# Comparison of multistage gyroamplifiers operating in the frequency-multiplication regime with gyroamplifiers operating at a given Cyclotron harmonic

**ABSTRACT** The operation of gyrodevices at cyclotron harmonics is very attractive because of the possibility to reduce the magnetic field requirement by s times, where s is the cyclotron harmonic number. In recent years, two methods of harmonic operation in multistage gyroamplifiers have been actively studied: operation at a given harmonic in all stages and operation in the frequency-multiplying regime when the input stage operates at a lower harmonic than the output one. The present paper is aimed at making a comparative analysis of these two schemes of operation. To do this, a simple analytical method is developed, which allows one to qualitatively describe saturation effects in both schemes and compare such performance characteristics as the efficiency, gain, and bandwidth in both schemes. The results are of interest for evaluating the pros and cons of both schemes.

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**ABSTRACT:**Experimental results of a high-harmonic gyro-klystron amplifier are presented along with small-signal theory and large-signal simulation data. In this device, axis-encircling electrons interact synchronously with high-order azimuthal cylindrical-cavity TE modes. Gain in excess of 20 dB has been achieved at the fifth and sixth harmonics of the cyclotron frequency. The requisite high-energy beam is provided by a gyro-resonant RF accelerator. Harmonic operation together with RF acceleration potentially constitute a compact high-power high-frequency amplifier.International Journal of Electronics 12/1984; 57(6):1151-1165. · 0.51 Impact Factor - SourceAvailable from: Baruch Levush[Show abstract] [Hide abstract]

**ABSTRACT:**This article explores the history and diversity of this remarkable technology, with emphasis on advances in vacuum-electronic amplifiers, including the microwave power module (MPM), that have been enabled by the ongoing development of modeling and simulation tools. These physics-based codes, enabled by rapid advances in computational hardware, allow simulation-based design and optimization of complex vacuum-electronic circuits. The growth of satellite-based digital communications technology over the past decade has opened lucrative commercial opportunities for vacuum-electronic amplifiers. This exciting new area requires the efficient production of high-frequency power and the ability to handle spectrally efficient modulations within stringent packaging constraints at affordable costIEEE Microwave Magazine 10/2001; · 1.50 Impact Factor - SourceAvailable from: caltech.edu[Show abstract] [Hide abstract]

**ABSTRACT:**This article surveys recent progress in the development of high-power microwave and millimeter-wave solid-state sources using spatial power-combining techniques. Several promising topologies are discussed, and four technology demonstrations are presented that have emerged from recent research in academia and industry. We also include a brief discussion of potential applications and systems insertion issuesIEEE Microwave Magazine 01/2001; · 1.50 Impact Factor

Page 1

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004957

Comparison of Multistage Gyroamplifiers Operating

in the Frequency-Multiplication Regime With

Gyroamplifiers Operating at a Given

Cyclotron Harmonic

Gregory S. Nusinovich, Fellow, IEEE, Oleksandr V. Sinitsyn, J. Rodgers,

Thomas M. Antonsen, Jr., Senior Member, IEEE, Victor L. Granatstein, Life Fellow, IEEE, and N. C. Luhmann, Jr.

Abstract—The operation of gyrodevices at cyclotron harmonics

is very attractive because of the possibility to reduce the magnetic

field requirement by

times, where

number. In recent years, two methods of harmonic operation in

multistage gyroamplifiers have been actively studied: operation at

a given harmonic in all stages and operation in the frequency-mul-

tiplying regime when the input stage operates at a lower harmonic

than the output one. The present paper is aimed at making a com-

parative analysis of these two schemes of operation. To do this, a

simple analytical method is developed, which allows one to qual-

itatively describe saturation effects in both schemes and compare

such performance characteristics as the efficiency, gain, and band-

widthinbothschemes.Theresultsareofinterestforevaluatingthe

pros and cons of both schemes.

is the cyclotron harmonic

Index Terms—Cyclotron harmonics, frequency multiplication,

gyroamplifiers, gyrotrons.

I. INTRODUCTION

F

in gyrodevices the magnetic field required for obtaining the cy-

clotron radiation at a given frequency is inversely proportional

to the cyclotron resonance harmonic number, , the gyrotron

operation at harmonics

time. In multistage gyroamplifiers, two concepts of harmonic

operation are known: 1) regime of frequency multiplication [1]

(for instance, operation of theinput stage at thefundamental cy-

clotron resonance,

, and the output stage operation at the

harmonic

) and 2) operation of all stages at the same

harmonic

[2]. Both concepts have been studied

for a long time. However, so far, no comparative discussion of

their potentials and comparative analysis of these two concepts

have been carried out. Such a comparative analysis is done in

the present paper.

ORMANYapplicationsofgyrodevices,thecriticalissueis

theuseofcryomagnetsorheavyandbulkysolenoids.Since

has been studied for a long

Manuscript received September 23, 2003; revised January 23, 2004. This

work was supported by the Multidisciplinary University Research Initiative on

Innovative Vacuum Electronics sponsored by the Air Force Office of Scientific

Research.

G. S. Nusinovich, O. V. Sinitsyn, J. Rodgers, T. M. Antonsen, Jr., and V. L.

Granatstein are with the Institute for Research in Electronics and Applied

Physics, University of Maryland, College Park, MD 20742-3511 USA (e-mail:

gregoryn@glue.umd.edu).

N. C. Luhmann, Jr. is with the University of California, Davis, CA 95616

USA.

Digital Object Identifier 10.1109/TPS.2004.827590

Before starting to describe its content, it makes sense to

discuss possible potential applications of both schemes and

their “pros and cons.” Clearly, the frequency multiplication

is a purely nonlinear process, occurring due to the nonlinear

properties of an electron beam, which being modulated at

a given frequency generates in the electron current density,

in addition to this frequency, also its harmonics. Therefore,

frequency-multiplying gyroamplifiers cannot be used in com-

munication systems that require a high degree of linearity. [For

example, if the carrier is simultaneously modulated by several

channels as in frequency-division multiple-access systems

(FDMA)]. At the same time, however, such devices can be used

in various radar and accelerator applications (see, for instance,

corresponding chapters in [3]) as well as in single-channel

digital communication systems possibly using code-division

multiple access (CDMA).

An obvious advantage of frequency-multiplying gyroampli-

fiers is operation of the first stage at the fundamental cyclotron

resonance. In comparison with a similar stage operating at

higher harmonic, operation at the fundamental can be realized

at a lower order mode that improves the stability of operation

and simplifies the design and configuration of an input coupler.

Also, the electron beam is more strongly coupled to the

radio-frequency (RF) field at the fundamental resonance than

at harmonics. The difference in the coupling can be roughly

estimated based on the fact that, in accordance with the Schott

formula (see, e.g., [4, eq. (74.8)]), the intensity of cyclotron

radiation, when electron orbital velocities are reasonably small,

is proportional to

. (Here,

normalized to the speed of light.) Therefore, one can use in

frequency-multiplying devices lower power drivers, which

also can operate at lower frequencies. This is a very important

advantage, especially at millimeter (and shorter) wavelengths,

where the availability of drivers of high enough power is a

serious issue.

Since the use of solid-state drivers allows the most compact

solution, it makes sense to briefly discuss the present state-

of-the-art in solid-state sources in the range of the wavelength

of our interest. As shown in [5], the maximum power of such

sources ranges from 10 to 20 W in the X-band to about 1 W

in the W-band and then falls rapidly at higher frequencies (less

than0.1Wat200GHz).So,thefrequencymultiplicationfactor,

is the electron orbital velocity

0093-3813/04$20.00 © 2004 IEEE

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958 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

which allows one to use lower frequency for driving the device,

is here important. It should be noted that these power levels can

beincreasedbyusingthetechniqueofspatialpowercombining,

especially in the case of quasi-optical power combining [6], [7].

