plasma physics and related challenges of millimeter-wave-to … · 2016-01-29 · plasma physics...

Plasma physics and related challenges of millimeter-wave-to-terahertzand high power microwave generationa…

John H. Booskeb�

Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Engineering Drive,Madison, Wisconsin 53706, USA

�Received 12 November 2007; accepted 8 January 2008; published online 27 February 2008�

Homeland security and military defense technology considerations have stimulated intense interestin mobile, high power sources of millimeter-wave �mmw� to terahertz �THz� regimeelectromagnetic radiation, from 0.1 to 10 THz. While vacuum electronic sources are a naturalchoice for high power, the challenges have yet to be completely met for applications includingnoninvasive sensing of concealed weapons and dangerous agents, high-data-rate communications,high resolution radar, next generation acceleration drivers, and analysis of fluids and condensedmatter. The compact size requirements for many of these high frequency sources require miniscule,microfabricated slow wave circuits. This necessitates electron beams with tiny transversedimensions and potentially very high current densities for adequate gain. Thus, an emerging familyof microfabricated, vacuum electronic devices share many of the same plasma physics challengesthat are currently confronting “classic” high power microwave �HPM� generators including long-lifebright electron beam sources, intense beam transport, parasitic mode excitation, energetic electroninteraction with surfaces, and rf air breakdown at output windows. The contemporary plasmaphysics and other related issues of compact, high power mmw-to-THz sources are compared andcontrasted to those of HPM generation, and future research challenges and opportunities arediscussed. © 2008 American Institute of Physics. �DOI: 10.1063/1.2838240�

I. INTRODUCTION

In the late 1880s Heinrich Hertz experimentally identi-fied the existence of radio frequency electromagneticradiation,1 confirming the theoretical prediction by Maxwellthat visible light was but a small portion of a vast electro-magnetic spectrum.2,3 Within just a few decades, Tesla pro-posed one of the first applications for powerful radio waves,i.e., radar.4 Immediately recognizing the implications of thisidea, numerous efforts began to develop the technology inEurope, the United States, and the Soviet Union between1920 and 1940. Many historical accounts regard a superior,high power radar technology as a significant, if not decisivemilitary advantage for Britain during World War II.5–7 Inparticular, the radar systems of Britain and the U.S. werecharacterized by superior, high power microwave cavitymagnetrons, based on the successful prototype developed byBoot and Randall in 1940.8 In the ensuing seven decades,continued increases in microwave generator power and fre-quency have driven a large fraction of the advances in de-fense, commercial industry, and science. Today, the enablingrole of high power microwave generators based on vacuumelectronic devices �VEDs�, is pervasive in many military,civilian, scientific, and industrial arenas9 as shown in Table I.

By combining the data from recent sources includingRefs. 9–19, a map of the current maximum average powerversus frequency of solid state, vacuum electronic, and quan-tum electronic devices can be constructed as shown in Fig. 1.For self-consistent comparisons, most of the data in Fig. 1assume long pulse or average power, with exceptions be-

tween 1 and 10 GHz for high power microwave �HPM�sources20,21 and above 1 THz for some of the peak poweradvances in THz lasers.

Figures 1�a� and 1�b� contain several features deservingmention. First, the highest single device powers at any fre-quency are all determined by vacuum electronic sources bymany orders of magnitude. We will discuss this shortly. Sec-ond, there are three boxes drawn in Fig. 1�a�. Each box in-dicates the current or anticipated applications for that portionof the high power spectrum. The primary application drivingresearch investment in region 1 is to develop sources forelectronic attack, that is, intense microwave sources that candisable an adversary’s electronics leaving personnel and in-frastructure unharmed.20,21 Device research in region 2 hasprimarily emphasized gyrotrons for several applications, in-cluding fusion plasma heating,22,23 advanced high resolutionradar,24,25 and nonlethal antipersonnel systems.26 The appli-cation possibilities for devices in region 3 are extensive, andinclude high data rate communications, concealed weapon orthreat detection, remote high resolution imaging, chemicalspectroscopy, materials research, deep space research andcommunications, and biomedical diagnostics.19,27–29

