Plasma and Fusion Research: Regular Articles

Volume 11, 2406085 (2016)

Experimental Study on W-Band (75 - 110 GHz) Oversized Surface
Wave Oscillator Driven by Weakly Relativistic Electron Beams∗)
Min Thu SAN, Kazuo OGURA, Kiyoyuki YAMBE, Yuta ANNAKA, Shaoyan GONG,
Jun KAWAMURA, Takuro MIURA, Shin KUBO1) , Takashi SHIMOZUMA1) ,Sakuji KOBAYASHI1) and Kohji OKADA1)
Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
1)
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan(Received 27 November 2015 / Accepted 2 April 2016)
A W-band (75 - 110 GHz) oversized surface wave oscillator driven by weakly relativistic electron beams withenergy in the range of 10 - 80 keV is studied. Rectangular corrugations are used as slow-wave structures (SWS)
having surface waves with an upper cutoﬀ frequency of approximately 100 GHz (W-band). Uniformly distributed
annular electron beams are generated by a disk-type cold cathode and then are injected into the W-band oscillator.
A longer SWS length causes the oscillator to function in both backward wave oscillator (BWO) and travellingwave tube (TWT) operations, and no meaningful oscillation occurs at the π-point or the Bragg condition. When
the SWS length is short enough, oscillation occurs in all regions: BWO, π-point and TWT. The operations of
the oscillator are strongly aﬀected by the structure length. The maximum radiation power is estimated to beapproximately 20 kW with the figure of merit of about 2 × 102 MW.GHz2 .
c 2016 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: surface wave, travelling wave tube operation, backward wave oscillator operation, π-point, W-band
DOI: 10.1585/pfr.11.2406085

1. Introduction
High-power microwaves are required for a variety of
applications, such as plasma heating, plasma diagnostics,
and radar systems. Slow-wave devices, such as backward
wave oscillators (BWOs) have been extensively studied
as candidates for high- and moderate-power microwave
sources. In these devices, a slow-wave structure (SWS) is
used to generate slow waves by reducing the phase velocityof electromagnetic waves to the beam velocity. For highfrequency operations in the terahertz frequency range (0.1 10 THz), oversized SWSs with diameter much larger than
the free-space wavelength of the electromagnetic waves
are suitable. The relativistic diﬀraction generator and themulti-wave Cherenkov generator are special versions ofoversized BWOs, and have produced peak powers above
GW levels in the frequency range of up to approximately
46 GHz (Q-band) [1, 2]. Such tremendously high-powerdevices use relativistic MV level pulsed power systems andTesla level magnetic field systems. For practical applications, operations at reduced voltages and reduced magnetic
fields are preferable. In Ref. 3, a power level of approximately 500 MW was achieved at 8.3 GHz (X-band) byreducing voltage to approximately 500 kV. However, thissystem still requires a bulky pulsed power system. For
lower voltage operations, the phase velocity of the electromagnetic wave in a SWS should be reduced, e.g., 0.55c
author’s e-mail: minthusan1@gmail.com∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

for 100 kV. Designing of the oversized SWSs to enable thetransmission of electromagnetic waves with such a slow
phase velocity is diﬃcult because high-frequency operations and lower voltage operations are incompatible.
Aiming at more compact devices, oversized BWOs
operating in weakly relativistic regions less than 100 kV
have been studied in the K- and Q-band by using uniformly distributed annular electron beams [4–6]. An annular beam of the order of 100 A completely covers the corrugated surface. Recently, the performance of the weakly
relativistic oversized BWO has been improved, and radiation of up to 500 kW (K-band) and 200 kW (Q-band) has
been achieved [5]. The radiation power level of kW has
been implemented above 150 GHz (G-band) with a moderate voltage of less than 100 kV [7, 8]. The unique features of these oversized BWOs are as follows: (1) the useof a cold cathode to obtain a uniformly distributed annularelectron beam [9, 10], (2) operation by a weakly relativistic electron beam of less than 100 kV, and (3) a guiding
magnetic field of less than 1.0 T.
The interaction of the beam and the electromagnetic
wave in SWSs may result in backward wave or travellingwave operations, depending on the group velocity of thesurface wave, as shown in Fig. 2. At high electron energy,
the group velocity of this wave is positive and the device
operates in the manner of a travelling wave tube (TWT).
At low electron energy, the group velocity is negative andoperates as a BWO. In addition, at an intermediate energy,

