High Power Microwave Sources and Technologies, Institute of Electronics,Chinese Academy of Sciences, P.O. Box 2652, Beijing 100190, People’s Republic of China

(Received 31 March 2011; accepted 1 July 2011; published online 5 August 2011)

The design of a ka-band gyrotron traveling wave (gyro-TWT) amplifier is presented. The gyro-

TWT amplifier with a severed structure operates in the fundamental harmonic TE01 circular

electric mode. The beam-wave interaction is studied by using a particle-in-cell (PIC) code. The

simulations predict that the amplifier can produce an output peak power of over 155 kW, 22%

efficiency, 23 dB gain, and a 3 dB bandwidth of 2 GHz for a 70 kV, 10 A electron beam with an

axial velocity spread Dvz=vz ¼ 5%. VC 2011 American Institute of Physics. [doi:10.1063/1.3620402]

I. INTRODUCTION

Gyrotron traveling wave (gyro-TWT) amplifiers are

strong attractive coherent radiation sources in millimeter

wavelength range due to their capabilities to provide high

power and broad bandwidth.1–4 They have many potential

applications such as high resolution radar and communication

system. In contrast to conventional linear beam devices, gyro-

TWT amplifiers based on the electron cyclotron maser insta-

bility usually employ an over-mode smooth waveguide as the

interaction circuit to produce high power and broad band-

width; however, this can generate several spurious oscilla-

tions. These oscillations are mainly three types of oscillations:

reflective oscillations due to reflections at the input–output

couplers and structural nonuniformity, the absolute instability

near the cutoff frequency of the operating mode, and gyrotron

backward-wave-oscillations (gyro-BWO).5,6

One of the most effective methods to suppress these

types of oscillations is the use of distributed-loss technology.

The distributed-loss circuit for beam wave interaction con-

sists of a long lossy section (namely, the linearly loaded

section) and a short conducting-wall section (namely, nonli-

nearly unloaded section). Another effective method to over-

come absolute instability and Gyro-BWO is a sever circuit

which is commonly used in the conventional TWT.

Over the past ten years, a number of experimental stud-

ies of the gyro-TWT have been reported. For example, at the

National Tsing Hua University (NTHU), Taiwan, a Ka band

TE11 mode gyro-TWT was conducted, which produced

93 kW saturated peak output power at 26.5% efficiency with

a 3 dB bandwidth of 8.6% and an ultrahigh gain of 70 dB.5

At the US Naval Research Laboratory (NRL), a TE01 mode

gyro-TWT employing the periodic lossy ceramic-loaded

interaction circuit was developed. A saturated peak power of

137 kW was achieved at 34.1 GHz, a saturated gain of

47.0 dB, and an efficiency of 17% with a 3 dB bandwidth of

1.11 GHz.7 Another mode-selective TE11 mode gyro-TWT

at the NRL demonstrated a measured peak output power of

78 kW, a gain of 60 dB, and a 3 dB bandwidth of 4.2 GHz.8

A ku-band second harmonic gyro-TWT with an axial sliced

cylindrical waveguide interaction circuit generated an output

power of 207 kW at University of California, Davis.9

Recently, a gyro-TWT with a helically corrugated interac-

tion circuit developed by Russian and United Kingdom

researches produced a maximum output power of 180 kW, a

maximum electronic efficiency of 27%, a saturated gain of

25 dB, and an instantaneous 3 dB bandwidth of nearly

10%.10 MIT conducted a 140 GHz quasi-optical gyro-TWT

amplifier operated in a very high order HE06 mode in a con-

focal waveguide. The hot test produced 30 kW peak power

with a gain of 29 dB and 2.3 GHz bandwidth.11

In previous study,12 the linear and self-consistent non-

linear theory had been applied to the uniform interaction cir-

cuit for gyro-TWT amplifier. A vector wave equation and

the relativistic Lorentz equation are solved to describe the

beam-wave interaction in the frequency domain, and the fol-

lowing assumptions are considered: omitting the space

charge of the electron beam, neglecting the beam effects on

the transverse field profiles, omitting the mode conversion

due to structural nonuniformity, and only considering a sin-

gle-mode in the interaction circuit. But considering the large

change in the radius of the interaction waveguide, especially

thinking of the collector waveguide, they are not applied

owing to limitation, so a new code is in urgent need of devel-

opment for designing the gyro-TWT amplifier.

FIG. 1. The radial profile of the interaction circuit.

1070-664X/2011/18(8)/083501/4/$30.00 VC 2011 American Institute of Physics18, 083501-1

PHYSICS OF PLASMAS 18, 083501 (2011)

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In this paper, the particle-in-cell (PIC) code is used to

simulate a ka-band gyro-TWT amplifier with a sever circuit.

