Proceedings of ITC/ISHW2007

Operation Characteristics of Microwave Sources Based onSlow-Wave Interaction in Rectangular Corrugation
Y. Takamura, Y. Kazahari, H. Oe, K. Ogura, A. Sugawara, M. Hirataa
Graduate School of Science and Technology, Niigata University, Niigata 950-2181, JapanaPlasma Research Center, University of Tsukuba, Tsukuba 305-8577, Japan(Received 15 October 2007 / Accepted 3 August 2007)

Studies of slow-wave device with a novel disk cathode and two types of rectangular corrugation are reported. The
beam voltage is weakly relativistic, less than 100kV. A disk cathode can generate a uniformly distributed annular beamin the weakly relative region. Rectangular corrugation having the ratio of corrugation width to periodic length of 50%
or 20% is used. By using the first one, output powers of about 200kW are obtained around 100kV. For the other, theeffect of slow cyclotron resonance is observed in the low energy region around 30kV. Output powers are in the rangeof a few W. For the slow cyclotron maser, the operation mode between axisymmetric and nonaxisymmetric modes canbe controlled by changing the end condition of rectangular corrugation.
Keywords: slow-wave device, weakly relativistic, disk cathode, annular electron beam, rectangular corrugation

1. Introduction

2. Cold CathodeSlow-wave high-power microwave devices such as
backward wave oscillator (BWO) can be driven by anaxially injected electron beam without initial perpendicularvelocity and has been studied extensively as a candidate
for high or moderate power microwave sources. In theslow-wave devices, slow-wave structure (SWS) is used toreduce the phase velocity of electromagnetic wave to thebeam velocity. In order to increase the power handlingcapability and/or the operating frequency, oversized SWSs
have been used successfully. The term “oversized” meansthat the diameter D of SWS is larger than free-space
wavelength λ of output electromagnetic wave by several
times or more.
In Refs. [1] and [2], K-band and Q-band oversized
BWO operating in the weakly relativistic region less than
100kV are reported. Output power in the range of hundredsof KW is obtained by using a sinusoidally corrugated SWS.
However, for moderate power level of MW or less, therectangular corrugation may be better than the sinusoidal
corrugation. We propose to use a novel disk cathode madeof metal only [2]. It can generate a uniformly distributed
annular beam in the weakly relativistic region and is usedin our slow-wave device. In this work, we use two types ofrectangularly corrugated SWSs for which the ratio ofcorrugation width to periodic length differs. Upper cut-off
frequency is about 25GHz for the both SWSs. We examine
operation characteristics of the slow-wave devices basedon each SWS, in high (around 100 kV) and low (around30kV) beam energy region.

We use a cold cathode to obtain a beam with highcurrent density. It is very difficult to generate a uniformly
distributed annular beam by the cold cathode, especially inthe weakly relativistic region less than 100kV. In the past,
we have used a hollow cathode with velvet on theaxsymmetric emitting edge in order to obtain an annularelectron beam [1]. By controlling velvet, fairly uniform
annular beams have been obtained as shown in Fig. 1. Thebeam shape is observed by the burn pattern on thermallysensitive paper. The average radius of the annulus is nearly
the same as the cathode diameter.
Recently, the uniformity of the beam is improved
much more by using a novel disk cathode. The idea of disk
cathode was presented by Loza et al [3], and used in therelativistic region [4]. In this paper, the disk cathode istested in the weakly relativistic region. The burn pattern isshown in Fig.1. The annular beam by the disk cathode
distributed more uniformly compared with the hollowcathode with velvet. Moreover, any coating on the disk
cathode surface is not required. The disk cathode issuitable for the weakly relativistic case.

author’s e-mail: f06e090g@mail.cc.niigata-u.ac.jp

Fig.1 The burn patterns of annular electron beam. Left-side is
the pattern of 5-shot overlay for the hollow cathode withvelvet at about 90kV. Right-side is the pattern of 1-shot
for the disk cathode without velvet at about 80kV.