2406085-1

c 2016 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 11, 2406085 (2016)

known as the Bragg condition or π-point, the group velocity of the evanescent wave vanishes. The overall operation from BWO to TWT has been studied theoretically andit has been shown that there is no operation near the πpoint [11]. To date, the theoretical prediction has not beenvalidated against experimental results.
The operation mechanism for the surface wave oscillator is still open, and a comparison between theories andexperiments of the oscillator is very important to develop
a high-frequency surface wave oscillator. It is commonly
believed that the operation of BWO occurs due to the absolute instability at the saddle point formed by the beammode and the backward surface wave. However, for a
finite-length BWO, the axial boundary conditions causedby the reflection at both ends should be considered. The
finite length eﬀect results in a new idea of the so-called“axial mode” or “surface wave cavity” which is a type ofcavity formed by the reflected surface waves. In addition,
the surface wave cavity has been demonstrated to generateintense terahertz radiation in the BWO region [7,8]. A surface wave cavity in the TWT region may also be available
in realistic devices. However, such a cavity has not beenstudied to date.
Here we studied a W-band oversized surface wave oscillator based on the surface wave cavity driven by weakly
relativistic electron beams. In this paper, the W-band refers
to the frequency range from 75 to 110 GHz of the Electronic Industries Alliance (EIA) standard WR-10 rectangular waveguide [12]. The oversized oscillator uses a SWS
that forms surface waves with an upper cutoﬀ frequency
of approximately 100 GHz. The SWS is designed so thatthe BWO and TWT operations are realized by weakly relativistic beams. The π-point operation occurs for the beam
at approximately 30 kV, shown in Fig. 2, at which the phasevelocity of the surface wave should be 0.33c. By varying
the beam voltage from 10 to 80 kV, the phase velocity ofsurface wave varies from 0.20c to 0.50c, and the overall
operation from BWO to TWT can be realized. To examine
the finite length eﬀect on the surface wave oscillation, the
SWS length is varied as 40, 80, and 120 periods.

Fig. 1 (a) One modular section of the W-band corrugated hollow
waveguide with length L = 80z0 . (b) Enlarged photo of
the rectangular corrugation. (c) Size parameters of therectangular corrugation R0 , h, d, and z0 .
Table 1 Parameters of W-band Corrugation.

Fig. 2 Dispersion curve of W-band oscillator with 30 and
80 keV beam lines.

2. W-Band SWS
The W-band SWS used in this work is the oversizedhollow waveguide with outer corrugation shown in Figs. 1(a) and (b). The SWS is made of aluminum and fabricatedby machining and has eighty periods (80z0 ). The size parameters of the rectangular corrugation shown in Fig. 1 (c)are the average radius R0 , the corrugation amplitude h, thecorrugation width d, and the periodic length z0 . The corrugation wave number is given by k0 = 2π/z0 . The dispersion
characteristics of the SWS are controlled by changing R0 ,h, d, and z0 . Table 1 presents the SWS corrugation parameters used in the experiment. For these parameters of corrugation, the electric field is concentrated in a very narrow
region within approximately 0.5 mm from the SWS wallnear the π-point, and the surface waves are formed. Twomodular sections of the oversized SWS are used: one has
eighty periods (80z0 ), and the other one has forty periods(40z0 ). The lengths of the SWSs used in the experimentare of 40z0 , 80z0 , and 120z0 . The last one is obtained by
combing the two modules.
The dispersion curves of the rectangular SWS are obtained by a numerical method based on the mathematicalformula in [12–14]. Figure 2 shows the dispersion curveof TM01 mode for W-band oversized oscillator. According
to Floquet’s theorem, the curve is periodic in wave number space (kz -space) with a period of k0 = 126 cm−1 andhas an upper cutoﬀ frequency of approximately 100 GHz