Also shown in Figs. 1 are two research frontier bound-aries. The dotted �red� line boundary in Fig. 1�a� representsthe current limits for mobile single device power—either av-erage or peak, while the solid �black� line in Fig. 1�b� repre-sents present-day mobile and compact average power devicelimits. The primary differences between the two boundariesare: �1� The difference between peak and average powerachievements by solid state lasers above 1 THz, and �2� be-low 1 THz, the recognition that high power mmw gyrotrons,while mobile when mounted on a small truck or similar ve-

a�Paper MR1 1, Bull. Am. Phys. Soc. 52, 186 �2007�.

b�Invited speaker. Electronic mail: [email protected].

PHYSICS OF PLASMAS 15, 055502 �2008�

1070-664X/2008/15�5�/055502/16/$23.00 © 2008 American Institute of Physics15, 055502-1

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http://dx.doi.org/10.1063/1.2838240

http://dx.doi.org/10.1063/1.2838240

http://dx.doi.org/10.1063/1.2838240

hicle, are not compact when compared with a mmw back-wards wave oscillator �BWO�, for example. Yet many of theapplications driving interest in region 3 specifically requirecompact sources typically driven by the requirement of mo-bility.

There are some relatively recent, impressive high powerachievements at frequencies above 200 GHz, as indicated byfour sets of data �squares, triangles, diamond, and circle datapoints�. Two of these sets are the result of impressive recordaverage powers obtained from the Novosibirsk free electronlaser �squares�30 and the Jefferson Laboratory free electronlaser �triangles�.31 Also plotted are record-level peak powersgenerated by both high-magnetic field gyrotrons18 and freeelectron lasers �FELs�.19,30,31 However, none of these facili-ties represent either mobile or compact sources, limiting theirpotential for commercial or military applications. Recent re-search has identified designs32 for region 3 FELs that wouldbe mobile �comparable to a gyrotron�, although no experi-mental results have yet been reported. The diamond datapoints record the demonstration of high-average-powerTHz regime radiation generated by high-magnetic-field gy-rotrons, including 1.5 kW at 326 GHz,33 tens of watts at800–900 GHz,34 and several watts generated at 460 GHz.35

The circle data point represents a recent regenerative TWToscillator36 that has reported a modest increase in power at670 GHz over what commercial BWOs can provide. Never-theless, this device represents a significant breakthrough in acompact and mobile source with its impressive 0.3% intrin-sic efficiency, a number that would have been close to 1%except for electron beam current losses of �50% due to wallinterception on the first prototype. These efficiencies are 1–2

orders of magnitude higher than BWOs operating at this fre-quency, for example.

The highest average powers for solid state sources atf �1 THz include �10 �W nonlinear multiplier sourcesabove 1 THz,37 and milliwatts at several THz using eitherquantum cascade lasers38,39 or difference frequencymixing.40 Note that quantum cascade lasers require cryo-genic cooling to suppress thermal broadening and achievehigh average power generation. In fact, it is this very prob-lem of thermal broadening disrupting population inversionsthat makes it so challenging to achieve significant power

TABLE I. High power microwave applications enabled by vacuum electrondevices. �Reprinted with permission from Ref. 9. Copyright 2005, IEEE/Wiley.�

Civilian infrastructureand consumer markets

Broadcast media transmission �TV, radio�Satellite communicationsCellular �wireless� communicationsRadar, e.g., air traffic control, weather,maritime Global positioning systemDomestic microwave cooking

Military Radar: Search, guidance, track,missile-seeker,weather, testElectronic counter measures �ECM�High power microwave �HPM�electronic attack

Scientific Plasma heating and fusion energy researchCharged particle acceleratorsAtmospheric radarRadio astronomyMedical/biomedicalSpectroscopyDeep space communicationsMaterials processing researchGround penetrating radar

Industrial Testing and instrumentationMaterials processingIndustrial plasmas, especially forsemiconductor manufacture