As an illustration of the advances, the work at Sanders can be

mentionedwheretheuseof272individualmillimeterintegrated

circuits (MMICs) arranged in a “tray” architecture resulted in

producing 35 W power at 61 GHz with a 60-dB small-signal

gain[8].Forcomparison,letusmentionasanexamplethatsuch

a vacuum tube as a W-band coupled-cavity traveling wave tube

(TWT) (millitron) provides 5-kW peak power with a 10% duty

with the bandwidth in excess of 1% [9].

After mentioning these more or less obvious arguments, let

us note that such issues as the preference of one of the dis-

cussed above schemes of gyroamplifiers with regard to the ef-

ficiency, gain, bandwidth, and other performance characteris-

tics is not obvious. Just an analysis of these issues is in the

focus of the present paper. The paper is organized as follows.

Section II briefly describes a general formalism, which we use

in our analysis. Section III contains the results of the analysis

of both schemes of interest for several multistage gyroampli-

fiers: two-cavity gyroklystrons, three-cavity gyroklystrons, and

two-stage gyro-TWTs. Also, some results of simulations for an

ultrahigh-gain gyro-TWT with distributed losses operating ei-

theratthefundamentalorsecondharmonicareincluded.InSec-

tion IV, we discuss the results obtained and consider a specific

example illustrating the application of our formalism to pos-

sible experimental conditions. Finally, Section V summarizes

our paper.

II. GENERAL FORMALISM

Our consideration is based on the general formalism devel-

oped for gyrodevices a long time ago [10]. Recently, the theory

of gyroklystrons based on this formalism was analyzed in de-

tail in [11] and [12]. The derivation of corresponding equations

describing the gyro-TWT and some results of the studies of

gyro-TWTs operating at cyclotron harmonics are given in [13].

Since the equations have been described in detail in those ref-

erences, here we will only outline the issues in this formalism,

whicharethemostimportant forourcomparativeanalysis.First

ofall,itshouldbenotedthatthechoiceofthegeneralformalism

was dictated by the fact that it is very difficult, if not impos-

sible, to draw any conclusion just from comparison of different

designs, while we will attempt to make these conclusions with

the use of the general formalism.

A. Gyroklystron Formalism

The operation of the gyroklystron can be described by the set

of equations that determine the electron motion in the cavities

and drift regions, and equations that describe the field excita-

tion in the cavities. Consideration of electron motion is greatly

simplified in thecase of a so-called point gap model also known

in linear-beam klystrons. (Originally, Yulpatov proposed to use

this model for studying the gyroklystrons [14]; later, Caplan

[15] used it for analyzing the small-signal gain of a five-cavity

gyroklystron.) This model represents a gyroklystron circuit as

a set of short cavities separated by long drift sections. When

the cavities are short enough, it is possible to neglect there the

effects associated with electron orbital bunching, and hence to

consider there only electron energy modulation by the RF field.

Then,theorbitalelectronbunchingcausedbythechangesinthe

electron cyclotron frequency due to the energy modulation pro-

ceeds in the long drift regions. In the framework of this model,

the equations for electron motion can be integrated analytically

even in large-signal regimes.

The field excitation in the cavities can be described by the

balance equations (assuming that we consider the stationary op-

eration of a device). For the input cavity, the balance equation

forthenormalizedintensityoftheRFfield,

as [11], [12]

,canbewritten

(1)

Here,

respect to the RF field in the first cavity. (In the framework

of the point-gap model, it can be calculated analytically.) The

first and second terms in the denominator describe the beam

loading and frequency pulling effects, respectively. In the latter,

is the normalized detuning of the

signal frequency

with respect to the cold-cavity frequency

. In (1),is the normalized intensity of the field excited in

the input cavity by the drive signal. This intensity relates to the

power of the driver,

, as [11]

is the electron beam susceptibility with

(2)

Here,

cavity having the loaded

is the beam power associated with the electron gyra-

tion,

andare the beam voltage and current, respectively,

is the initial orbital velocity of electrons normalized to the

speed of light, and

energy normalized to the rest energy. (The derivation of (2) is

given in [16].)

In (1) and (2), we used the normalized beam current param-

eter, which for cylindrical cavities operating at

equal to

is the coupling or externalfactor of the input

denoted by ,

is the initial electron

-modes is

(3)

Here,

is the cyclotron resonance harmonic number,

is the normalized axial coordinate, the function

describes the axial distribution of the cavity field,

is the eigenvalue of the operating mode in a cavity of a

radius

, is the radius of electron guiding centers in a thin

annular electron beam, and

is the Bessel function of the first

kind.

The most important for our consideration is the fact that this

normalized beam current parameter is proportional to

This means that, for all other parameters being equal, the nor-

malizedcurrentparameterforthecaseofoperationatthesecond

harmonic is

times smaller than for operation at the funda-

mental cyclotron resonance. So, in addition to the issue of the

availability of high-power drivers at different frequencies, we

.

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NUSINOVICH et al.: COMPARISON OF MULTISTAGE GYROAMPLIFIERS OPERATING IN THE FREQUENCY-MULTIPLICATION REGIME 959

get here one more factor, which weakens the RF field amplitude

in the case of operation at harmonics.

Then, the integration of equations for electron motion in the

drift sections and in other cavities yields the expression for the

susceptibility as the function of the bunching parameter,

. Here

length of the drift section. Note that in frequency-multiplying

devices, in order to have the bunches in all beamlets in the

same phase with respect to the RF field of the output stage,

the azimuthal indices of operating modes and the cyclotron har-

monic numbers should obey the phase synchronization con-

dition

[17], [18]. In the case of multicavity

gyroklystrons, there are more than one bunching parameters,

which account for the bunching caused by the modulation in

corresponding cavities. Then, the efficiency can be calculated

as

is the normalized

(4)

where the orbital efficiency relates to the imaginary part of the

susceptibility of the beam with respect to the output cavity field

as

(5)

As was mentioned above, in the framework of the point-gap

model this susceptibility can be calculated analytically. Corre-

spondingly, one can easily find that the maximum orbital effi-

ciency of the two-cavity gyroklystron is equal to

(6)

(In the case of a larger number of cavities, the expression for

the efficiency is more complicated.) In (6),

frequencymultiplicationfactor,whichisequaltooneinthecase

of operation at the same harmonic in all stages and larger than

one in frequency-multiplying devices.

The gain, in accordance with [11] and [12], can be presented

as a superposition of two terms

is the

(7)

where

depend on the signal frequency variation. For the two-cavity

gyroklystron, it is equal to

is the constant part of the gain, which does not

(8)

Correspondingly,

of the gain, which for the two-cavity gyroklystron is equal to

is the frequency-dependent variable part

(9)

Here,

sence of bunching effects, which for the point-gap model is

equal to

(see [11]), and

parameters now should be given for the second cavity. Also,

is the bunching parameter independent on the

beam loading and frequency pulling effects, while the previ-

ously introduced bunching parameter

account. As follows from (1), the parameters are related as

is the susceptibility of the second cavity in the ab-

is determined by (3), where all

takes these effects into

(10)

Equations (8) and (9) are written for the large-signal regime of

operation. In the small-signal regimes, the bunching parameter

is small, and therefore the Bessel functions describing the sat-

uration effects can be presented in a simple polynomial form,

viz.

fication of these equations (see [11] and [12]). These equations

become especially simple when the normalized beam current

parameter is small enough, so one can neglect the beam loading

and frequency pulling effects in (1) and below. For our analysis,

it is important that, afterthe polynomial expansionof the Bessel

function, the term in the figure brackets in (9) becomes propor-

tional to

, i.e., in the case of small bunching parame-

ters the gain of frequency-multiplying devices becomes much

smaller than that in the case of operation at a given harmonic.