2406085-2

Plasma and Fusion Research: Regular Articles

Volume 11, 2406085 (2016)

Fig. 3 Schematic diagram of the experimental set-up.
Fig. 4 Disk-type cold cathode with velvet at the outer surface.
(b) Burn pattern of the electron beam.

at the π-point, with kz = k0 /2. The TM01 mode is a surface wave in the slow-wave region with a phase velocity
less than the light velocity, and the dispersion curve is flataround the upper cutoﬀ. In addition, the interaction point
between the beam line of the slow space charge mode andthe TM01 mode shifts toward the TWT region at 80 keV,and with decreasing beam energy to 30 keV, the interaction point moves to the BWO region. At approximately
30 keV, the interaction point is at the π-point.

3. Experimental Set-Up
A schematic of the experimental set-up is shown in
Fig. 3. An output voltage of up to 80 kV from a pulse
forming line (PFL) is applied to a disk-type cold cathode, which is shown in Fig. 4 (a). The cathode is madeof oxygen free copper, and its diameter is 29 mm. In order to obtain a uniform electron beam, a velvet band is
attached to the axisymmetric emitting edge of the cathode. By adjusting the velvet band, fairly uniform annular beams are obtained. The beam limiter with a diameterof 29.7 mm is placed at the entrance of the waveguide toprevent the erosion of the corrugation by the high-energy
beams. Uniform annular beams in the weakly relativistic
region are obtained with nearly the same diameter as thatof the cathode. The inner and outer diameters of the annular electron beam shown in Fig. 4 (b) are 26 and 30 mm,
and the thickness of the beam is typically 2 - 3 mm. For
beam propagation, a uniform axial magnetic field is provided by 10 solenoid coils. The value of the magnetic field
can be changed from zero to approximately 1 T; the field
is 0.82 T in this study. The microwave output is picked up
by rectangular horn antennas of F- and G-bands, which are
EIA standard rectangular waveguides with cutoﬀ frequencies of 74 and 116 GHz [15], respectively, located typically
600 mm away from the output window. After providing anadequate amount of attenuation, the output powers are detected by crystal detectors.

4. Experimental Results
Typical waveforms of the W-band oversized oscillator with 40-period SWS length are shown in Fig. 5.
The microwave signals are detected by the F-band (90 140 GHz) rectangular horn antenna with 10 dB attenuation,and the G-band (140 - 220 GHz) rectangular horn antenna

Fig. 5 Waveforms of the measured signals: (a) beam voltage,(b) beam current, (c) detected signal by F-band antenna,and (d) detected signal by G-band antenna.

with 0 dB attenuation, at a position of 600 mm away fromthe output window. We evaluated the detected powers using the F-band voltage signals, which are calibrated to absolute powers by using a Gunn oscillator at 100 GHz.
Figure 5 (c) shows that the microwave signal is detected by the F-band antenna. However, no meaningful signal is detected by the G-band antenna, as shown in Fig. 5(d). The operation frequency is examined using rectangular waveguides with various cutoﬀ frequencies. We used
F-band and G-band waveguides as high-pass filters with
cutoﬀ frequencies of 74 and 116 GHz, respectively. Figure 6 shows the dependence of the microwave power on
the beam voltage for the SWS length of 40 periods. In theexperiment, the voltage and current change with time, andtheir values at the time of the microwave peak are plotted.

2406085-3

Plasma and Fusion Research: Regular Articles

Volume 11, 2406085 (2016)

Fig. 6 Peak value of the W-band signal and beam current versus beam voltage for the SWS length of 40 periods. The
beam voltages at the radiation peaks are used. The magnetic field is approximately 0.82 T.

Fig. 7 Peak value of the W-band signal and beam current versus beam voltage for the SWS length of 80 periods. The
beam voltages at the radiation peaks are used. The magnetic field is approximately 0.82 T.