FIG. 1. �Color online� Power vs frequency of solid state and vacuum elec-tronic devices. �a� Both average and peak power devices. The dashed red�thick� line is the maximum power research frontier. The filled diamond datapoints represent THz regime average power gyrotron oscillator operation,the filled square data points represent the Novosibirsk FEL average powerachievements, the filled triangle data points represent the Jefferson Lab FELaverage power results, and the filled circle data point represents a regenera-tive traveling wave tube oscillator. The open diamond data points representTHz regime gyrotron peak powers, the open square data points are peakpowers from the Novosibirsk FEL, and the open triangles are peak powersfrom the Jefferson Lab FEL. �b� The same plot with only compact andmobile, average power �single� device results. Again, the circle data pointrepresents a regenerative traveling wave tube oscillator result of Ref. 36.

055502-2 John H. Booske Phys. Plasmas 15, 055502 �2008�


with quantum electronic devices below several THz.It is instructive and relevant for later discussion to re-

mind ourselves why the single device powers of VEDs ex-ceed those of solid state devices by such large margins, atleast up to �1 THz. There are several differences between avacuum and a solid state electronic source of microwaveelectromagnetic radiation. Both devices convert the kineticenergy from an electron stream into electromagnetic fieldenergy. The most obvious difference is that in a vacuumdevice, the electron stream �beam� flows collisionlessly in avacuum while in a solid state device the collision-dominatedstream diffuses through a semiconducting solid. Thus, thesolid state device will ultimately be limited by the inabilityto conduct away excessive heat generated by the electroncurrent in the “interaction” region and/or dielectric break-down at high microwave electric field strengths. To lowestorder, these limitations are nonexistent with a vacuum, mak-ing the VED the superior option for applications requiringhigh power in a small volume. On the other hand, thevacuum device requires a three-dimensional high-vacuum-sealing enclosure around the entire periphery of the devicewhich can make the manufacture of VEDs more challenging.A second difference is that the collisional electron transportin solid state devices limits their architectures to that of tran-sit time switches. Thus, they are limited to lower voltages inorder to keep the source-drain or emitter-base electric fieldsbelow breakdown. In contrast, VEDs generally require ve-locity synchronism between ballistic electron flow and elec-tromagnetic energy propagating at a few to tens of percent ofthe velocity of light. Consequently, VEDs require highervoltages for the acceleration of the electron beam. A moredetailed discussion of the differences between solid state andvacuum electronic devices can be found in Chap. 1 of Ref. 9.However, from the data in Fig. 1, we can empirically inferthat the challenges of three-dimensional vacuum enclosuremanufacture and higher voltage electronics design of VEDsare far outweighed for high power applications by the supe-rior ability of the VED to withstand higher power densitieswhile operating at relatively high efficiencies. Given this ro-bust characteristic of an evacuated device, one may wonderwhat physical processes limit the attainable maximum pow-ers for VEDs. As we shall see from subsequent discussion inthis paper, the limitations are still, ultimately related to limitson the maximum sustainable power density. In fact, we shallsee that these limits involve surface physics and charged par-ticle confinement challenges, in that sense similar to chal-lenges facing fusion plasma devices. This is no mere coinci-dence, as both classes of devices seek to push the limits ofproducing and managing high densities of electromagneticand charged particle energies.

As a general rule, the maximum achievable solid statesingle device power scales as the inverse square of the fre-quency, as shown in Fig. 1�a�. This is a consequence of lat-eral dimensions scaling with the wavelength in order toavoid dielectric breakdown and excessive phase lag across atransistor �transit-time� device.41,42 Similarly, the maximumachieved power levels of VEDs between 1 and 100 GHzalso scale as �f−2. Again, this is related to scaling of thelateral dimensions of vacuum interaction circuit dimensions

with the radiation wavelength. In stark contrast, however,above 100 GHz, the frequency scaling of maximum demon-strated powers for mobile and compact devices deviates re-markably from the f−2 scaling, as seen in either Fig. 1�a� orFig. 1�b�. This gives rise to what has been referred to as aTHz gap �labeled in Fig. 1�b�� of adequately powerful sourcetechnologies, precisely in region 3 where the application po-tential is so substantial.

