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High Power Microwave Tubes: Basics and TrendsVolume 1

Vishal Kesari and B N Basu

Chapter 1

Introduction

The simplest electron tube is a vacuum diode, also known as a Flemming valve,which was invented by John Ambrose Flemming in 1904. In 1906 Lee DeForestinvented the vacuum triode valve. In fact, the first two decades of the 19th century(1901–1920), besides the invention of the diode and the triode, saw the manufactur-ing of electron tubes by the Radio Corporation of America (RCA). In the secondtwo decades of the same century (1921–1940), the invention of vacuum microwavetubes (MWTs), namely, the klystron, the travelling-wave tube (TWT) and themagnetron took place (table 1.1). Following the invention of an early form ofmagnetron by H Gerdien in 1910 and a split-anode magnetron by Albert Hull in1920 and the subsequent experimentation on such magnetrons in the 1920s and1930s, which had, however, operated at lower frequencies, the first magnetron ofmultiple-cavity type was developed independently by K Posthumas and H EHollmann in 1935 and improved by John Randall and Harry Boot in 1940 in thecentimeter-wave frequencies for radar. The invention and development of theklystron by George F Metcalf and William C Hahn in 1936 and by RusselVarian and Siguard Varian in 1937 was a significant event in the historical timeline.The TWT was independently invented by A V Haeff in 1933, N E Lindenblad in1940 and Rudolf Kompfner in 1942 (table 1.1).

In the third two decades of the 19th century (1941–1960), study in the area ofTWTs intensified and the basic concept of electron cyclotron maser interaction,relevant to understanding the principle of the gyrotron, was developed (table 1.1).We had to wait until the fourth two decades of the 19th century (1961–1980) to seethe development of the earliest versions of the gyrotron. The Joint EuropeanTokamak (JET) and International Thermonuclear Experimental Reactor (ITER)programmes considered the gyrotron as the RF source for fusion plasma in the ninthdecade of the same century (1981–1990), while during the period beyond 1990various manufacturing companies, namely the Institute of Applied Physics (IAP) inRussia; Gycom in Russia; Forschungszentrum Karlsruhe (FZK) in Germany; Japan

doi:10.1088/978-1-6817-4561-9ch1 1-1 ª Morgan & Claypool Publishers 2018

Atomic Energy Research Institute. (JAERI) and Toshiba in Japan;Communications & Power Industries (CPI) in the USA; and Thomson TubesElectroniques (TTE) in France, developed the technology of developing gyrotrons(table 1.1).

The vacuum diode consists of two metallic electrodes: namely the cathode, whichemits electrons, and the anode, also known as plate, raised to a higher electricpotential than the cathode, which attracts electrons emitted from the cathode to

Table 1.1. Historical timeline.

1901–1920Fleming valve (vacuum tube diode) John Ambrose Fleming 1904First rudimentary radar C Hülsmeyer 1904Audion or triode valve Lee DeForest 1906Physics of electric oscillation and

radio telegraphyG Marconi and K F Braun (Nobel prize) 1909

Magnetron in early form H Gerdien 1910Commercial electron tube Radio Corporation of America (RCA) 1920

1921–1940Smooth-wall, split-anode magnetrons A W Hull 1921Tube scanning system for television Philo T Farnsworth 1922Iconoscope or cathode-ray tube and

kinescopeVladimir K Zworykin 1923

Tetrode valve Albert Hull and N H Williams at GeneralElectric and Bernard Tellegen at Phillips

1926

Beam diffraction oscillogram (beamand helix-wave interaction)

A V Haeff 1933

Travelling-wave tube A V Haeff 1933Multi-cavity magnetron K Posthumas, H E Hollmann 1935Linear beam MWT theory Oskar Heil 1935Klystron George F Metcalf and William C Hahn 1936Klystron Russel Varian and Siguard Varian 1937Improved cavity magnetron for radar J T Randall and H A H Boot 1939Travelling-wave tube N E Lindenblad (US patent 2,300,052 filed on