This is, of course, obvious because the frequency multiplication

is a purely nonlinear effect.

, that causes a certain simpli-

B. Gyro-TWTs Formalism

There are also some analytical methods to analyze the op-

eration of multistage gyro-TWTs. The simplest one was pro-

posed in [19] and then used in [20] and in later publications.

This model of a gyro-TWT, in which there are input and output

waveguides separated by a sever, is based on the following as-

sumptions. First, we assume that the input waveguide operates

in the small-signal regime, which is valid for practically all

known devices. Then, the orbital electron bunching in the drift

region between the input and output waveguides causes the ap-

pearance of harmonics of the signal frequency in the electron

current density, whichis the nonlinearprocess thatcan be easily

analyzed analytically as in gyroklystrons. Finally, we assume

that the output waveguideis reasonably short, and hence, can be

considered in a specified current approximation. This approx-

imation implies that we consider the excitation of the output

waveguide by a given current, but neglect the effect of the ex-

cited wave on the electrons.

Without going into further description of this formalism, let

us present here the expression for the gain

(11)

Here,

second waveguide (this parameter is quite similar to that given

above by (3) for a cavity; see [21] for more details),

normalized amplitude of the wave at the entrance to the input

waveguide, which depends not only on the input power, but

is the normalized beam current parameter for the

is the

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960IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

also on the choice of mode and the resonance harmonic number

[22]:

. As follows from this dependence,

in which the drive power should also be multiplied by the

coupling impedance of a beam to the wave, which is similar to

the last term in the right-hand side of (3), the operation in the

input waveguide at the fundamental increases the amplitude

of the excited wave at a given level of the drive power. This

increase becomes even larger when in the input waveguide

operating at the fundamental resonance a lower order mode

is used than in the case of the second harmonic operation.

The bunching parameter in (11) is proportional to the product

of the normalized length of the drift section to the function

describing the wave amplification in the input waveguide [21].

This function describing the wave amplification in the input

waveguide, in the framework of the small-signal theory, is lin-

early proportional to the input wave amplitude,

that, in the case of operation at the fundamental resonance in

the input waveguide, the saturation can be achieved at shorter

lengths of drift sections. Also important is the fact that in the

case of operation in lower order modes at the fundamental

resonance it is easier to provide the stability, since lesser

number of parasitic waves can be excited. (This statement,

of course, does not mean that one cannot provide stability of

the operation at the second cyclotron harmonic; see [23] for a

convincing example of the successful operation at the second

harmonic at the 200-kW level in the

The gain given by (11) can again be represented as a sum of

the constant and variable parts. In the small-signal regime, cor-

responding expressions can be properly simplified. Of course,

expanding the Bessel function in (11) as a polynomial, we get

thesameconclusion aboutthegaindependence onthebunching

parameter as we made above for gyroklystrons. So, in general,

for all frequency-multiplying devices, the same dependence of

the output power on the input power,

whichwasobtainedforlinear-beamTWTsalongtimeago[24].

The Bessel function present in (11) also determines the nor-

malized intensity of the outgoing radiation

. This means

-wave.)

, is valid,

(12)

This intensity, in accordance with the energy conservation law,

determines the orbital efficiency of the device

(13)

which in the framework of the specified current approximation

is small. (As was shown in [21], this approximation is valid for

the normalized lengths of the output waveguide not exceeding

4 and 2 for the normalized beam current parameters

to 0.01 and 0.1, respectively. In longer waveguides, the effect of

the excited wave on the electron motion becomes significant.)

equal

III. RESULTS

A. Two-Cavity Gyroklystron

The orbital efficiency of the two-cavity gyroklystron (GKL)

was givenabove by (6). As follows from this equation, the max-

imum efficiency of the frequency-doubling GKL with

Fig. 1.

the optimal drift section length is shorter in frequency-multiplying GKLs and

vice versa. The solid line corresponds to the case of equal coupling impedances

in input cavities of both schemes; the broken line illustrates the case when

the input cavity operates at the ??

- and ??

schemes, respectively.

Regions of preferable operation in one of two schemes: below the lines

- mode in the 1-2 and 2-2

andis approximately equal to 0.12 and the corre-

sponding optimum value of the bunching parameter is equal to

. Similarly, the maximum orbital efficiency of the

GKL, in which both cavities operate at the second harmonic

is equal to 0.17 and

lowing, we will designate these schemes of GKLs by their har-

monicnumbersineachstage,i.e.,wewillcallthecaseof

and“1-2 scheme,” the case

and so on.

So,atthefirst glance,the2-2 schemeoffersmuchhighereffi-

ciencythanthe1-2scheme.Twofacts,however,shouldbetaken

into account here. First, numerical analysis of such schemes of

GKLs with a finite length of output cavities carried out in [25]

shows that the maximum efficiencies of both schemes with an

optimumlengthoftheoutputcavitiesaremuchhigherandmuch

closer: 0.60 and 0.65 for the 1-2 and 2-2 schemes, respectively.

Second, it is important to bear in mind that optimal values of

bunching parameters can correspond to different lengths of the

drift sections, because the amplitude of the RF field excited in

the input cavity, as follows from (1) through (3), depends on the

resonant cyclotron harmonic number. Clearly, it is preferable to

have a device in which the drift section length is shorter, be-

cause such a device is more compact and its operation is less

sensitive to electron velocity spread and fluctuations in oper-

ating parameters. In our case, the preference depends not only

on the harmonic number

, but also on the choice of the op-

erating mode. The results are shown in Fig. 1. Here, the solid

and dotted lines show the borders between the region of shorter

drift section length for a 1-2 scheme (below the line) and a 2-2

scheme (above the line). The solid line corresponds to the case

when in both schemes the same operating mode is chosen; the

dotted line corresponds to the case when the input cavity oper-

atesateither

- or-modeinthe1-2and 2-2schemes,

respectively. (It is assumed that

. In the fol-

“2-2 scheme,”

-factors of input cavities and

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NUSINOVICH et al.: COMPARISON OF MULTISTAGE GYROAMPLIFIERS OPERATING IN THE FREQUENCY-MULTIPLICATION REGIME961

the drive power in both cases are the same.) This figure shows

that,withregardtothechoiceofthedriftsectionlength,thepref-

erence depends on such parameters as the beam voltage and the

orbital-to-axial velocity ratio, which determine the electron or-

bitalvelocity.Ofcourse,whentheinputcavityinthe1-2scheme

operates at the lowest order

preferable in a larger region of the parameters. (In accordance

with the above mention phase synchronization condition, when

theinputcavityoperatesatthefundamentalresonanceatamode

with the azimuthal index equal to one, the output cavity, which

operates at the second harmonic, should utilize a mode with the

azimuthal index equal to two, e.g.,

Let us now compare the gain and bandwidth of the two

schemes. The constant part of the gain, which is given by (8),

can be the same in both schemes when the output cavities

operate at the same mode, the drift section length is the

same, and the beam loading in the input cavity is negligibly

small, so the difference in the factor

The variable gain given by (9) is, however, different. As we

already mentioned in the previous section, there is no sense

to discuss the small-signal gain in frequency-multiplying

devices, because this gain is negative. Therefore, it is better

to compare the variable gain in two schemes in the cases

when the bunching parameter is optimal for each of them.