In the remainder of this paper, we shall discuss theplasma physics and related challenges of producing higherpower, compact devices for this mmw-to-THz regime or THzgap, and we shall draw out the commonalities and differ-ences that exist between these challenges and those facingfurther increases in peak power for lower frequency HPMdevices �between 1 and 10 GHz�. For expediency, we willrefer to the entire regime between 0.1 and 10 THz as theTHz regime, even though a more accurate, but more elabo-rate terminology might include millimeter-wave,submillimeter-wave, and THz. Finally, from some of thequantitative analyses, it may become apparent that the poten-tial for VEDs to fill in the THz gap will probably be limitedto �1 THz, with the exception of FEL user facilities such asthose at Jefferson Lab31 or in Novosibirsk, Russia.32 How-ever, this latter remark is a speculative prognostication basedon current knowledge and as such should always be regardedwith a certain measure of skepticism.

The remainder of this paper is organized as follows: Sec.II reviews the recent research of challenges resulting fromscaling current vacuum electronic device architectures toeven higher powers. Particular issues include rf breakdown,fabricating robust yet precisely dimensioned high frequencyelectromagnetic structures, magnetic focusing and generationof high current density electron beams, and the physics ofhigh power density electron beam impact on circuits andcollectors. Section III reviews the challenges and opportuni-ties offered by distributed electron beams. Section IV sum-marizes both the challenges and research opportunities forextending power beyond current performance achievements,and general conclusions are drawn in Sec. V.

II. THE CHALLENGES OF SCALINGTO HIGHER POWERS

Figure 1 reveals a contrast in the pursuit for higherpower between HPM devices for electronic attack and com-pact devices that would populate the THz gap above100 GHz. To advance HPM devices for electronic attack, theneed is for higher power in a relatively modest band of fre-quencies, i.e., between 1 and 10 GHz. A simple estimateshows how this becomes a challenge in managing highpower densities. For example, in this frequency range, thetypical device’s circuit cross-sectional dimensions, deter-mined roughly by the free space wavelength �0 of the radia-tion, will be on the order of �10 cm�10 cm, or �100 cm2.For power levels in excess of 100 MW, one must managepower densities in excess of 1 MW /cm2. Meanwhile, topopulate the THz gap, one could �and generally does� viewthe challenge to be achieving some desired power, such as,say 100 W, at frequencies greater than 100 GHz. For ex-

055502-3 Plasma physics and related challenges… Phys. Plasmas 15, 055502 �2008�


ample, in order to realize practical beam-wave interactionefficiencies, the circuit cross-sectional dimensions of com-pact �i.e., slow-wave or transit-type� VEDs at high frequen-cies will roughly be proportional to one-tenth of the free-space wavelength, or 0.1��0. Hence, to achieve 100 W at300 GHz, one must manage power densities in excess of�100 W� / �0.1�0�0.1�0��1 MW /cm2. From this we seethat although the basic approach to higher power is differentfor these two distinct frequency regimes, the end result isvery much the same. In the remainder of this section, we willdiscuss how this general challenge of managing high powerdensity leads to both similar and complementary physicsproblems to solve.

A. High electromagnetic power density

Perhaps the most obvious challenge associated with highelectromagnetic power density is the potential for rf break-down due to very high electric fields. Although spontaneousbreakdown of a vacuum by sufficiently strong electric fieldswas predicted by Schwinger43 and conditions have been ap-proached or even realized in laser and high energy physicsexperiments,44–46 it is far beyond the regime of a microwaveVED. Nevertheless, at moderately high electric fields, anumber of breakdown phenomena are indeed possible andhave been observed at material interfaces, including conduct-ing and dielectric surface breakdown �vacuum side� and airbreakdown outside the vacuum window. Meanwhile, espe-cially for the higher frequency high power devices, one en-counters fundamental questions about how to construct theminiature electromagnetic structure or circuit with adequateprecision so that it that will confine the radiation, provide theprecise phase velocity, produce intense electric fields nearthe beam �for efficient beam-wave interaction�, and toleratethe potentially high rf Ohmic heating losses in the walls.

