Concept and Theory of Clustered-Cavity
Gyroklystrons
G.S. Nusinovich1, H. Guo, T.M. Antonsen, Jr., and V.L. Granatstein
IREAP, University of Maryland, College Park
Abstract. The concept of clustered cavities was originally proposed by R. Symons for use in
linear-beam klystrons operating in TM-modes. It was proven experimentally that the use of this
concept allows developers to double the instantaneous bandwidth of klystrons without changing
their overall dimensions or sacrificing gain and bandwidth. Recently, H. Guo suggested applying
this concept to gyroklystrons operating in TE-modes. In the present paper this concept is
formulated and a simple analytical theory describing qualitatively the performance of clusteredcavity gyroklystrons is developed. Results of the analysis of a simple two-stage gyroklystron
indicate that the clustered-cavity concept has potential for improving the performance of
gyroklystrons.
INTRODUCTION
Nowadays, there is a strong interest in the development of high-power, high-gain,
large-bandwidth gyroamplifiers for driving future linear accelerators as well as for
radar applications (see, e.g. Ref. 1). As is well known, gyroklystrons are capable of
high-gain and high-power amplification of electromagnetic waves in a relatively
narrow bandwidth. To increase the bandwidth, the resonant eigenfrequencies of
gyroklystron cavities can be slightly detuned. This method known as stagger tuning is
widely used in conventional linear-beam klystrons. Stagger tuning in gyroklystrons
has been actively studied both theoretically [2] and experimentally [3].
Recently, another concept for enlarging bandwidth in high-gain gyroklystrons has
been proposed [4]. This concept is based on the use of clustered cavities. A similar
concept was previously proposed for conventional klystrons by R. Symons [5]. The
essence of this concept is based on the replacement of individual intermediate cavities
of a multi-cavity klystron by pairs or triplets of artificially loaded cavities with Qfactors of each cavity in a cluster reduced to one-half or one-third, respectively, of the
single cavity they replace. By using this principle, the bandwidth of two high-power,
five-cavity klystrons has been doubled without changing the overall dimensions of the
tubes and with minimal degradation in efficiency and gain [6].
Below we analyze some possibilities of improving the performance of
gyroklystrons by using the cluster cavity concept.
1
Author contact: [email protected]
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
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THEORETICAL FORMALISM AND MODEL
A simple theoretical formalism describing qualitatively the performance of
clustered-cavity gyroklystrons has been described in Ref. 7. Therefore, referring
interested readers to that paper, we will briefly outline below only the most important
features of the formalism and the model under study.
A set of equations describing any gyroklystron consists of equations for electron
motion, which describe the changes in the electron orbital momentum and gyrophase
under the action of the RF field, and balance equations, which determine the amplitude
and phase of the RF field excited in each cavity by an electron beam. In drift regions
between the cavities, electrons experience ballistic bunching due to electron energy
modulation by the RF fields in preceding cavities.
To qualitatively describe the performance of gyroklystrons, it is possible to use a
so-called point-gap model, which is known in the theory of conventional klystrons.
This model implies that a device consists of short cavities separated by long drift
sections. Then, in short cavities, only the energy modulation should be accounted for,
while the phase bunching will occur in long drift regions. To apply this model to
clustered-cavity devices, we will assume that each cluster consists of closely located,
but well isolated cavities. Thus, the phase bunching inside each cluster can be ignored.
This assumption allows us to develop an analytical theory describing the operation of
clustered-cavity gyroklystrons with stagger-tuned cavities even in the large-signal
regime [7].
RESULTS
For the sake of simplicity, we compared the results obtained for a point-gap model
of two-cavity gyroklystron with results for a point-gap model of two-cluster
gyroklystron, in which each cluster in turn consists of two cavities, as is shown in
Fig. 1. It was shown that the maximum efficiency in both cavities is the same. Then, it
was shown that the optimum length of the drift section in the clustered-cavity
gyroklystron is much shorter than in the conventional gyroklystron.
It was also shown that the doubling of cavities in each stage of a two-cavity device
can result in gain increase by 6 dB. When the Q-factors of cavities in clusters are two
times smaller than Q-factors of cavities in a conventional gyroklystron, the maximum
gain is the same, however, the lowering of Q-factors results in the doubling of the
bandwidth.