The gyro-TWT can generate high peak power stably. Rela-

tive to previous research, the interaction length of the sev-

ered gyro-TWT is very short in favor of compact and high

average power. The remainder of the paper is organized as

follows. Section II presents the simulation model. Section III

gives the simulation results by the PIC method. The results

are summarized and conclusions are drawn in Sec. IV.

II. SIMULATION MODEL

A distributed-loss interaction circuit of a gyro-TWT am-

plifier consists of a long lossy section combined with a short

copper section (see Fig. 1(a)). In order to increase the loss, the

long lossy section is generally coated with attenuation material

or loaded with ceramic rings; but coating the waveguide wall

with lossy material is incompatible with high average power

operation, the ceramic loading way is also not suitable for

high average power because the gas seriously ejects from the

long ceramic rings due to the temperature rising. To increase

the high average power, a short severed structure of a gyro-

TWT amplifier is proposed and is shown in Figure 1(b), it

consists of input coupler, interaction circuit, drift tube, and

output waveguide. The interaction circuit is separated into two

stage by the attenuating sever; thus, the interaction sections

are shorter than the critical length (namely, start-oscillation

length). The sever length is very short in favor of compact and

high average power, but also simulation results illustrate stable

at zero derive. Previously, we only considered the uniform

interaction or the structural nonuniformity was sufficiently

weak, so that the change of radius was negligible. In this struc-

ture, the output collector waveguide is considered, thus, the

radius of waveguide varies greatly. The previous theory is not

applied, so in order to simulate the realistic interaction pro-

cess, the PIC code is used. Previously, we employed CHIPIC

code to simulate and design a ka-band second harmonic

gyroklystron amplifier, the simulation result was very good

agreement with the experiment test.13 CHIPIC is a friendly

interface code that solves Maxwell’s equation together with

relativistic Lorentz particle motion. It can completely describe

the process of the beam wave interaction using finite-differ-

ence electromagnetic algorithms. Before analyzing the beam-

wave interaction of gyro-TWT, there is much work to do,

including model constructing, boundary condition setting,

data post processing, and so on. In Sec. III, we study the sev-

ered gyro-TWT amplifier by using CHIPIC code.

III. SIMULATION RESULTS

In this section, we have used CHIPIC code aforemen-

tioned to model the gyro-TWT interaction circuit. The coor-

dinate system and geometry are cylindrical. The circuit starts

from the left-hand drift tube and ends in the output section

(the output port waveguide radius is the same of collector ra-

dius), input coupler and output taper are included in the

physical model of a severed gyro-TWT in order to be more

close to actual state. All the metallic surface are perfect con-

ductors, and dielectric material is assigned to the attenuation

sever. The generated microwaves are emitted out through the

FIG. 2. (Color online) The effects of the critical current for the absolute

instability on the nonlinear length.

TABLE I. Parameters used in the simulation.

Electron voltage 70 kV

Electron beam current 10 A

aðv?=vzÞ 1.0

Guiding center radius, rg 0.48 rw

Applied magnetic field 1.27 T

Operate mode TE01

Cyclotron harmonic 1

Circuit radius, rw 5.4 mm

Sever length 40 mm

FIG. 3. (Color online) (a) Simulation model and distribution of azimuthal electric field in the circuit. (b) A frequency spectrum obtained from Fourier transfor-

mation of the electric fields.

083501-2 Xu et al. Phys. Plasmas 18, 083501 (2011)

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output port. The input coupler is driven through the current-

density source. Particles are directly absorbed on the surface

of metal neglecting secondary electron emission.

Unless otherwise stated in all the runs, a 70 kV annular

electron beam with a ¼ v?=vz ¼ 1:0 is injected from left-

hand emission surface passing through drift tube.

In order to improve the stability of the system, �1%

down tapered magnetic field is used in the circuit region and

decreases linearly to reach a zero value at z¼ 277 mm. The

spent beam is collected beyond the output collector waveguide,

where the electrons are no longer in resonance with the wave.

We chose grid sizes as Dr ¼ Dz ¼ 0:2 mm and the inter-

action region evenly into 90 sections along the r-axis and 1980

sections along the z-axis (about 30 cells per wavelength). The

time step is chosen as Dt ¼ 0:5 ps to meet the Courant condi-

tion ( Dx > cDt, where Dt is the time step, Dx is the minimum

grid size). The number of simulation macroparticle is around

70 300. The total simulation time is 100 ns which is long

enough for the system stability. As a class of fast-wave device,

the performances of the gyro-TWT such as bandwidth, effi-

ciency, and gain interact each other. The design of the gyro-

TWT is a process of the tradeoffs among the performances.