May 4, 1940 issued on October 27, 1942)1940

1941–1960Travelling-wave tube Rudolf Kompfner 1942Travelling-wave tube Lester M Field (US Patent 2,575,383) 1946Travelling-wave tube J R Pierce (US Patent 2,602,148) 1946Generation of microwaves by

rotational energy of helical electronbeam

H Kleinwachter 1950

Maser James P Gordon 1954Electron cyclotron maser interaction

theoryJ Schneider 1957R Twiss 1958A Gaponov 1959

High Power Microwave Tubes: Basics and Trends

1-2

form an electron beam—a flow of electrons—from the cathode to the anode. In 1906Lee DeForest added another electrode in the tube called the grid consisting of ascreen of wires through which the electrons can pass, and thus he invented thevacuum triode (figure 1.1). The word ‘triode’ is derived from the Greek τρίοδος,tríodos, from tri- (three) and hodós (road, way), originally meaning the place wherethree roads meet. The electric potential of the grid of the triode controls the flow ofelectrons in the tube. In fact, a new era of telephony, sound recording andreproduction, radio, television and computer in the beginning of the 20th centurybegan after the advent of vacuum electron tubes.

A directly or indirectly heated cathode, called the thermionic cathode, serves thepurpose of an electron emitter in an electron tube (chapter 4). The potential on thegrid of a triode can be changed to control the beam current that can be experiencedin an external circuit connected to the tube. More and more electrodes can be addedto an electron tube for additional functions. Thus, the fourth and the fifth grids canbe added to make the so-called vacuum tetrode and vacuum pentode, respectively, inorder to realize additional control of the flow of electrons [1–5] The present bookdeals with a particular type of vacuum electron tube, namely the MWT, in which theelectrons in flow are bunched and the electron bunch is made to transfer its kinetic or

Figure 1.1. Vacuum triode.

1961–1980Gyrotrons (earliest version) in Russia 1965 1965

1981–1990Gyrotron in JET and ITER

1990 onwardsModern gyrotron technology

IAP, Russia; Gycom, Russia; FZK, Germany; JAERI, Japan; Toshiba, Japan; CPI, USA; TTE,France; Centre de Recherches en Physique des Plasmas (CRPP), France, Multidisciplinary

University Research Initiative (MURI), USA, and so on.

High Power Microwave Tubes: Basics and Trends

1-3

potential energy to electromagnetic waves supported by an interaction structureprovided in the device [5, 6].

There are also other types of electron tubes such as the photo tube, in which thephotoelectric effect is used for electron emission, and the gas-filled tube such as thethyratron, which contains a gas at a relatively low pressure that makes the devicecapable of handling much higher currents than the conventional vacuum tubes,thereby making it suitable as a high power electrical switch or a controlled rectifier.In a vacuum tube the accumulation of electrons or space charge in the path ofelectron beam flow exerts a repelling force on such flow of electrons thereby limitingthe value of the current. High-current limitation of electron tubes due to theaccumulation of such space charge can be alleviated by assisting MWTs, such asTWT, gyrotron, etc, by plasma. In some tubes, such as the virtual cathode oscillator(VIRCATOR), the space charge is used as an advantage to form the so-called‘virtual cathode’. In the VIRCATOR, the electrons execute oscillatory motionacross a wall of a resonant cavity between the actual cathode situated outside thecavity and the virtual cathode inside the cavity to generate microwaves [7–9].

In this book we intend to outline the basics of, and trends in, MWTs, addressingthe various issues related to their high power, high efficiency, wideband and highfrequency performances. The phrase ‘high power’ in the title of the book has to bejudged vis-à-vis the application of the tube. What is usually ‘low power’, obtainableby a tube developed by vacuum microelectronics technology, can be considered as‘high power’ in the terahertz frequency regime of application. Similarly, what isusually ‘high power’, for example in a radar system, becomes ‘low power’ fordirected energy weapons (DEWs) [7–9].

Order of vacuumThe vacuum is needed in a MWT to prevent the electrons emitted from the cathode(electron emitter) from colliding with the atoms thereby losing their energy beforecrossing or passing through the anode of the tube. Besides, the vacuum preventsionization inside the tube caused by electrons colliding with atoms that producespositive ions, which can strike the cathode and damage it. A high order of vacuumprevents high power tubes from high voltage breakdown and arcing. The vacuum inMWTs depending on their applications (chapter 2) is created in the range of highvacuum (10−5–10−7 Torr) to ultra high vacuum (<10−7 Torr) (where 1 Torr = 1.33322 millibar = 1 mm Hg = 133 Pascal).

High-frequency limitations of electron tubesThe factors responsible for setting a high-frequency limit of electron tubes aremainly (i) power loss due to skin effect (ii) I 2R loss caused by the capacitor chargingcurrents, (iii) radiation losses, (iii) issues related to the thermal management of tinytubes, (iv) interelectrode capacitance and lead inductance effects, (v) finite transittime of electron flight between electrodes and (vi) constancy of gain-bandwidthproduct [2–5].