The effect of stagger tuning on the bandwidth enlargement was analyzed for three
cases. First, the case was considered when the cavities in each cluster are not stagger
tuned, however, the cold-cavity frequencies in the input cluster are not equal to coldcavity frequencies in the output cluster. In this case, the trade-off between gain and
bandwidth is quite similar to that in conventional gyroklystrons [7]; viz. the maximum
stagger tuning allows one to increase the bandwidth by more than 4.6 times at the
expense of the gain reduction by 13.5 dB. It should be noted, however, that, when in
clustered-cavity gyroklystrons with two cavities in each cluster cavities are used
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whose Q-factors are two times lower than in conventional gyroklystrons, this doubles
the bandwidth.
In a similar fashion, the case was considered when there is no stagger tuning
between mean frequencies of clusters, but there is a stagger tuning in each cluster.
This kind of stagger tuning allows one to increase the bandwidth by 2.7 times at the
expense of the gain degradation by slightly more than 6 dB. Finally, we studied the
case of all non-zero stagger tunings (within each cluster and between the clusters). In
this case the bandwidth can be increased up to 8.5 times due to the stagger tuning.
However, this bandwidth enhancement will be accompanied by 17-18 dB gain
degradation. Clearly, the maximum gain-bandwidth product corresponds to smaller
stagger tuning [2].
EXAMPLE
To illustrate the benefits of the cluster-cavity concept, let us apply it to a 35 GHz,
two-cavity gyroklystron recently developed at the Naval Research Laboratory (NRL)
[8]. This tube was driven by a 70 kV, 8.2 A electron beam with the orbital-to-axial
velocity ratio of 1.43. Both cavities operated in the TE0n-mode excited at the
fundamental cyclotron resonance. The Q-factors of both cavities were close to 190 and
their cold-cavity frequencies were slightly stagger tuned by about 5 MHz only. An
experimentally measured bandwidth was about 0.36%.
To apply the cluster-cavity concept, we assumed that each cavity of this device is
replaced by a cluster consisting of two cavities with Q-factors equal to 100, while the
beam parameters and the drift section length remain the same. Our analysis based on
consideration of the point-gap model discussed above showed that this replacement of
individual cavities by two-cavity clusters allows one to increase the bandwidth from
0.34% to about 1.2%. Simultaneously, the efficiency slightly increases. The gain
increases as well, although it can be modified by the variation of the drift section
length.
SUMMARY
A cluster-cavity concept, which was originally proposed for the use in linear-beam
klystrons operating in TM-modes, has been applied to gyroklystrons operating in TEmodes. A simple analytical theory allowing for the qualitative analysis of clusteredcavity gyroklystrons has been developed. This theory showed that the use of clusters
with reduced Q-factors of individual cavities can lead to significant bandwidth
enhancement and increase the gain-bandwidth product.
At the same time, there are two important issues to be addressed, which make the
advantages of this concept less obvious. The first issue is the requirement to uncouple
the cavities in each cluster. These cavities can be simply isolated by using short cutoff
dielectrically-loaded tubes between them when the cavities operate in low-order
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modes (such as TEm or TE0n modes). These modes, as any other modes, have some
evanescent fields in short cutoff tubes between cavities, and these fringe fields can be
attenuated further with the use of lossy materials. However, in the case of operation in
higher-order TEmp-modes (with the radial index /?>!), this problem is much more
severe, because in any cavity a high-order operating mode experiences a certain
conversion into modes with smaller radial indices (/?'</?). To prevent propagation of
modes with (p'< p) through the space between the cavities in one cluster can be very
difficult.
Another issue is the method of comparison. So far, we have compared an N-cavity
gyroklystron with an N-cluster device. However, one can argue that the N-cluster
device where each cluster contains M individual cavities should be compared with N
times M cavity gyroklystron. This means that, for instance, a two-cluster gyroklystron
with two cavities in each cluster, which is shown in Fig.l, should be compared not
with a two-cavity gyroklsytron (also shown there), but with a four-cavity gyroklystron.
Such a comparison has not been done yet.
ACKNOWLEDGMENTS
This work has been supported by the Multidisciplinary University Research
Initiative (MURI) on Vacuum Electronics sponsored by the Air Force Office of
Scientific Research. Authors would also like to thank Jay Hirshfield for fruitful
discussions.
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Guo, H., et al., in Conf. Digest, 25th Int. Conf. on Infrared and Millimeter Waves, Bejing, P. R.
China, Sept. 12-15, 2000, Eds. S. Liu and X. Shen (IEEE, 2000), p. 317.
Symons, R.S., U. S. Patent, No. 4,800,322
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Choi, J.J., et al., IEEE-PS 26, 416 (1998).
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A
FIGURE 1. Schematic representation of a two-cavity gyroklystron (a) and a two-clustered
gyroklystron with two cavities in each cluster (b).
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