Proceedings of ITC/ISHW2007

3. Rectangular SWS

Table 1 Parameters of rectangular SWS

Type A
Type BR0 [mm]15.115.38h [mm]1.1
1.38z0 [mm]32.2d/z0 [%]5020dFREQUENCY [GHz]3080keV(a)20100030

FREQUENCY [GHz]

Cylindrical SWS is periodically corrugated as shownin Fig.2. Dispersion characteristics of SWS are determinedby average radius R0, corrugation amplitude h, corrugation
width d and periodic length z0. The corrugation wave
number is given by k0=2π/z0. The dispersion characteristics
of structure are controlled by changing R0, h, d and z0.
Dispersion characteristics of rectangular SWS are
obtained by a numerical method based on a mathematicalformula in Ref. [5]. Figure 3 shows the each dispersion
characteristic of axisymmetric transverse magnetic (TM01)
mode for type A and B, whose parameters are listed intable 1. The slow space charge mode and the slow
cyclotron mode coupling to fundamental TM01 mode maylead to the Cherenkov and slow cyclotron instability. Fortype A SWS in Fig.3 (a), slow-wave device operate as
BWO based on Cherenkov instability. The interacting pointof beam is around the upper cut off at π-point. For type B
SWS in Fig.3 (b), dispersion curve around upper cut-off at
π-point becomes flat, compared with type A. And theinteraction point between beam line of slow space charge
mode and TM01 mode shifts toward traveling wave region
at 80keV. Decreasing beam energy to 30keV, theinteraction point moves to backward wave region.
In this work, each rectangular SWS of type A and B isused. We examine operation characteristics of theslow-wave device using each SWS in high (around 100kV) and low (around 30 kV) energy region.

10-1
WAVE NUMBER [cm ](b)80keV2030keV2010001020
WAVE NUMBER [cm -1]

Fig.3 Dispersion characteristics of TM01 for rectangular SWS.
(a) is for type A. (b) is type B. Solid and dashed lines are
the beam line of slow space charge mode and slow
cyclotron mode at 0.8T, respectively.

4. Experiment with rectangular SWS
The experimental setup is schematically shown inFig.4. Output voltage up to 100 kV from the pulse forming
line is applied to the cold cathode. A disk cathode is used
as a cold cathode. A uniform axial magnetic field B0 for thebeam propagation is provided by ten solenoid coils. The
value of B0 can be changed from 0T to 0.9T. The
microwave output is picked up by a rectangular hornantenna typically located 600 mm away from the outputwindow.

R0Cathode

Beam Limiter

Rogowski CoilhMagnetic Field Coils

Z 0 =2π/k 0Fig.2 Periodically corrugated cylindrical SWS.

Detecting
HornSystem

Antenna
Slow Wave Structure

Fig.4 Schematic diagram of the experimental setup.

1000

5000020406080100

Cathode Voltage[kV]Fig.6 Output powers versus the cathode voltage for a 10-periodtype A SWS.

Detected power[W]2100.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Magnetic Field[T]Fig.7 Output powers versus the magnetic field for a 10-period
type B SWS. The beam voltage is around 30kV.

(a)