Highly conducting materials should be used to make the tube parts to reducepower loss caused by the skin effect. I 2R loss caused by the capacitor charging

High Power Microwave Tubes: Basics and Trends

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currents and associated losses can be reduced by reducing the interelectrodecapacitances and by increasing the number of shunt paths along which the chargingcurrent flows. At high frequencies when the dimensions of the tube becomecomparable with wavelengths, electromagnetic waves may radiate out from thetube (interaction structure). In order to reduce such radiation losses the spacingbetween the electrodes needs to be reduced to the order of 1/100 of wavelengths,although at the cost of RF resistance of the conductors. Shielding the tube using ahighly conducting shield is very effective in reducing radiation losses. At highfrequencies, when the tube uses tiny parts, thermal management should beperformed to cool the parts [4].

At high frequencies, the interelectrode capacitances and lead inductances of thetube become comparable with the capacitance and inductance, respectively, of thecircuit connected to the tube, a resonant circuit for example, the dimensions of whichare reduced at high frequencies [1, 2]. Thus, at such high frequencies, the reactanceof the grid and cathode lead each increase and the reactance of the interelectrodecapacitance between the grid and the cathode and that between the grid and theplate (anode) each decrease. Also, there can be a resonance between the leadinductance and the interelectrode capacitance of the tube at such frequencies. Thesehigh-frequency effects have been studied by the equivalent-circuit representation ofan electron tube. For instance, a triode can be replaced by a constant source ofcurrent g em g between the anode (plate) and the cathode, in parallel with the plateresistance rp. Here, gm is the transconductance of the tube and eg the incrementalgrid-cathode voltage Egk. We can find the input resistance Rg of the triode byanalyzing the equivalent circuit of the triode connected to a load impedance Zl. Forthis purpose, we can consider the effect of only the cathode lead inductance Lk andignore the effect of the grid lead inductance. We can also make the approximationthat the potential across the cathode lead inductance is much less than Egk and

ω>> +r Z j Lp l k. The grid-cathode capacitanceCgk can also be taken much larger thanthe grid-plate capacitance. Thus, such equivalent circuit analysis leads to thefollowing expression for the input resistance Rg of the triode:

ω≅R

g L C1

. (1.1)gm k gk

2

We can then appreciate from (1.1) that when the effect of the cathode leadinductance is much more significant than that of the grid lead inductance, the inputresistance Rg of the triode is inversely proportional to the square of the operatingfrequency. Therefore, at high frequencies, energy is drawn from the signal sourcebecause of the coupling between the grid and cathode circuits caused by the cathodelead inductance [4].

Similarly, we can easily obtain the following approximate expression for the inputadmittanceYg if we set =L 0k and consider only the effect of ≠L 0g [4]:

ωω

≅−

= ≠Yj C

L CL L

1( 0, 0). (1.2)g

gk

g gkk g2

High Power Microwave Tubes: Basics and Trends

1-5

Interestingly, it follows from (1.2) that at the frequency ω = L C1/( )g gk1/2, → ∞Yg ,

which corresponds to the occurrence of the resonance of the input circuit caused bythe grid lead inductance Lg coupled to the grid-to-cathode capacitanceCgk. In otherwords, at this frequency of resonance, the signal input to the triode is short-circuitedthereby making the input fail to cause any effect in the plate circuit [3]. The physicaldimensions of the tube should be therefore reduced to minimize the effect of theelectrode lead inductances and interelectrode capacitances. The reduction of thesetube inductances and capacitances will also increase the maximum resonancefrequency of a resonator circuit connected to the tube.