The results are shown in Fig. 2. Here, (a) and (b) show the

variable gain for 1-2 and 2-2 schemes, respectively. The gain

is shown as the function of the normalized signal frequency

detuning,

is the mean frequency of the cold-cavity

frequencies) for several values of the stagger-tuning parameter

-mode, this scheme becomes

-mode.)

there does not matter.

(here,

. For the 1-2 scheme,

the parameter

describes the difference in

equal to 0.12, which is the optimal value of

[12];forthe2-2scheme

shows that in the case of zero detuning, when the variable gain

is maximal,

dB, while

So, the 2-2 scheme exhibits the gain higher by 6 dB in this case.

Results shown in Fig. 2 allow one also to analyze the effect of

stagger-tuning on the bandwidth enlargement at the expense of

the gain degradation. Correspondingresults are shown in Fig. 3,

where solid and dotted lines correspond to the 2-2 and 1-2

schemes, respectively. These results show that in both schemes

the stagger tuning allows one to increase the bandwidth in

practically the same fashion. In comparison with the case of no

stagger tuning, the maximum increase in bandwidth due to the

stagger tuning is 4.83 [11] and 5.3 [12] times in schemes with

and, respectively. However, this bandwidth

enlargement corresponds to the gain degradation by 16.7 dB

and about 17 dB

gain and bandwidth has been analyzed in more detail in [11]

and [12].

, which

-factors of cavities, was taken to be

for this scheme

.ComparisonofFig.2(a)and(b)

dB.

. The tradeoff between the

B. Three-Cavity Gyroklystron

The bunching processes in multicavity gyroklystrons, of

course, are more complicated than those in the two-cavity

device considered above. These processes can be characterized

Fig. 2.

(a) 1-2 scheme with the optimum bunching parameter ?

(b) 2-2 scheme with ?

? ????.

Modification of the large-signal variable gain with the stagger tuning:

? ????, and

Fig. 3. Gain degradation and bandwidth enlargement with stagger tuning.

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962IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

by a so-called “bunching” efficiency,

orbital efficiency introduced above as

is the harmonic number in the output cavity. This bunching

efficiency is determined by the intensity of the corresponding

harmonic in the electron current density exciting the output

cavity,

. Such harmonics in three- and four-cavity GKLs

and their effect on the efficiency, gain, and bandwidth of GKLs

were studied in detail in [11], and [26]–[28]. Therefore, here

we will only outline the issues that are the most important for

our comparative analysis.

As shown in [26], the bunching efficiency in 1-2-2 and

2-2-2 schemes can exceed 0.6 (so, the orbital efficiency can

be higher than 0.3 in both cases). The 1-1-2 scheme yields a

lower bunching efficiency exceeding 0.4 only. It is interesting

to note that in the 1-2-2 scheme the efficiency is maximal

when the second cavity is located closer to the input one,

while in the 2-2-2 scheme it should be located closer to the

output cavity. (This conclusion is the same as one done in

[29] for a three-cavity GKL, in which all cavities operate at

the fundamental resonance.) The optimal values of the first

bunching parameter for 1-2-2 and 2-2-2 schemes are about 2.5

and 1.5, respectively. The ratio of these values is approximately

the same as the ratio of optimal bunching parameters for

two-cavity 1-2 and 2-2 schemes considered above. Therefore,

the results presented above (in particular, Fig. 1) are valid for

the present consideration as well. The optimal values of the

second bunching parameter for different schemes are different

[26]. These values can be realized by adjusting not only the

second drift section length, but also the

cavity. (The latter, however, affects the bandwidth.)

The gain of three-cavity GKLs can be analyzed in the same

manner as in two-cavity devices. Since corresponding expres-

sions for the gain now are more complicated, it makes sense

to restrict our consideration by the case of operation close to

the small-signal one, when the bunching parameter is small,

and hence, the Bessel functions can be represented by poly-

nomials. Corresponding expressions readily show that the op-

timalpositionofthesecondcavity,whichresultinthemaximum

gain, is 2/3 and 1/2 of the total drift length for 1-2-2 and 2-2-2

schemes, respectively. For this choice of the second cavity po-

sition and negligibly small beam loading in the input cavity, the

constant part of the gain in the 1-2-2 scheme is smaller than that

in the 2-2-2 scheme by

that the variable gain in frequency-multiplying GKLs contains

also an additional term, which describes the dependence on the

bunching parameter

[cf. (9)]. At small

the difference in gains for 1-2-2 and 2-2-2 schemes even larger;

however, at large

’s, this term can increase the gain.

The bandwidth of these two schemes can be analyzed using

the expressions for the variable part of the gain, which are quite

similar, but more complicated than (9). Some results, neverthe-

less,canbeobtainedanalyticallyeveninthiscase.Suchananal-

ysis, for instance, was done for a 1-2-2 scheme with two last

cavities having equal

-factors, equal values of the normalized

beam current parameter

cold-cavity frequencies symmetrically situated with respect to

, i.e.,

cific case the maximum bandwidth can be realized when the pa-

, which relates to the

, where

-factor of the second

dB. Recall

’s, this term makes

and stagger-tuned

. It was shown that in this spe-

rameter

the stagger tuning parameter

is equal to 7.9. In the case of such a maximal stagger tuning the

bandwidth expressed in terms of the detuning

isequalto13.4,whileintheabsenceofstagger

tuningitwasequalto1.135,i.e.,itincreasesbyalmost12times.

Thisbandwidthenlargementis,however,accompaniedbyabout

32-dB gain degradation.

Theseresults canbe comparedwith similarresultsfor a2-2-2

scheme, which in terms of normalized parameters is identical

to the 1-1-1 scheme studied in [11]. In this case, the optimal

value of

is 0.25 and the maximum bandwidth corresponds

to the stagger-tuning parameter equal to 6.066. This stagger

tuning increases the normalized bandwidth from 1.2 (when

) to 17.0, i.e., by more than 14 times, at the expense of

the gain degradation by about 36 dB. So, in this sense both

schemes look quite similar. Of course, the gain-bandwidth

product, which is often treated as a figure-of-merit of various

amplifiers, corresponds to smaller stagger-tunings than those

that yield the largest bandwidth. (This issue was discussed

elsewhere [11], [12].)

is equal to 0.0504 and

C. Two-Stage Gyro-TWT

Comparison of two concepts of gyro-TWTs leads to the con-

clusions that are quite similar to those derived for two-cavity

GKLs above. The constant part of the gain in the both fre-

quency-multiplying gyro-TWT and two-stage gyro-TWT oper-

ating at the second harmonic in both stages is the same. The

variablepartofthegain,asfollowsfrom(11),isagaincharacter-

ized by the ratio of the Bessel function of the order

to the input wave amplitude. Therefore, the gain degradation

caused by the variable gain is smaller in the case of operation at

a given harmonic in all stages. Also, at small bunching param-

eters, the operation at a given harmonic

gain; however, the saturation can be realized faster in the case

of frequency-multiplying devices.

In addition to the comparison based on the use of a very

simplified approach described in Section II-B, we have also

carried out some numerical studies with the use of nonlinear

theory. It was considered a two-stage gyro-TWT experimen-

tally studied at the University of Maryland. We assumed that

the beam parameters such as the beam voltage and current, and

the orbital-to-axial velocity ratio are fixed: 60 kV, 5 A, and 1.0,

respectively. We also assumed that the lengths of all sections

and their transverse dimensions are the same as in the experi-

ment. Then, we did simulations for three cases: 1) operation in

both stages at the fundamental cyclotron resonance (operating

modes are

in both stages); 2) 1-2 scheme with the op-

erating modes

and

respectively; and 3) 2-2 scheme where the operating mode is

in both stages.