The oscillation starting voltage is approximately 10 kV. No
meaningful output power is detected for the beam voltageof less than 10 kV. Output powers increase by increasing
the beam voltage. The microwave output powers can be detected until the beam voltage of approximately 80 kV. The
oscillations occur through the beam voltage of 10 - 80 kV.
As shown in Fig. 2, the beam interaction point with TM01
is in BWO region while the beam energy is under approximately 30 keV. When the beam energy is above 30 keV,
the interaction is near to the π-point. In addition, even nearthe π-point, meaningful microwave output signals are detected, as shown in Fig. 6. By increasing the beam energy
up to 80 keV, the interaction point between the slow spacecharge mode and the TM01 mode shifts toward the TWT
region.
Microwave signals and beam currents versus beam
voltages for SWS lengths of 80 and 120 periods are shownin Figs. 7 and 8, respectively. Radiation is clearly detected

Fig. 8 Peak value of the W-band signal and beam current versus beam voltage for the SWS length of 120 periods. The
beam voltages at the radiation peaks are used. The magnetic field is approximately 0.82 T.

Fig. 9 Radiation pattern for the TWT operation of the 80-period
SWS length. The operating parameters are approximately 70 kV, 200 A and 0.82 T. The solid curve is the calculated radiation pattern for the TM01 waveguide mode.

within the range of beam voltages approximately 10 and
25 kV. Meaningful radiation disappears within the range ofbeam voltages of 25 and 40 kV. In addition, the microwave
outputs are observed again above 40 kV and increase inaccordance with the beam voltage increment up to about
80 kV. In Figs. 7 and 8, at the starting energy of approximately 10 keV, the interaction point is in the BWO. Increasing the beam energy from 25 to 40 keV, the beam interaction point with TM01 is close to the upper cutoﬀ at
the π-point, as shown in Fig. 2. Over the beam energy of
40 keV, the interaction point moves into the TWT region.
In order to examine the mode, the radiation patterns
were obtained by moving a receiving horn antenna in an
equatorial plane around a pivot at the center of the output
window. The horizontal components of the electric field
were measured. The pattern for TWT operation of the 80period SWS length is shown in Fig. 9. As a reference, atheoretical radiation curve for the TM01 waveguide modeis shown. The measured pattern appears to be axisymmetric with a dip at the center. The pattern is broad and cannot be explained by a single TM01 mode. Higher order2406085-4

Plasma and Fusion Research: Regular Articles

Volume 11, 2406085 (2016)

Fig. 10 Radiation pattern for the π-point operation of the
40-period SWS length. The operating parameters are approximately 30 kV, 150 A and 0.82 T. The solid curve isthe calculated radiation pattern for the TM01 waveguidemode.

waveguide modes are required to explain this broad radiation. The radiation patterns for the BWO operation are alsobroad, as shown in Fig. 9. The W-band oversized surface
wave oscillator is found to be a multimode system in the
BWO and TWT regions, and many modes may be excited
simultaneously.
The radiation pattern for π-point operation of the 40period SWS length is shown in Fig. 10. The operating parameters are approximately 30 kV, 150 A and 0.82 T. In thiscase, the radiation pattern approaches the TM01 mode. In
other words, the higher order modes in the multimode system are suppressed around the π-point and the oscillation
approaches a single mode operation.
The maximum detected power is observed in the TWT
region, as shown in Fig. 8, at approximately 80 kV. By integrating the detected power over the broad pattern, the corresponding maximum radiation power is estimated to beapproximately 20 kW.