Furthermore, at high frequencies, the transit time of the electrons between thecathode and grid becomes comparable with the time period of the modulatingelectric field in the cathode-grid space. As a result, the field may reverse its phasebefore electrons traverse this space, thereby causing the electrons to oscillatebetween the cathode and the grid or return to the cathode. The phenomenon canbe easily understood considering the flight of an electron carrying a negative chargeaccelerated between a large, planar electrode to another similar electrode at a higherpotential and studying the induced charges on these two electrodes while the electronis in transit between these electrodes. During the flight of the electron, the positivecharge induced on the approaching electrode increases with time and that on thereceding electrode decreases at the same time such that the sum of the two inducedcharges at any instant of time is equal to the magnitude of the electron charge. Wecan find the induced charge on the approaching electrode at any instant of time byequating the work done in transferring the induced charge to the approachingelectrode, raised to a given potential with respect to the receding electrode, to thework done by the electron to move through a distance from the receding electrode atthat instant of time. The induced charge so found becomes directly proportional tothe distance of the electron from the receding electrode at that instant and,consequently, the induced current obtained by differentiating the induced chargewith respect to time becomes proportional to the electron velocity at that instant.However, this electron velocity varies linearly with time since the electron has aconstant acceleration, subject to the constant electric field between the electrodes. Asa result, the induced current, which is proportional to the electron velocity, alsovaries linearly with time. Corresponding to this induced current, there will be acurrent flowing in the external circuit connected to the triode while the electron is inflight between the electrodes, contrary to the notion that some might have that thecurrent would flow when the electron strikes the positive electrode and completes thepath through the external circuit. The current ceasing to flow as the electron strikesthe positive electrode is essentially a triangular pulse. For an electron beam, the totalinduced current is the addition of such triangular pulses of current associated withthe motion of all the electrons in flight between the electrodes.

Interestingly, current may even be induced in an electrode to which no flows ofelectrons are collected (for instance, the grid of a triode), if the number or velocity ofelectrons approaching the grid is greater than the number or velocity of electronsreceding from it or vice versa depending on the grid bias voltage. From the conceptof the induced current due to a finite transit time of electrons between the electrodes

High Power Microwave Tubes: Basics and Trends

1-6

developed here, it can be appreciated by simple analytical reasoning that the gridconductance Gg is jointly proportional to the square of signal frequency f and thetransit time τ of electrons in the tube [2–5]:

τ=G Cg f . (1.3)g m2 2

A finite value Gg, due to the transit-time effect given by (1.3), is responsible for thepower loss to the grid. The grid power loss can be reduced by increasing the platevoltage to reduce the value of τ, however, at the cost of the plate dissipation and/orby decreasing the interelectrode spacing, which, however, causes an undesirableincrease of the interelectrode capacitance. This calls for the simultaneous decrease ofthe interelectrode spacing and electrode areas to avoid an increase of capacitancewith allowable plate dissipation.

The gain-bandwidth product limitation of an electron tube can be appreciated bystudying the output of an electron tube in the form of a tuned resonator circuitcomprising a tuning inductance L for the stray capacitance C of the tube. With theincrease of the operating frequency, in the limit, the terminating leads form a shortloop or a quarter-wave line terminated within the tube by the interelectrodecapacitances [2–5]. The circuit analysis of such a tuned amplifier replacing theelectron tube by a constant current source, supplying a current g em g, in parallel withthe plate resistance rp, yields the following expression for the gain-bandwidthproduct in terms of the transconductance gm of the tube and the stray capacitanceC :

=g

Cgain-bandwidth product . (1.4)m

It follows from (1.4) that the gain-bandwidth product of an electron tube amplifier isa constant, being independent of the operating frequency and depending only on gmandC of the tube, suggesting that the gain of the amplifier can be increased only atthe cost of its gain [4].

Tiny electron tubes to alleviate high-frequency limitationThe lead inductance and interelectrode capacitance effects, as well as the transit-timeeffect, which limit the high-frequency performance of electron tubes, have beenalleviated in tubes such as the acorn, doorknob and lighthouse tubes [2, 10]. Thephysical dimensions of these tubes are reduced in the same proportion as the high-frequency limiting effects are reduced without reducing the amplification capabilityof the tube. Although the operating frequencies of these tubes can be increased toUHF, the reduction of their size entails the reduction of their power handlingcapability as well. (The acorn tube is so named due to its glass cap resembling thecap of an acorn and the doorknob tube is an enlarged version of the acorn tube thatenables the former to deliver higher power than the latter.) The limiting factor of thistube is the power dissipating ability of the grid in the proximity of the cathode [2].The grid and plate of some of the acorn and doorknob tubes are each provided withtwo leads so that, if required, a section of parallel-wire line may be connectedbetween each pair of grid and plate leads. Such an arrangement makes it possible to

High Power Microwave Tubes: Basics and Trends

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make the lead impedance high, for instance, if a quarter-wave is connected to thelead and is short-circuited at its load end [2]. The lighthouse tube has a planarconstruction—made of the cathode, grid and plate discs—to reduce interelectrodecapacitance and lead inductance, which makes it resemble a lighthouse tower. Theinterelectrode distances of the tube are made a fraction of a mm and the terminalsare made of flat discs welded to the end faces of glass cylinders; the edges of thesediscs projecting outside the vacuum tube envelope so that they could be connected tosections of coaxial lines of an oscillatory system [2]. The resonant circuit load of thelighthouse tube is constructed as the integral part of the tube (unlike the acorn anddoorknob tubes) so that the undesirable effects of the lead inductance andinterelectrode capacitance resulting from the tube and the resonant circuit load ofthe tube being separate units could be alleviated.