Detected power[W]43210-30-20-100102030

Angle[degree]3
Detected power[W]Figure 5 shows an example of detected signals. Thebeam voltage and current are about 100kV and 300A, atthe microwave peak time. The operation frequency
estimated from delay time is about 26GHz.
Figure 6 shows the dependence of the microwave
power on the cathode voltage with type A SWS. Theoscillation starting voltage is about 60kV. Output powers
increase by increasing the cathode voltage. For type A
SWS, the estimated maximum power is about 200kW at
100kV. For type B SWS, the microwave output can not be
obtained in the high energy region from 60kV to 100kV.
However, the microwave power in the range of a few W is
obtained in the low energy region around 30kV, less thanthe oscillation starting voltage. In Fig. 7, the power
dependence on the magnetic field for type B SWS isshown. The microwave outputs resonantly increase around
0.65T. This might be caused by slow cyclotron resonanceas discussed later. For type A SWS, such an effect of slow
cyclotron resonance cannot be observed in the low energy
region, less than the oscillation starting voltage.
In our slow-wave device, both axisymmetric TM01
mode and nonaxisymmetric hybrid HE11 mode exist as a
candidate of the operation mode. To examine the mode, theradiation patterns are measured by shifting the receiving
horn antenna in an equatorial plane around a pivot at thecenter of output window. The electric fields component ofEθ and Eφ is measured by the horn antenna. Eθ (Eφ) ishorizontal (vertical) component of the electric field in theequatorial plane. Figure 8 show the radiation patterns withtype B SWS. The beam voltage is about 30kV. The
magnetic field is 0.6T, around peaks of output in Fig.7. The
operation mode changes by the straight cylinder length
before SWS in Fig.4. For the straight cylinder of 34mm,
the operation mode is TM01 mode as Fig.8 (a). Bychanging the straight length to 68mm, the radiation patternchanges to the pattern HE11 mode as Fig.8 (b). The
axisymmetric and nonaxisymmetric mode can becontrolled by the axial condition of SWS.

Detected Power[W]Proceedings of ITC/ISHW2007

(b)

2
10-30

-20-100102030

Angle[degree]

Fig.8 Radiation patterns with the straight cylinder of (a) 34mmand (b) 68mm for type B SWS. (●) and (△) arerespectively Eθ and Eφ components. Dashed curves areFig.5 Waveform of measured signals: 1 prompt signal, 2delayed signal, 3 beam current signal and 4 beam
voltage.

theoretical curves of (a) TM01 and (b) HE11 mode,respectively.

Proceedings of ITC/ISHW2007

5. Discussion and Conclusion

Acknowledgments

We study slow-wave device with a disk cathode andtwo types of rectangular SWS. The beam voltage is
weakly relativistic, less than 100kV. We propose a novel
cold cathode, which is a disk type cathode made of metal
only. It can generate a uniformly distributed annular beamin the weakly relativistic region.
The estimated output power of about 200kW isobtained by using type A SWS at about 100kV. However,
the microwave can not oscillate for type B SWS, because
the interacting point of beam shifts to traveling wave
region in high energy region around 100kV. Around about
30kV less than the oscillation starting voltage, radiations in
the range of a few W is obtained. The dispersion
characteristic of TM01 mode for type B is shown in Fig.9.
Beam interactions are taken into account, based on a field
theory developed in Ref. [6] for cylindrical SWS driven byan annular beam. The slow cyclotron mode depends on theaxial magnetic field B0. By increasing B0, the beam line ofslow cyclotron mode shifts to the right in Fig.9. The
Cherenkov interaction resonantly synchronizes with slow
cyclotron interaction at the fundamental frequency with
1.35T. This is a slow cyclotron maser operation reported inRefs. [7] and [8]. In our experiments, the resonance occurs
around 0.65T and might be a combined operation of theCherenkov and the second harmonic slow cyclotroninteractions. For the slow cyclotron maser, it isdemonstrated that the axisymmetric and nonaxisymmetricmode can be controlled by changing the end condition ofSWS.

This work was partially supported by a Grant-in-Aidfor Scientific Research from Ministry of Education,Science, Sports and Culture of Japan, and partiallyperformed under the Collaborative Research Program
between NIFS and University of Tsukuba in cooperation
with Japanese universities.

Fig.9 Dispersion curves of fundamental TM01 for type B
SWS. The beam energy is 30keV.

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[3] O. T. Loza and P. E. Ivanov, Proc. 13th Int. Conf.
High-Power Particle Beams, Nagaoka, Japan, pp.603-606(2000).
[4] Kelly Han et al., IEEE Trans. Plasma Sci., 30, No.3, June
2002.
[5] P. J. Clarricoats and A. D Olver, Corrugated Horns for
Microwave Antenna (Peter Peregrinus, London, 1984).
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