Some results of the simulations are shown in Figs. 4–6.

Fig. 4 shows the case of operation at the fundamental in both

stages. In Fig. 4(a), where vertical lines separate the regions

of the first waveguide, drift section and output waveguide, the

axial dependencies of the output power are shown for several

values of the cyclotron resonance detuning in the output stage

yields a higher

in the first and second stage,

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NUSINOVICH et al.: COMPARISON OF MULTISTAGE GYROAMPLIFIERS OPERATING IN THE FREQUENCY-MULTIPLICATION REGIME963

Fig. 4.

operating at the fundamental harmonic in both stages for several values of the

cyclotron resonance detuning in the output stage. (b) Dependence of the output

power on the normalized cyclotron resonance detuning for 50- and 100-W input

power levels.

(a) Axial dependence of the output power in a two-stage gyro-TWT

; this detuning in the

input stage was taken equal to zero because this corresponds

to the maximum growth rate of the wave. (The variation in the

detuning can be realized by a weak tapering of the external

magnetic field.) As one can see, in this case the length of the

output section is long enough to reach saturation when the input

power equals 100 W. Resulting dependencies of the output

power on the detuning in the output stage are shown in Fig. 4(b)

for 50- and 100-W input power. For 50-W input power, the

output waveguide is not long enough to reach the maximum

power and efficiency. Therefore, the maximum power shown in

Fig. 4(b) for this case is lower than for 100 W. Results shown

in Fig. 4(b) indicate that this device can operate with the gain

exceeding 30 dB.

Fig. 5 shows some results of simulations for the frequency-

doubling gyro-TWT. Here figures (a) and (b) correspond to 50-

Fig. 5.

gyro-TWT for several values of the cyclotron resonance detuning in the output

stage for (a) 50 W and (b) 100 W levels of the input power.

Axial dependence of the output power in a frequency-doubling

and 100-W input power, respectively. In this case, as follows

fromFig.5(b),toreachmaximumoutputpowereveninthecase

of 100-W input power it is necessary to increase the length of

the output stage by about 60%. This will result in about 40-kW

output power, while in the1-1 scheme themaximum output was

higher than 100 kW for the same 100-W input power, as shown

in Fig. 4(b).

Finally, Fig. 6 shows some results of simulations for the 2-2

scheme. In thiscase, as follows from Fig.6(a), to reach the peak

ofthemaximumoutputpowerinthecaseof100-Winputpower,

itisnecessarytomorethandoublethelengthoftheoutputwave-

guide.Fig.6(b)illustratesthesensitivityoftheoperationofsuch

a device to variation of the external magnetic field. As one can

see, the efficient operation is possible in the range of magnetic

fields about

1% or less of the nominal value. As follows from

Fig. 6(b), the bandwidth corresponding to this nominal value of

the magnetic field,

, is about 1.7%.

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964IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

Fig. 6.

withbothstagesoperatingatthesecondharmonic.(b)Dependenceoftheoutput

power on the operating frequency in this tube for several values of the external

magnetic field (lengths of the input waveguide, the drift section, and the output

waveguide are equal to 15.2, 9.0, and 14.6 cm, respectively).

(a) Axial dependence of the output power in a two-stage gyro-TWT

D. Ultrahigh-Gain Gyro-TWT

Regardless of the chosen operating harmonic, the problem

of obtaining high-frequency drive sources capable of saturating

the gyroamplifier in question can be relaxed somewhat if the

gain is high enough. Recently, single-stage gyro-TWTs with

distributed loss have been investigated as a means of achieving

gains as high as 70 dB while maintaining operation free of

oscillations from reflective and absolute instabilities [31].

Conceivably, systems with such high gain gyroamplifiers could

achieve output powers as high as several hundred kilowatts in

W-band using low-noise solid-state drivers. In view of the ob-

vious advantages of such configurations, not the least of which

is saving the cost of an intermediate vacuum tube amplifier,

there are other issues that require attention. Depending on the

application, signal integrity issues such as linearity, noise, and

phasecharacteristicsmaybeofequalorgreaterimportancethan

Fig. 7.

harmonic gyro-TWT configurations with distributed loss applied to the first

15 cm of the interaction circuit followed by 7 cm of high conductivity wall.

The arrows indicate the location of the beam guiding center radius.

Schematic of MAGY model for (a) fundamental and (b) second

cost reduction. It seemed prudent to consider whether similarly

high gains could be achieved in distributed loss harmonic

gyro-TWTs as well.

A numerical study using the Maryland Gyrotron code

(MAGY) [30] was conducted to compare the performance of

gyro-TWTs with distributed loss operating at the fundamental

and second harmonic of the cyclotron frequency. Fig. 7 shows

a schematic of the two models we considered. The basic

parameters governing synchronism between the fast cyclotron

and EM waves were fixed by comparing a

circuit with radius of 5.5 mm with a

circuit with radius 10.07 mm, both with a length of 22 cm.

Thus, the cutoff frequencies and dispersion characteristics for

the operating modes in both cases are the same, and maximum

gainwas expectedarounda frequencyof35 GHz.Themagnetic

field strength for grazing intersection

as follows:

fundamental

second harmonic

could be determined

(14)

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NUSINOVICH et al.: COMPARISON OF MULTISTAGE GYROAMPLIFIERS OPERATING IN THE FREQUENCY-MULTIPLICATION REGIME965

TABLE I

MAGY PARAMETERS FOR COMPARISON OF DISTRIBUTED LOSS GYRO-TWTS

where

ativistic mass factors and

waveguide. Equation (14) shows that this field depends on the

appliedvoltageandtheelectronorbital toaxial velocityratio.In

our simulations, we usedthe electronbeam voltageand electron

velocity pitch fixed at 80 kV and 1.0, respectively. The beam

current and distributed loss rate were left as free parameters and

optimized for each case for maximum gain. Table I summarizes

the model parameters, and Fig. 8 gives the results.

The results show that, while impressive fundamental gain

is realized, the compression slope has fairly dramatic conse-

quences on output phase. In applications where linearity is

important, the output power should be “backed-off” below

the peak value to minimize AM-PM conversion. We note

that neither model was comprehensively optimized for all

performance figures of merit; rather, the importance was direct

comparison. In the second harmonic case, 45 dBm of drive

power was needed for saturation while in the fundamental

harmonic case the device saturates at less than 20 dBm. This

value (45 dBm) is above the capability of solid-state sources

in the millimeter-wave region. The results should not be

interpreted to mean that a distributed-loss, second harmonic

gyro-TWT could not achieve higher gain and meet this crite-

rion. Higher perpendicular velocity (with bandwidth reduction)

and increased gain length may mitigate this shortcoming and

should be investigated further.

is the ratio of the unperturbed total to axial rel-

is the cutoff frequency of the

IV. DISCUSSION

Let us illustrate our theoretical analysis by one more ex-

ample. Assume (as it was done in [12] for 1-1 and 1-2 schemes

of GKLs) that we have an electron beam, which was used in the

experiments with a W-band gyroklystron at NRL [32]: 65-kV

beam voltage, 6-A beam current, orbital-to-axial velocity ratio

equal to 1.4. Let us consider the performance characteristics

of two-cavity GKLs driven by such a beam for the following

three cases: 1) 1-1 scheme with both cavities operating at the

-mode; 2) 1-2 scheme with the first cavity operating

at the fundamental at the same

cavity operating at the second cyclotron harmonic at the

-mode; and 3) 2-2 scheme with both cavities operating

at the

-mode. In all cases, for the sake of simplicity, we

-mode and the second

Fig. 8.

versus drive power for (a) fundamental, and (b) second harmonic gyro-TWTs

with distributed loss placed in the interaction circuit to achieve high gain and

stable operation.