Advent of transit-time microwave tubesThe adverse effect of electron transit time in conventional electron tubes, such as thetriode, which imparts a finite value of the grid conductance responsible for the powerloss to the grid of the tube, can be used to advantage in MWTs. Thus, the conceptof the induced current in an electrode of such a tube when the number or velocity ofelectrons approaching the electrode is different from the number or velocity ofelectrons receding from it can be used in a MWT such as the multi-cavity klystron.However, as the operating frequency is increased to the millimeter-wave regime, thesizes of the interaction structures of conventional MWTs need to be reduced limitingthe device RF output powers. This has led to the development of fast-wave MWTssuch as the gyrotron, which can deliver high powers even in the millimeter-waveregime since the sizes of the interaction structures of these devices do not reduce asmuch as those of conventional MWTs. Further, with the advent of vacuummicroelectronic technology, the high-frequency capability of MWTs has beenextended to the terahertz regime.

Solid-state devices versus microwave tubesMWTs continue to be important despite competitive incursion from solid-statedevices (SSDs) (figure 1.2). MWTs enjoy superiority over their solid-state counter-parts with respect to having a lesser heat generated due to collision in the bulk of thedevice, a higher breakdown limit on maximum electric field inside the device, asmaller base-plate size (determined by the cooling efficiency), higher peak pulsed-power operability, ultra-bandwidth (three-plus octave) performance above a giga-hertz, and so on (table 1.2). Further, unlike SSDs, MWTs—being fabricated out ofmetals and ceramics—are inherently hardened against radiation and fairly resistantto temperature and mechanical extremes (table 1.2). In fact, attempts were made toreplace space-TWTs with SSDs, however, with limited success in view of therequired ∼ ×5 106 h MTBF (mean time between failures) in satellite qualifieddevices. Thus, although SSDs were tried in satellite communication systems duringthe last decade of the 20th century, for instance, replacing ∼50% TWTs with SSDs in1995, such replacements declined beyond 1998 to only ∼10% making space TWTsmore relevant than their SSD counterparts.

High Power Microwave Tubes: Basics and Trends

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Figure 1.2. Solid-state and vacuum device average power capabilities [11].

Table 1.2. Solid-state devices versus microwave tubes [10].

Issue Solid-state devices Microwave tubes

Collisional heat produced byelectron stream

Throughout volume Only at the collector

Operating temperature Lower temperature operationfor a longer life (lowermobility—a greater drag orinertial forces due to collision)Degradation at a highertemperature due to dopantmigrating excessively, latticebecoming imperfect, mobilitybecoming reduced impairinghigh frequency performanceWide-band-gapsemiconductors such as SiCand GaN to be used for hightemperature operation

Higher temperatureoperation

Breakdown limit on maximumelectric field inside the device

Lower Higher

Base plate size determined bycooling efficiency increasingwith (i) the temperaturedifference between the hotsurface and the coolenvironment and (ii) thesurface area of the hot surface

Larger Smaller (higher collectortemperature)

(Continued)

High Power Microwave Tubes: Basics and Trends

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Organization of the bookThe book is divided into two volumes comprising of ten chapters. Chapters 1through 5 are contained in volume 1, and chapters 6 through 10 in volume 2. Thepresent introductory chapter has presented the historical timeline of the develop-ment of MWTs (chapter 1, volume 1). Moreover, in this chapter, the order ofvacuum required in conventional electron tubes and the high frequency limitationsof these tubes have been discussed. How the development of tiny electron tubes andthen the advent of transit-time tubes alleviated the high-frequency limitation ofconventional electron tubes have also been discussed. An explanation for thesustenance of MWTs despite competitive incursions from solid-state devices hasalso been given. In the subsequent chapters, the classification and applications of