Fig. 2 gives the effects of the critical current for the absolute

instability on the nonlinear length. On the basis of the prelimi-

nary design parameters, the optimum parameters can be

achieved by PIC code. The optimum parameters of the des-

igned gyro-TWT amplifier are given in Table I, and these

parameters must lie within the stable operating region.

Fig. 3(a) gives the simulation model and the distribution

of electric field in the circuit. From the graph, we can see

that the operating mode is primary TE01 mode and the RF

amplitude gradually strengthens along the z-axis. A Fourier

transformed frequency spectrum of the electric field is given

in Fig. 3(b). As shown in Fig. 3(b), a single frequency is

observed at 34.80 GHz without any mode competition.

Fig. 4 gives the moving electron trajectory. Helically

moving electrons are injected from the left hand emission

surface and pass through the input coupler; in this process,

electron bunches are formed by interacting with the trans-

verse electric field. In the linear amplification region, the

electron bunching is enhanced, and in the nonlinear amplifi-

cation region, the drive wave is amplified while the electrons

lose their kinetic energy and are collected by collector wave-

guide. In order to further clarify electron azimuthally bunch-

ing process from initial state to stable state, Figure 5 shows

the electron distribution in the momentum space at the input

and output end (where radial momentum PR is actually nor-

malized to the relativistic mass, thus, PR is actually cpR=m,

etc. and the units are meters per second). From the figure, we

can see that at the entrance of the interaction, electronic

transverse momentum is uniformly distributed in a very thin

circle; it is obviously that macro particles have the same

energy and uniform phase distribution. After beam-wave

interaction, a center of bunch is formed and the electrons are

not uniformly distributed on the gyrating orbit.

The change of the relativistic factor also reflects electron

azimuthally bunching and energy exchange process. From

Fig. 6, we can see that in the linear section, the relativistic

factors of all electrons slowly change from 1.37, and in the

nonlinear section, some electrons obtain the energy, their rel-

ativistic factors increase, but most electrons lose the energy,

their relativistic factors reduce, as is expected.

FIG. 4. (Color online) Helical moving electron trajectory.

FIG. 5. (Color online) The electron distribution in the momentum space (a) at the entrance of the interaction and (b) at the output port.

FIG. 6. (Color online) The relativistic factors of the electrons along the z axis.

083501-3 Particle simulation of a ka-band gyrotron traveling wave amplifier Phys. Plasmas 18, 083501 (2011)

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Figure 7 shows the time history of the output power at

the output port. We can see that the production of RF power

saturates at a time around 40 ns, reaching a peak value of 254

kW with an efficiency of 36%, 25 dB gain for a 70 kV, 10 A

beam with injection pitch-ratio of 1.0. The calculated output

power is shown in Fig. 8 as a function of the frequency for

various axial velocity spreads ( dvz=vz) of the electron beam.

The output power drops rapidly as the beam velocity spread

increases. When the axial spread increases to 10%, the output

power drops from 254 kW to 88 kW at 34.8 GHz. Fig. 9

shows the output power as a function of the beam current.

We can see that the output power increases with the beam

current. When the beam current reaches 15 A, the output

wave profile is fluctuation and the absolute instability occurs.

IV. CONCLUSION

Employing a particle simulation code, we have studied a

severed gyro-TWT amplifier. Simulations predict that the

peak output power is 254 kW at 34.8 GHZ corresponding to

power conversion efficiency of 36%, when a 70 kV, 10 A an-

nular electron beam with a perpendicular velocity to parallel

velocity ratio of 1.0 is used. The 3 dB instantaneous band-

width is about 5.7%.

On the basis of a PIC code, a parameterization study is

carried out to determine how sensitive the output power is to

change in beam current and velocity spread. The highest

peak power dissipated on the attenuation sever is calculated

to be approximately 5 kW, the average power loading is as

high as 39 W=cm2, assuming a duty cycle of 10%. At this

level of average power loading, the temperature of high ther-

mal conductivity lossy ceramic material will not rise signifi-

cantly and the outgoing gas will not be serious. So the

average-power handling capability will increase greatly.

ACKNOWLEDGMENTS

This work has been supported by the National Science

Fund of China under Contract Nos. 60971072 and 61072024.

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FIG. 7. (Color online) Time development of the output power at output

port. Note that power saturation occurs at approximately 40 ns.

FIG. 8. (Color online) The bandwidth of the output power for an axial ve-

locity spread of 0%, 5%, and 10%.

FIG. 9. (Color online) Output power as a function of beam current for a

beam voltage of 70 kV and all other parameters set at constant values.

083501-4 Xu et al. Phys. Plasmas 18, 083501 (2011)

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