An improved suppression method of the transverse-electromagnetic mode leakagewith two reflectors in the triaxial klystron amplifierZumin Qi, Jun Zhang, Huihuang Zhong, Qiang Zhang, and Danni Zhu Citation: Physics of Plasmas (1994-present) 21, 073103 (2014); doi: 10.1063/1.4889901 View online: http://dx.doi.org/10.1063/1.4889901 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/21/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A non-uniform three-gap buncher cavity with suppression of transverse-electromagnetic mode leakage in thetriaxial klystron amplifier Phys. Plasmas 21, 013107 (2014); 10.1063/1.4862557 High power operation of an X-band coaxial multi-beam relativistic klystron amplifier Phys. Plasmas 20, 113101 (2013); 10.1063/1.4825357 Design and 3D simulation of a two-cavity wide-gap relativistic klystron amplifier with high power injection Phys. Plasmas 19, 083106 (2012); 10.1063/1.4742179 XBand Triaxial Klystron AIP Conf. Proc. 691, 141 (2003); 10.1063/1.1635115 CARM-klystron amplifier for accelerator applications AIP Conf. Proc. 569, 695 (2001); 10.1063/1.1384396

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An improved suppression method of the transverse-electromagnetic modeleakage with two reflectors in the triaxial klystron amplifier

Zumin Qi (戚祖敏), Jun Zhang (张军), Huihuang Zhong (钟辉煌), Qiang Zhang (张强),and Danni Zhu (朱丹妮)College of Optoelectric Science and Engineering, National University of Defense Technology, Changsha,Hunan 410073, China

(Received 18 February 2014; accepted 30 June 2014; published online 11 July 2014)

Suppression of the transverse-electromagnetic (TEM) mode leakage is crucial in the design of a

triaxial klystron amplifier with high gain, because a small microwave leakage from the buncher or

the output cavity could overwhelm the input signal with low power. In this paper, a specially

designed reflector is proposed to suppress the TEM mode leakage, whose axial electric field is

approximately zero at the beam radial position. Theoretical analysis indicates that the reflector

introduces little influence on the normal modulation of the beam while keeping a high reflection

coefficient. By using two such reflectors with different eigen frequencies located in front of the

buncher cavity and the output cavity, respectively, an improved triaxial klystron amplifier is

presented. The simulation results show that the reflectors substantially decrease the TEM mode

leakage power and achieve very good isolation among the cavities. The improved triaxial klystron

amplifier can operate normally with 10’s kW microwave injection without self-oscillations.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4889901]

I. INTRODUCTION

The triaxial klystron amplifier (TKA)1–4 is an effective

scheme to amplify microwave at high frequencies (such as

X-band) with 10’s kW low power injection and over 1GW

high power output. However, since the transverse-

electromagnetic (TEM) mode is not cut off by the coaxial

waveguide, the TEM mode leakage from the buncher cavity

and the output cavity to the input cavity could either disturb

the normal modulation of the beam, even result in self-

oscillation in the TKA. A non-uniform three-gap buncher

cavity has been previously designed to decrease the TEM

mode leakage from the second and the third gaps of the

buncher cavity and the output cavity.5 However, the non-

uniform three-gap buncher cavity cannot fully isolate the

TEM mode leakage. If the leakage power to the input cavity

is comparable to or even exceeds the injected power, particu-

larly when the injected power is low (corresponding to high

gain case), the TKA with the non-uniform three-gap buncher

cavity can hardly operate normally. Additionally, the TEM

mode leakage from the output cavity could influence the

normal operation of the buncher cavity.5 Therefore, an

improved suppression method to isolate the TEM mode leak-

age between the coaxial cavities should be developed.