MAGY simulation results showing the output power, gain, and phase

will neglect the beam loading and frequency pulling effects.

This allows us to simplify the relation given by (1) between

the normalized field amplitude in the first cavity and the

amplitude of the field excited by a driver there. Then, in order

to estimate the relation between the latter amplitude and the

drive power given by (2), assume that the axial profile of the

input cavity is sinusoidal and the cavity length is equal to one

wavelength; also assume that a thin annular beam is positioned

in the peak of the coupling impedance to the operating mode,

the cavity

-factor is equal to 100, and the cavity is critically

coupled, i.e.,

. For this set of parameters, (2)

yields

section length can be found under assumption that for a given

drive power and the case of exact resonance between the

signal frequency and the cold-cavity frequency the bunching

parameterhas an optimal value. For instance, if we want tohave

an optimal bunching parameter,

the normalized length of the drift section should be equal to

that corresponds to

similar fashion, we can also evaluate the normalized parameters

. Then, the optimal drift

, for W,

. In a

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966IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

Fig. 9.

different schemes in the framework of the point-gap model.

Dependence of the output power and gain on the input power for

for two other schemes. In the case of a 1-2 scheme, it was

assumed that the beam position remains the same as for the

1-1 scheme; it was also assumed that, to provide the maximum

bandwidth in the case of the stagger-tuning, in accordance with

[12], we should have the

-factor of the second cavity about

2.9 times higher than that for the first one, i.e., it should be

. This value of the

cavities in the third case (2-2 scheme). Of course, the bunching

parameters were chosen to be optimal for each case.

Resultsshowingthedependenceoftheoutputpowerandgain

on the drive power in all three schemes are shown in Fig. 9.

Since the normalized length of the drift section is rather long,

saturation effects in the schemes without frequency multiplica-

tion appear at input power level of about a few watts. Therefore,

the gain curves for 1-1 and 2-2 schemes shown in Fig. 9(b) that

start from

W have almost linear slops demonstrating

the saturation. Of course, the 1-1 scheme has a superior per-

formance; it also offers a larger bandwidth, since in this case

the

-factors are lower. So, the main obstacles for the use of

-factor was also used for both

this simple scheme could be either the necessity to create strong

magnetic fields with the use of large solenoids increasing the

mass and volume of a microwave system, or the tendency to

operate at high power levels, for which it is difficult, if not im-

possible, to realize optimal operating conditions in the case of

low-order modes operating at the fundamental resonance. Com-

parison of two latter schemes shows that the 2-2 scheme offers

higher gain and output power than the 1-2 scheme. To the great

extent, this is the result of describing the saturation effects by

the Bessel functions corresponding to the account of the bal-

listic bunching in the drift sections of the point-gap model only.

To consider a more realistic case, we replaced in the formula

for the orbital efficiency given by (6) these functions by the

corresponding polynomials of the bunching parameter

(15)

and determined the coefficients

the conditions that approximations given by (15) yield for the

optimal values of bunching parameters (

) the orbital efficiencies equal to their maximum

valuesfound in [25] (

spondingresultsareshowninFig.10,wherethegainandoutput

powerare shownas functionof theratioof thedrivepowertoits

optimum value (100 W). Now the performance characteristics

of the 1-2 and 2-2 schemes are closer, but still the 2-2 scheme

exhibits a higher gain; for instance, for the optimal drive power

the difference in the gain is a little smaller than 5 dB in favor

of the 2-2 scheme. Recall that our analysis done in Section III

showed that the tradeoff between the gain and the bandwidth

due to the stagger tuning in both schemes yields approximately

the same results.

So far, we focused our consideration on the analysis of sev-

eralimportantcharacteristics(efficiency,power,gain,andband-

width) only. For many applications, various signal distortion ef-

fects are also important. Some of them can be caused by the

effect of the input signal amplitude modulation on the ampli-

tude and phase of the output radiation. Although the effect of

the input signal modulation on the output phase (a so-called

AM/PM conversion, see, e.g., [33]) cannot be studied in the

framework of the point-gap model [11], one can easily use this

model for estimating the effect of the input signal modulation

on the amplitude of the output radiation (AM/AM conversion).

In accordance with [33] and the formalism developed above,

this conversion for a point-gap model can be characterized by

the function

As follows from this simple formula, at small values of the

bunching parameter (small-signal regime) the 2-2 scheme oper-

ates with 1 dB/dB conversion as any linear amplifier, while the

1-2 scheme yields 2 dB/dB conversion, which is caused by the

frequencydoublingoperationandcanbebeneficialinsomespe-

cific cases of AM signals. Of course, the maximum efficiency

operation corresponds to

Anotherimportantparameterofanyamplifieristhesignal-to-

noise ratio. As known, the noise of any amplifier is predom-

inantly determined by the noise generated in the input stage

and for each scheme from

and

and). Corre-

, where.

in any scheme.

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NUSINOVICH et al.: COMPARISON OF MULTISTAGE GYROAMPLIFIERS OPERATING IN THE FREQUENCY-MULTIPLICATION REGIME967

Fig. 10.

different schemes in the case of corrected polynomial approximation for the

orbital efficiency.

Dependence of the output power and gain on the input power for

by a driver and by an electron beam. (This noise in the fun-

damental harmonic GKLs was studied theoretically and exper-

imentally in [34] and [35], respectively.) Then, this noise, to-

gether with a signal, is amplified in other stages of the device.

In the case of operation at a given harmonic, this process has a

linear nature, but it is a nonlinear process in frequency-multi-

plying devices. This nonlinearity weakens the role of noise with

respect to the signal. Therefore, the signal-to-noise ratio in fre-

quency-multiplying devices can be higher than in the devices

operating without multiplication. This issue was recently ana-

lyzed in [36] in detail.

Beforeclosingthissection,letusnotethattheformalismused

and the results obtained are applicable for large-orbit gyrode-

vices (LOGs) [37]. As was pointed out in [38], the theory of

these devices can be based on the formalism developed for con-

ventional, small-orbit gyrodevices. The peculiarity of LOGs is

the necessity to consider the coupling impedance present in the

definition of the normalized beam current parameter given by

(3)forelectronshavingzeroguidingcenterradius,

immediately yields the rule of mode selection in LOGs [39],

, which is the only case of nonzero coupling impedance

for electrons with

. Note that, in order to enhance radia-

tion at high cyclotron harmonics, instead of smooth-wall cylin-

drical cavities/waveguides, various magnetron-type microwave

circuits are often used in LOGs [40], [41]. In such cases, not

only the numerator, but also denominator in (3) should be prop-

erly modified.

.This

V. SUMMARY

A simple theory is developed that allows one to make

a comparative analysis of various schemes of multistage

gyroamplifiers. The results of the analysis done for the fre-

quency-multiplying devices and devices, which operate at a

givenharmonicinallstages,showthatsomeoftheperformance

characteristics considered are better for the devices operating

at a given harmonic (gain and efficiency), while others (such

as the bandwidth) can be better in frequency-multiplying

gyroklystrons where the operation of the input stage at the

fundamental resonance allows one to use the low-

Without going into details of the analysis performed, it can be

stated that the preference of one of two schemes considered

stronger depends on the practical issues (such as a specific

application, availability of drivers at different frequencies,

ability to provide a stable operation at higher order mode in the

input stage, etc.) than on the details of the saturation effects

and possibilities to increase the bandwidth and gain-bandwidth

product by using the stagger tuning (the latter is essentially

the same in both schemes). Thus, it makes sense to continue

analysis of both schemes.

cavities.