Meanwhile, generating high electromagnetic power den-sity requires even larger electron beam power density, givenpower conversion efficiencies of less than 100%. This intro-duces challenges of generating and confining intense, highcurrent density electron beams as well as understanding thephysics and limitations of the beam-surface interactions as-sociated with beam impact �on the collector, anode, or circuitwalls�. We will look at each of these issues in more detail.

1. rf breakdown

Breakdown on the vacuum side of a high power densitymicrowave VED can result in pulse shortening and/or dam-aged surfaces.21,47 Breakdown on the high pressure side of avacuum window can result in window heating, window dam-age or high density cutoff plasma that prevents transmissionof the radiation.48

Breakdown on the vacuum side can initiate from eithermultipactor or field emission. Multipactor49,50 is a low pres-sure electron multiplication process. Seed electrons emittedfrom a surface are accelerated by rf fields and strike eitherthe same or a second surface releasing a shower of secondaryelectrons. Acceleration of the secondaries before they, too,energetically strike the surface and produce even more sec-ondaries leads to a cascade buildup of electrons, surface

heating, release of gas via either thermal or stimulateddesorption,51 and either an arc or plasma discharge. Gener-ally, for conducting materials, it requires two surfaces49 andsynchronism between the rf field and the orbits.52 Dielectricwindows, can experience single-surface multipactor.53 Thisprocess does not require synchronism but it does require suf-ficient charge to build up on the dielectric to reattract emittedsecondaries. As a result, susceptibility curves for both two-metallic-surface and single-dielectric-surface multipactor canbe generated, and have generally been found to be consistentwith experimental studies.53,54 In general, multipactor tendsto occur at lower electric field strengths, and avoidance ofvacuum surface multipactor is possible by careful design ofelectromagnetic mode patterns, surface geometries, and ma-terials. Some of these measures are required for certifiedspace-based VEDs.

Field emission is also an important mechanism forvacuum rf breakdown and is believed to be responsible forarcing and damage in high gradient rf linac cavities.55,48

Field emission requires large electric field strengths and forconditioned surfaces the breakdown threshold appears tobe55,56 between 100 and 1000 MV /m. Interestingly, the mostrecent research indicates that the breakdown field thresholdis insensitive to frequency55 and pressure. Cleaning, etching,polishing, and heat treating the surfaces can be helpful, but itis extremely difficult �perhaps impossible� to eliminate allmicroscopic flaws that can intensify surface fields or locallydepress the work function for electron emission.56 Mean-while, although these field intensities can occur in high-Q rflinac cavities, they are unlikely in the foreseeable future inhigh power microwave VEDs. For a rough estimate, one canassume a cavity volume V=g�0

3, where g is a scaling factor.Approximating the cavity power loss by the output-coupledpower, Pout, the breakdown threshold cavity factor Qth can beestimated as

Qth � ��0�E�2g�03�/2Pout � 1013g/PoutfG

2 , �1�

where �0 is the permittivity of free space, fG is the frequencyin GHz, and a breakdown field threshold of �E � �108 V /mand a uniform electromagnetic energy density have been as-sumed. First consider the example of fG=3 �GHz� and Pout

=109 W. Exceeding the field emission cavity breakdownthreshold requires Qth�1000g. For g�1, this is consider-ably larger than the Q values used in typical HPM oscilla-tors. The same estimate of Qth�1000g is obtained at higherfrequencies if one assumes Pout=106 W and fG=300 �GHz�.This is considerably larger than what one encounters withhigh power gyrotrons, where typically g�1000 �highly over-moded cavities�, but Q�100–1000.