Peak pulsed power Lower (calls for powercombining by multipletransistors and proportionateincrease in package size)

Higher Beam may bepulsed in the regionseparated from theinteraction region

Ultra-bandwidth performance(three-plus-octaves)

Possible below 1 GHz(corresponding to longerwavelengths ensuringnegligible phase difference inthe voltage between theemitter and base)

Usually not possible(controlling thestructure dispersion isa challengingproblem)

Hardening against radiation andtolerance to temperature andmechanical extremes

Not possible Can be hardened and isfairly resistant totemperature andmechanical extremes

Direct cooling of heat zone Not possible PossibleEnergy recovery out of waste

beamNo recovery out of waste beam Significant recovery of

spent beam energyIonization Ionization of lattice Ionization of residual

gasses (much less)Permissible operating

temperatureLower (mobility of electrons is

less at elevated temperature)Higher

Handling power in interactionvolume

Less power in smallerinteraction volume

More power in smallerinteraction volume

Noise figure Lower HigherEfficiency Lesser HigherProcess cost Lesser HigherPerformance Linear NonlinearWarm-up delay Short LongPeriodic maintenance Not required RequiredHigh voltage power Supply

requirementNot required Required

High Power Microwave Tubes: Basics and Trends

1-10

MWTs and trends in their research and development (chapter 2, volume 1), theenabling concepts involved in understanding the principles of MWTs (chapter 3,volume 1), and the formation, confinement and collection of an electron beam inMWTs (chapter 4, volume 1) have been discussed. We have also analyticallyappreciated the various aspects of beam-absent and beam-present slow-wave andfast-wave interaction structures—the former typically with respect to a helical slow-wave structure and disc-loaded cylindrical waveguide, respectively, and the lattertypically with reference to the conventional TWT and the gyro-TWT, respectively(chapter 5, volume 1). A qualitative description has been presented for conventionaland familiar microwave tubes, namely, TWTs, klystrons including multi-cavity andmulti-beam klystrons, klystron variants, which include reflex klystron, inductiveoutput tube, extended interaction klystron (EIK), extended interaction oscillator(EIO) and twystron, and also crossed-field tubes, namely, magnetron, crossed-fieldamplifier (CFA) and carcinotron (chapter 6, volume 2). Fast-wave tubes have alsoreceived attention encompassing the gyrotron, gyro-backward-wave oscillator, gyro-klystron, gyro-travelling-wave tube, cyclotron auto-resonance maser (CARM),slow-wave cyclotron amplifier (SWCA), hybrid gyro-tubes and peniotron (chapter7, volume 2). The book has further brought within its purview vacuum micro-electronic, plasma-filled and high power microwave (HPM) tubes (chapter 8, volume2). Handy information about the frequency and power ranges of common micro-wave tubes has also been given (chapter 9, volume 2) though more such informationhas been provided at relevant places in the rest of the book as and where necessary.An epilogue at the end summarizes the authors’ attempt to elucidate the variousaspects of the basics of, and trends in, high power microwave tubes (chapter 10,volume 2).

References[1] Terman F E 1947 Radio Engineering (New York: McGraw Hill)[2] Spangenberg K 1948 Vacuum Tubes (New York: McGraw Hill)[3] Reich H J, Skalnik J G, Ordung F F and Krauss H L 1957Microwave Principles (New York:

Van Nostrand Reinhold Co)[4] Soohoo S F 1971 Microwave Electronics (Reading, MA: Addison-Wesley)[5] Hutter R G E 1960 Beam and Wave Electronics in Microwave Tubes (Princeton: D Van

Nostrand)[6] Gilmour A S Jr 1986 Microwave Tubes (Norwood: Artech House)[7] Benford J and Swegle J A 1991 High Power Microwaves (Boston: Artech House)[8] Gaponov-Grekhov A V and Granatstein V L (ed) 1994 Applications of High-Power

Microwaves (Boston: Artech House)[9] Benford J, Swegle J A and Schamiloglu E 2015 High Power Microwaves 3rd edn (New York:

CRC Press)[10] Barker R J, Luhmann N C, Booske J H and Nusinovich G S (ed) 2005 Modern Microwave

and Millimeter-wave Power Electronics (Piscataway: Wiley-IEEE Press)[11] Gilmour A S 2011 Klystrons, Traveling Wave Tubes, Magnetrons Crossed-Field Amplifiers,

and Gyrotrons (Boston: Artech House)

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