REFERENCES

[1] H. R. Jory, “U. S. Army Electronics Command Research and Develop-

ment,” Tech. Rep. ECOM-01873-F, 1968.

[2] D. S. Furuno, D. B. McDermott, N. C. Luhmann, Jr., and P. Vitello, “A

high-harmonic gyro-klystron amplifier: Theory and experiment,” Int. J.

Electron., vol. 57, pp. 1151–1166, 1984.

[3] A. V. Gaponov-Grekhov and V. L. Granatstein, Eds., Applications of

High-Power Microwaves. Boston, MA: Artech House, 1994.

[4] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 4th

Revised English ed.Oxford, U.K.: Pergamon, 1975.

[5] R. H. Abrams, B. Levush, A. A. Mondelli, and R. K. Parker, “Vacuum

electronics for the 21st century,” IEEE Microwave Mag., vol. 2, pp.

61–72, Sept. 2001.

[6] J. Harvey, E. R. Brown, D. B. Rutledge, and R. A. York, “Spatial power

combining for high-power transmitters,” IEEE Microwave Mag., vol. 1,

pp. 48–59, 2000.

[7] M. P. DeLisio and R. A. York, “Quasioptical and spatial power com-

bining,” IEEE Trans. Microwave Theory Tech. (Special 50th Anniver-

sary Issue), 2001.

[8] J. J. Sowers et al., “A 36 W, V-band, solid-state source,” in Proc.

IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, 1999, pp.

559–562.

[9] B.G.JamesandM.Kreutzer,“HighpowermillitronTWT’sinW-band,”

in Proc. 20th Int. Conf. Infrared and Millimeter Waves, R. J. Temkin,

Ed., Orlando, Fl., Dec. 11–14, 1995, Paper M1.7, pp. 13–14.

[10] A.V.Gaponov, M.I.Petelin,andV.K.Yulpatov,“Theinducedradiation

ofexcitedclassicaloscillatorsanditsuseinhigh-frequencyelectronics,”

Radiophys. Quantum Electron., vol. 10, pp. 794–813, 1967.

[11] G. S. Nusinovich, B. G. Danly, and B. Levush, “Gain and bandwidth

in stagger-tuned gyroklystrons,” Phys. Plasmas, vol. 4, pp. 469–478,

1997.

Page 12

968 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

[12] G. S. Nusinovich, B. Levush, and B. G. Danly, “Gain and bandwidth in

stagger-tuned gyroklystrons and gyrotwystrons,” IEEE Trans. Plasma

Sci., vol. 27, pp. 422–428, Apr. 1999.

[13] G. S. Nusinovich and H. Li, “Theory of gyro-traveling-wave tubes at

cyclotron harmonics,” Int. J. Electron., vol. 72, pp. 895–907, 1992.

[14] V. K. Yulpatov, private communication, 1968.

[15] M. Caplan, “Gain characteristics of stagger-tuned multi-cavity gyro-

klystron amplifier,” presented at the 8th Int. Conf. Infrared and Mil-

limeter Waves, Miami Beach, FL, 1983, Paper W4.2.

[16] G.S.Nusinovich,Introductiontothe Physicsof Gyrotrons.

MD: The Johns Hopkins Univ. Press, 2004.

[17] M. A. Moiseev and G. S. Nusinovich, “Concerning the theory of multi-

mode oscillations in a gyromonotron,” Radiophys. Quantum Electron.,

vol. 17, pp. 1305–1311, 1974.

[18] D. Dialetis and K. R. Chu, “Mode competition and stability analysis of

the gyrotron oscillator,” in Infrared and Millimeter Waves, K. J. Button,

Ed. New York: Academic, 1983, pt. II, vol. 7, ch. 10.

[19] M. A. Moiseev, “Maximum amplification band of a CRM twystron,”

Radiophys. Quantum Electron., vol. 20, pp. 846–849, 1977.

[20] A. K. Ganguly and S. Ahn, “Large-signal theory of a two-stage

wide-band gyro-TWT,” IEEE Trans. Electron Devices, vol. ED-31, pp.

474–482, 1984.

[21] G. S. Nusinovich, W. Chen, and V. L. Granatstein, “Analytical theory of

frequency-multiplying gyro-traveling-wave-tubes,” Phys. Plasmas, vol.

8, pp. 631–637, 2001.

[22] G. S. Nusinovichand M. Walter, “Theory of the inverted gyrotwystron,”

Phys. Plasmas, vol. 4, pp. 3394–3402, 1997.

[23] Q. S. Wang, D. B. McDermott, and N. C. Luhmann Jr., “Demonstration

of marginal stability theory by a 200 kW second-harmonic gyro-TWT

amplifier,” Phys. Rev. Lett., vol. 75, pp. 4322–4325, 1995.

[24] D. J. Bates and E. L. Ginzton, “A traveling-wave frequency multiplier,”

Proc. IRE, vol. 45, pp. 938–944, 1957.

[25] V. I. Belousov, V. S. Ergakov, and M. A. Moiseev, “Two-cavity CRM at

harmonics of the electron cyclotron frequency,” Elektronn. Tekhn., ser.

1, no. 9, pp. 41–50, 1978.

[26] G. S. Nusinovich, G. P. Saraph, and V. L. Granatstein, “Scaling law for

ballistic bunching in multicavity harmonic gyroklystrons,” Phys. Rev.

Lett., vol. 78, pp. 1815–1818, 1997.

[27] G. S. Nusinovich and O. Dumbrajs, “Two-harmonic prebunching

of electrons in multicavity gyrodevices,” Phys. Plasmas, vol. 2, pp.

568–577, 1995.

[28] G. S. Nusinovich, B. Levush, and O. Dumbrajs, “Optimization of mul-

tistage harmonic gyrodevices,” Phys. Plasmas, vol. 3, pp. 3133–3144,

1996.

[29] E. V. Zasypkin, M. A. Moiseev, E. V. Sokolov, and V. K. Yulpatov,

“Effect of penultimate cavity position and tuning on three-cavity

gyroklystron amplifier performance,” Int. J. Electron., vol. 78, pp.

423–433, 1995.

[30] S.Y.Cai,T.M.AntonsenJr.,G.Saraph,andB.Levush,“Multifrequency

theory of high power gyrotron oscillators,” Int. J. Electron., vol. 72, pp.

159–777, 1992.

[31] K. R. Chu, H. Y. Chen, C. L. Hung, T. H. Chang, L. R. Barnett, S. H.

Chen,T.T.Yang,andD.J.Dialetis,“Theoryandexperimentofultrahigh

gain gyrotron traveling wave amplifier,” IEEE Trans. Plasma Sci., vol.

27, pp. 391–404, Apr. 1999.

[32] M. Blank, B. G. Danly, B. Levush, and D. E. Pershing, “Experimental

investigation of W-band (93 GHz) gyroklystron amplifier,” IEEE Trans.

Plasma Sci., vol. 26, pp. 409–415, June 1998.

[33] A. S. Gilmour, Jr., Principles of Traveling Wave Tubes.

Artech House, 1994, ch. 16.

[34] T. M. Antonsen, Jr. and W. M. Manheimer, “Shot noise in gy-

roklystrons,” IEEE Trans. Plasma Sci., vol. 26, pp. 444–450, June

1998.

[35] J. P. Calame, B. G. Danly, and M. Garven, “Measurements of intrinsic

shot noise in a 35 GHz gyroklystron,” Phys. Plasmas, vol. 6, pp.

2914–2925, 1999.

[36] J. C. Rodgers, T. M. Antonsen Jr., and V. L. Granatstein, “Harmonic

gain and noise in a frequency-doubling gyro-amplifier,” IEEE Trans.