The reflectors with high reflection coefficient in hollow or

coaxial waveguides are widely applied in the relativistic back-

ward wave oscillators6,7 and the transit-time oscillators8 to

suppress the microwave leakage to the diode. Yu and Wilson

proposed a choke cavity along a beam tunnel to suppress com-

munication between adjacent cavities in a sheet-beam klys-

tron,9 in which the TE mode will convert to other modes

containing axial electric field components. The choke cavity

could influence the normal modulation of the beam. Usually,

such reflectors or choke cavities are designed with high reflec-

tion coefficient, without considering their field distribution,

which results in the modulation to the beam. As for TKAs, an

appropriate TEM mode reflector should satisfy three qualifica-

tions: (1) high reflection to the TEMmode at the operation fre-

quency; (2) little modulation to the beam at the operation

frequency; and (3) no excitation of the eigen modes of the

reflector itself by the electron beam. In this paper, a specially

designed reflector is proposed to meet such demands with its

characteristic analyzed. By using such two reflectors with dif-

ferent eigen frequencies, very good TEM mode isolation is

achieved, which ensures the TKA can operate normally with

10’s kWmicrowave injection without self-oscillations.

II. SCHEMATIC STRUCTURE AND COLD CAVITYANALYSIS

The proposed reflector is shown in Fig. 1 schematically.

If the radial depth (ro � ri) is approximate one wavelength,

the axial electric field will be zero at the radial position

r ¼ ðro þ riÞ=2, because the boundary condition decides that

the axial electric field is zero at the surfaces of r ¼ ro and

r ¼ ri. Therefore, an annular beam with radius of ðro þ riÞ=2

FIG. 1. Schematic structure of the reflector.

1070-664X/2014/21(7)/073103/5/$30.00 VC 2014 AIP Publishing LLC21, 073103-1

PHYSICS OF PLASMAS 21, 073103 (2014)

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will experience zero axial electric field when passing through

the reflector, while the reflector does not modulate the beam.

The lengths of the cavities in the inner and outer walls and

the offset Dl are chosen to achieve high reflection coefficient

at the operation frequency.

For example, in the TKA5 with the operation frequency

of 9.375 GHz, the beam radius is 6 cm, and the outer radius

and inner radius of the coaxial waveguide are 5.5 cm and

6.5 cm, respectively. Figure 2 illustrates the reflection coeffi-

cient dependence on the frequency of an optimized reflector.

It can be seen that the reflection coefficient at the operation

frequency is higher than 99.98%. Figure 3 plots the distribu-

tion of the total electric field and the axial electric field in the

reflector when a TEM mode microwave at 9.375GHz is

injected from the right port. There is nearly no microwave

leakage to the left port and the axial electric field is approxi-

mately zero at r¼ 6 cm.

III. BEAM-LOADING EFFECT IN THE REFLECTOR

Although the axial electric field at the beam radial posi-

tion is nearly zero, the actual beam has finite thickness and

the beam could be slightly modulated by the electric field in

the reflector. It is necessary to evaluate the exchange energy

between the beam and the electric field quantitatively.

According to the distribution of the axial field along the

gaps, the gap electric field Ez(rti,to, z) can be expressed as

follows:

Ezðrti; zÞ ¼ a1eb1z þ c1e

d1z 0 � z � li0 otherwise

;

�(1a)

Ezðrto; zÞ ¼ a2eb2ðz�DlÞ þ c2e

d2ðz�DlÞ Dl � z � lo þ Dl0 otherwise

;

�(1b)

where rti and rto are the inner and outer radii of the coaxial

waveguide, respectively, and an, bn, cn, and dn (n¼ 1, 2) are

the fitting parameters. The original position (z¼ 0) is defined

as the left edge of the outer gap. According to the defini-

tion,10,11 the beam coupling coefficient based on the outer

gap voltage at arbitrary r can be obtained as follows:

M rð Þ ¼ 2p

g rto; be; lð ÞK0 Certið Þ � g rti; be; lð ÞK0 Certoð ÞI0 Certoð ÞK0 Certið Þ � I0 Certið ÞK0 Certoð Þ I0 Cerð Þ þ g rto; be; lð ÞI0 Certið Þ � g rti; be; lð ÞI0 Certoð Þ