5. Discussion and Conclusion
The performance of the W-band oversized surface
wave oscillator is compared with that of the previous
K-, Q-, and G-band oversized BWOs driven by an annular beam with energy less than 100 keV. The radiation powers of the K-, Q-, and G-band oversized BWOs
are approximately 500, 200 and 15 kW, respectively [5,7, 8]. The figure of merit of the BWO is approximately
3.5 × 102 MW.GHz2 , as shown in Fig. 11. Here, P is theradiation power, and f is the frequency. For the W-bandoversized surface oscillator, the maximum radiation power
is approximately 20 kW with the figure of merit of about
2 × 102 MW.GHz2 , which is nearly the same as the previously obtained ones of the BWO as shown in Fig. 11. Notethat the figure of merit of the W-band oscillator based on
the surface wave cavity in the TWT region has nearly thesame value as those of the BWOs.
Here the uniqueness and usefulness of the π-point operation are discussed. In general, oversized SWSs are a

Fig. 11 Figure of merits of X-, K-, Q-, W- and G-band oscillators
based on the oversized SWS.

multimode system. The presented W-band oversized surface wave oscillator also has a multimode nature and radiates many modes in the BWO and TWT regions. To date,
operations near the π-point have not been studied well. Our
experiments show that the radiations from the W-band oscillator disappear for the long SWS length of 120 periods.
This disappearance qualitatively agrees with a theoreticalprediction in [11]. Moreover, we demonstrate that the πpoint operation is possible by shortening the SWS length.
This π-point operation has a single mode nature; this is aunique and useful result, which may provide one possible
solution for the mode competition problem. Mode control
is a very diﬃcult problem. To solve this problem, double
SWSs are usually examined [16, 17]. The π-point operation presented may give an alternative way to control theoperation mode.
In conclusion, we experimentally studied the operation of a W-band oversized surface wave oscillator driven
by weakly relativistic electron beams. The microwave output signals and the starting beam energies have nearly thesame values for various SWS lengths. The interactionsin the BWO and TWT regions are pronounced for longer
SWS lengths. At the π-point, meaningful radiation is notdetected for the long SWS length. The microwave signals
with a suﬃciently short SWS length are observed from theπ-point operation as well as the BWO and TWT operations. Therefore, the length of the SWS of the oscillator
must to be considered for the operation of the W-band oscillator. The W-band oscillator includes a compact terahertz microwave power source with the output microwave
power of some tens kW in the weakly relativistic region.
The oscillator may be of considerable interest for practicaluse and for developing compact tunable THz wave sources.

Acknowledgement

This work was partially supported by NIFS Collaboration Research Program Nos. NIFS12KLER014 and
NIFS14KLER031.
[1] S.P. Bugaev et al., IEEE Trans. Plasma Sci. 18, 518 (1990).
[2] S.P. Bugaev et al., IEEE Trans. Plasma Sci. 18, 525 (1990).

2406085-5

Plasma and Fusion Research: Regular Articles

Volume 11, 2406085 (2016)[3] A.N. Vlasov et al., IEEE Trans. Plasma Sci. 28, 550 (2000).
[4] K. Ogura et al., IEEJ Trans. FM 125, 733 (2005).
[5] S. Aoyama et al., Trans Fusion Sci. Technol. 51, 325(2007).
[6] K. Ogura et al., IEEJ Trans. FM 127, 681 (2007).
[7] S. Magori et al., Plasma Fusion Res. 9, 3406032 (2014).
[8] S. Gong et al., IEEE Trans. Plasma Sci. 43, 3530 (2015).
[9] H. Oe et al., J. Plasma Fusion Res. SERIES 8, 1477 (2009).
[10] K. Yambe et al., IEEE Trans. Plasma Sci. 41, 2781 (2013).
[11] H.L. Andrews et al., Phys. Rev. ST Accel. Beams 8,050703 (2005).
[12] D.M. Pozar, Microwave Engineering, 4th ed. New York,NY, USA: Wiley, (2012), p. 720.
[13] Y. Takashima et al., J. Plasma Fusion Res. SERIES 8, 1512
(2009).
[14] K. Ogura et al., IEEE Trans. Plasma Sci. 41, 2729 (2013).
[15] K. Ogura et al., Plasma Fusion Res. 9, 3406022 (2014).
[16] K. Mizuno et al., IEEE Trans. Electron Devices ED-20,
749 (1973).
[17] I.V. Konoplev et al., Phys. Rev. E 76, 056406 (2007).

2406085-6