Electron Devices, vol. 50, pp. 1785–1792, Aug. 2003.

[37] K. R. Chu, D. S. Furuno, N. C. Luhmann, Jr., D. B. McDermott,

P. Vitello, and K. Ko, “Theory, design, and operation of large-orbit

high-harmonic gyroklystron amplifiers,” IEEE Trans. Plasma Sci., vol.

PS-13, pp. 435–443, 1985.

Baltimore,

Boston, MA:

[38] G. S. Nusinovich, “Non-linear theory of a large-orbit gyrotron,” Int. J.

Electron., vol. 72, pp. 959–967, 1992.

[39] P. Vitello and K. Ko, “Mode competition in the gyro-peniotron oscil-

lator,” IEEE Trans. Plasma Sci., vol. PS-13, pp. 454–463, 1985.

[40] Y. Y. Lau and L. R. Barnett, “Theory of a low magnetic field gyrotron

(gyromagnetron),” Int. J. Infrared Millim. Waves, vol. 3, pp. 619–644,

1982.

[41] W. W. Destler, E. Chojnacki, R. F. Hoeberling, W. Lawson, A. Singh,

and C. D. Striffler, “High-power microwave generation from large-orbit

devices,” IEEE Trans. Plasma Sci., vol. 16, pp. 71–95, Apr. 1988.

Gregory S. Nusinovich (SM’92–F’00) received the

B.Sc., M.Sc., and Ph.D. degrees from Gorky State

University,Gorky,U.S.S.R.,in1967,1968,and1975,

respectively.

In 1968, he joined the Gorky Radiophysical

Research Institute, Gorky. From 1977 to 1990,

he was a Senior Research Scientist and Head of

the Research Group at the Institute of Applied

Physics, the Academy of Sciences of the U.S.S.R.,

Gorky. From 1968 to 1990, his scientific interests

included developing high-power millimeter- and

submillimeter-wave gyrotrons. He was a Member of the Scientific Council on

Physical Electronics of the Academy of Sciences of the U.S.S.R. In 1991, he

immigrated to the U.S. and joined the Research Staff at the Institute for Plasma

Research (presently, the Institute for Research in Electronics and Applied

Physics), University of Maryland, College Park. Since 1991, he has also served

as a Consultant to the Science Applications International Corporation, McLean,

VA, the Physical Sciences Corporation, Alexandria, VA, and Omega-P, Inc.,

New Haven, CT. He is the author of Introduction to the Physics of Gyrotrons

(Baltimore, MD: The Johns Hopkins University Press, 2004). He has authored

and coauthored more than 150 papers published in refereed journals. His

current research interests include the study of high-power electromagnetic

radiation from various types of microwave sources.

Dr. Nusinovich is a Member of the Executive Committee of the Plasma Sci-

ence and Application Committee of the IEEE Nuclear and Plasma Sciences

Society. He is a Fellow of the American Physical Society (APS). In 1996 and

1999, he was a Guest Editor of the Special Issues of the IEEE TRANSACTIONS

ON PLASMA SCIENCE on High-Power Microwave Generation and on Cyclotron

Resonance Masers and Gyrotrons, respectively. Presently, he is an Associate

Editor of the IEEE TRANSACTIONS ON PLASMA SCIENCE.

Oleksandr V. Sinitsyn was born in Kharkiv,

Ukraine, in 1978. He received the B.S. degree in

radio physics from V. Karazin Kharkiv National

University, Kharkiv, Ukraine, in 2000 and the M.S.

degree in electrical engineering from the University

of Maryland, College Park, in 2002. He is currently

working toward the Ph.D. degree in electrical and

computer engineering at the University of Maryland.

His research interests include theory and design of

high-power microwave sources.

J. Rodgers, photograph and biography not available at the time of publication.

Page 13

NUSINOVICH et al.: COMPARISON OF MULTISTAGE GYROAMPLIFIERS OPERATING IN THE FREQUENCY-MULTIPLICATION REGIME969

Thomas M. Antonsen, Jr. (M’82–SM’96) was born

in Hackensack, NJ, in 1950. He received the B.S. de-

gree in electrical engineering in 1973, and his M.S.

and Ph.D. degrees in 1976 and 1977, all from Cor-

nell University, Ithaca, NY.

He was a National Research Council Post Doc-

toral Fellow at the Naval Research Laboratory, from

1976 to 1977, and a Research Scientist in the Re-

search Laboratory of Electronics at MIT, Cambridge,

from 1977 to 1980. In 1980, he moved to the Univer-

sity of Maryland, College Park, where he joined the

faculty of the Departments of Electrical Engineering and Physics in 1984. He

is currently a Professor of physics and electrical and computer engineering. He

has held visiting appointments at the Institute for Theoretical Physics (UCSB),

theEcolePolytechniqueFederaledeLausanne,Switzerland,andtheInstitutede

Physique Theorique, Ecole Polytechnique, Palaiseau, France. He served as the

Acting Director of the Institute for Plasma Research, University of Maryland

from 1998 to 2000. His research interests include the theory of magnetically

confined plasmas, the theory and design of high-power sources of coherent ra-

diation,nonlineardynamicsinfluids,andthetheoryoftheinteractionofintense

laser pulses and plasmas. He is the author and coauthor of over 200 journal ar-

ticles and co-author of the book Principles of Free-Electron Lasers.

Dr. Antonsen has served on the editorial board of Physical Review Letters,

The Physics of Fluids, and Comments on Plasma Physics. He was selected as

a Fellow of the Division of Plasma Physics of the American Physical Society

in 1986. In 1999, he was a co-recipient of the Robert L. Woods award for Ex-

cellence in Vacuum Electronics Technology, and in 2003 he received the IEEE

Plasma Science and Applications Award.

Victor L. Granatstein (S’59–M’64–SM’86–F’02–

LF’02) received the Ph.D. degree in electrical

engineering from Columbia University, New York,

in 1963.

After a year of postdoctoral work at Columbia, he

wasa ResearchScientist at BellTelephoneLaborato-

ries from 1964 to 1972, where he studied microwave

scattering from turbulent plasma. In 1972, he joined

the Naval Research Laboratory (NRL), Washington,

DC, as a Research Physicist, and from 1978 to 1983,

heservedasHead ofNRL’sHighPower Electromag-

netic Radiation Branch. In August 1983, he became a Professor in the Electrical

Engineering Department, University of Maryland, College Park. From 1988 to

1998, he was Director of the Institute for Plasma Research at the University of

Maryland. He spent semesters in both 1994 and 2003 as a Visiting Professor

at the University of Tel Aviv, Tel Aviv, Israel. He is currently leading studies

of high pulsed power gyroklystron amplifiers for driving high-gradient electron

accelerators, efficiency enhancement in high average power gyrotron oscilla-

tors for heating and stabilizing magnetic fusion plasmas, advanced concepts in

high-power, wideband millimeter-wave amplifiers for radar applications, and

the effect of high-power microwave pulses on electronic components and sys-

tems. He has co-authored more than 220 research papers in scientific journals

and has co-edited three books. He holds a number of patents on active and pas-

sive microwave devices.

Dr.GranatsteinisaFellowoftheAmericanPhysical Society.Hehas received

a number of major research awards including the E.O. Hulbert Annual Science

Awardin1979,theSuperiorCivilianServiceAwardin1980,theCaptainRobert

Dexter Conrad Award for Scientific Achievement (awarded by the Secretary of

the Navy in 1981), the IEEE Plasma Science and Applications Award in 1991,

and the Robert L. Woods Award for Excellence in Electronics Technology in

1998.

N. C. Luhmann, Jr., photograph and biography not available at the time of

publication.

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