K0 Certoð ÞI0 Certið Þ � K0 Certið ÞI0 Certoð Þ K0 Cerð Þa2b2

eb2lo � 1ð Þ þ c2d2

ed2lo � 1ð Þ ; (2)

where

g rti; be; lð Þ ¼ 1

pa1 e

b1þjbeð Þli � 1½ �b1 þ jbe

þ c1 ed1þjbeð Þli � 1½ �d1 þ jbe

( );

g rto; be; lð Þ ¼ ejbeDl

pa2 e

b2þjbeð Þlo � 1½ �b2 þ jbe

þ c2 ed2þjbeð Þlo � 1½ �d2 þ jbe

( );

Ce ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2e � ðx=cÞ2

q; be ¼ x=te;

and x is operation angular frequency. te and c are the beam ve-

locity and the speed of light in the vacuum, respectively. I0 andI1 are the first modified Bessel functions of order zero and one,

and K0 and K1 are the second modified Bessel functions of order

zero and one, respectively. The relative beam loading conduct-

ance of the beam with a finite thickness can be obtained10

Ge

G0

¼ � 1

2 rbo2 � rbi2ð Þðrborbi

be@M2

@berdr; (3)

FIG. 2. Reflection coefficient of the reflector.FIG. 3. Field distributions in the reflector at the operation frequency. (a)

Total electric field; (b) axial electric field.

073103-2 Qi et al. Phys. Plasmas 21, 073103 (2014)

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where rbi and rbo are the inner and outer radiuses of the

beam, respectively. G0 is the beam loading conductance of a

dc beam. Substituting Eq. (2) and the fitting parameters

shown in Fig. 4 to Eq. (3), the relative beam loading con-

ductance is obtained, as shown in Fig. 5. The reflector at the

operation frequency cannot be excited as long as the beam

voltage is higher than 85 kV. The relative beam loading con-

ductance is extremely low at 0.02% of the conventional cav-

ity,10 which indicates that the reflector has little modulation

on the beam.

However, as a cavity the reflector has its own eigen

modes, the simulation results show that the reflector has one

eigen frequency of 6 GHz range from dc to 10GHz, and the

eigen mode is coaxial TM010 mode. The relative beam load-

ing conductance of the beam with the eigen mode is calcu-

lated, also as shown in Fig. 5. The eigen mode cannot be

excited as long as the beam voltage exceeds 20 kV.12

IV. APPLICATION IN THE TKA

By using two such reflectors located in front of the

buncher cavity and the output cavity, respectively, the

previously reported TKA5 is improved, as shown in Fig. 6.

The edge-to-edge distance between the reflector and the

buncher cavity or the output cavity is optimized to minimize

the influence of the reflector on the resonant frequency of the

cavities. In simulation, the diode voltage is 500 kV, the beam

current is 6.4 kA, and the guiding magnetic field is 1 T. The

power and frequency of the input signal are 100 kW and

9.375GHz, respectively, and an average power of 80 kW is

absorbed by the beam in the input cavity.

Unfortunately, PIC (particle-in-cell) simulation shows

that if the two reflectors are identical, the eigen mode with a

frequency of 6 GHz of the reflector is excited, which is indi-

cated in the voltage and its spectrum at the output port, as

illustrated in Fig. 7. Although a single reflector cannot be

excited by the beam, two identical reflectors could be easily

coupled and excited for the coaxial waveguide providing a

positive feedback channel.

To avoid the self-oscillation introduced by two identical

reflectors, two different reflectors, whose eigen frequencies

are 6 GHz and 5.4GHz, respectively, are designed satisfying

the three qualifications. The significant difference of the two

eigen frequencies reduces the coupling risk of two reflectors

and avoids the self-oscillation. One reflector locates in front

of the buncher cavity and the other locates in front of the out-

put cavity, as presented in Fig. 6. The output cavity is located

at the position where the fundamental current reaches its

maximum. The output power achieves 1.1GW and stops af-

ter the input signal is stopped at 120 ns, as shown in Fig. 8,

which indicates that the TKA operates as an amplifier.

FIG. 4. Axial electric field distribution of the inner and outer gap of the

reflector at the operation frequency.

FIG. 5. Relative beam loading conductance in the reflector.

FIG. 6. Schematic structure of the improved TKA with two reflectors.

FIG. 7. Voltage and its spectrum at the output port when locating identical

reflectors in front of the buncher cavity and the output cavity, respectively.

073103-3 Qi et al. Phys. Plasmas 21, 073103 (2014)

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To check the isolation effect of the reflectors, the

backward-flowing power in the coaxial waveguide of

the improved TKA is observed, as illustrated in Fig. 9. The

power leakage to the input cavity through the coaxial wave-

guide is lower than 15 kW, which is less than 0.023% of the

65MW backward-flowing power in the buncher cavity. The

power leakage from the output cavity to the buncher cavity

is lower than 900 kW, which is less than 0.067% of the

1.35GW backward-flowing power in the output cavity.

Therefore, very good isolation is achieved. Figure 10

presents the output power and the gain of the improved

TKA. The output power increases from 190MW to 1.2GW

and the gain decreases from 42.8 dB to 39 dB as the input

power varies from 10 kW to 140 kW. It can be concluded

that the improved TKA amplifies a microwave with low

power level.

Although good isolation effect is achieved, the

backward-flowing power in the coaxial waveguide cannot be

cut off completely, and there is still �1 MW leakage from

the output cavity to the buncher cavity and 10 kW leakage

from the buncher cavity to the input cavity. Therefore, the

average power at the input port and the output port are

obtained with different distances d to evaluate the influence

of the leakage, where d is the length of the smooth coaxial

waveguide between the buncher cavity and the output cavity,

as shown in Fig. 11. The phase difference between the

microwave in buncher cavity and the leakage microwave

from the output cavity will vary as the distance d is altered.

The output power is over 1GW in most cases, which indi-

cates that there is no excessive power leakage either from

the buncher cavity or the output cavity to the input cavity,

even though the power in the input port varies a little with

the distance d. Figure 12 presents the fundamental current

modulation depths dependence on axial position at time

t¼ 110 ns. The fundamental current modulation depths vary

between �95% and �100% before entering into the output

cavity, and the maximal difference of the output power is

less than 110MW with the distance d. When d¼ 11 cm or

d¼ 14 cm, the TEM mode leakage from the output cavity to

the buncher cavity weakens the modulation of the beam, and

that is why the output powers are a little lower than the cases

when d¼ 12 cm (the position where the fundamental current

reaches its maximum) and d¼ 13 cm. When d¼ 15 cm, the

output cavity is located at the decline stage of the fundamen-

tal current and is a little far from the maximum. Therefore,

the output power is a little lower than the cases when

FIG. 8. Output power of the improved TKA.

FIG. 9. Backward-flowing power in the coaxial waveguide of the improved

TKA.

FIG. 10. Output power and gain of the improved TKA.

FIG.11. Output power and power at the input port with the distance d.

073103-4 Qi et al. Phys. Plasmas 21, 073103 (2014)

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d¼ 12 cm and d¼ 13 cm. The results indicate that although

the TEM mode leakage is not cut off completely, the power

of the leakage can be acceptable.

V. CONCLUSIONS

An improved suppression method of the TEM mode

leakage with specially designed reflectors for TKAs is pro-

posed in this paper. Theoretical analysis indicates that the

reflectors introduce little influence on the normal modulation

of the beam and cannot be excited by the beam while keep-

ing a high reflection coefficient. An improved TKA with the

two reflectors in the front the buncher cavity and output cav-

ity is presented. A significant difference in the eigen frequen-

cies of the two reflectors is obligable to avoid the coupling

of the two reflectors. The PIC simulation results show that

the leakage power to the input cavity or the buncher cavity is

lower than one thousandth of the backward-flowing powers

in the buncher cavity or the output cavity, and the improved

TKA can operate normally with 10’s kW microwave

injection.

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073103-5 Qi et al. Phys. Plasmas 21, 073103 (2014)

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