Based on the above observations, one may conclude thatvacuum rf breakdown presents a physical limitation for highgradient rf linac design, but is unlikely to be the power-limiting effect for high power vacuum electronic microwavesources. On the other hand, air breakdown has been observedas a power limiting mechanism for pulsed HPM devices atboth low57 and high pressure.58 Recent research has beenfocused on understanding high power microwave air break-down near dielectric windows in order to identify the bestoptions for delaying or suppressing its onset.50,59,60 Although



there is still much to be researched about the factors thatdetermine the thresholds and delay times for air breakdown,there are a number of fundamental insights that have beenacquired. The rf electric field breakdown threshold is ob-served to depend on pressure and microwave pulse length,Eth�p ,�, in ways generally consistent with basic principlesestablished by MacDonald61 and many others. Other findingsinclude:

• At conventional HPM frequencies, f 10 GHz, and lowerpressures, p300 Torr, the breakdown threshold is influ-enced by the presence and roughness of the surface, gascomposition �e.g., nitrogen versus air� and illumination byUV radiation59 and x rays.

• At atmospheric pressure and higher frequency,f =110 GHz, the breakdown threshold is much less studieduntil most recently. However, at these short wavelengths,the breakdown plasma manifests as a regular spatial arrayof filaments with quarter wavelength spacing.60 Evidenceindicates the filament array formation involves coherentdiffraction.

• Across all frequencies between 1 and 100 GHz,58–60 andeven with proper scaling to 193 �m wavelengths,62 thebreakdown threshold for the effective electric field in at-mospheric pressure air �adjusted61 for frequency � andcollision frequency �coll� appears to be a consistent valueof

Eeff =E0/�2

�1 + ��/�coll�2� 20 – 30 kV/cm. �2�

• At low pressures, the plasma formation kinetics are initi-ated by multipactor while at higher pressure the kineticsare governed by collisional discharge physics.50 For noblegases, the transition between the two regimes appears tooccur at63 p�10−8 T s. For air plasmas, the transition be-tween the two regimes is still under investigation.

• For the high pressure collisional discharge regime, a sim-plified scaling law appears to approximately describe all ofthe recent experimental findings within a factor of 2 orbetter accuracy,63,64

Eeff�V/cm� � K�p�T��s�

, K � 0.05, noble gases,

1, air,

�3�

where Eeff is defined in Eq. �2�.One of the inferences to draw from the scaling law of

Eq. �3� is the reminder that there are some important funda-mental differences between air and noble gas breakdown,which is most likely due to the complexities of airchemistry.65 A challenge for ongoing research investigationsis to attempt, as done in Ref. 66 to isolate from amongsthundreds of air chemistry reactions a few dominant chemicalpathways that largely account for the large difference in theleading coefficient of Eq. �3� while at the same time, explain-ing from a fundamental basis the apparent �approximate�universality of the scaling with pressure and pulse length.Meanwhile, from Eq. �2� and its apparent universality for

atmospheric air breakdown over a very broad frequencyspectrum, we can speculate that the electric field threshold,and thus the power density threshold for air breakdown isrelatively insensitive to frequency from 1 GHz to 1 THz�for an electron-neutral collision frequency at 760 Torr of�4�1012 s−1, the breakdown threshold for Eeff is approxi-mately constant within a factor of 2 from 1 to 1000 GHz�.Given that power density scales as Pf2, air breakdown,which is currently one of the factors limiting HPM peakpowers between 1 and 100 GHz, is not a significant con-straint for increasing power �or power density� in the THzgap of Fig. 2.

Finally, the mechanisms of dc breakdown67 bears sub-stantial resemblance to rf breakdown for the low frequencyrange.48

2. Fabricating THz regime circuits

Compact and mobile vacuum electronic devices gener-ally utilize either slow-wave or cavity �transit-time� electro-magnetic structures. From basic principles of the beam-waveinteraction physics as summarized in Refs. 9, 68, and 69, andelsewhere one may infer that an efficient beam-wave energytransfer requires the transverse dimensions of the circuit tobe less than or equal to approximately 0.1�0. Meanwhile, forreliable device performance �that is, measured performancethat is acceptably close to theoretical predictions for the de-sign� the dimensional tolerances the circuit should be 10%error between the fabricated dimensions and the intended�design� values.70 This translates to tolerance requirementsapproaching 1 �m at f �500 GHz. This is considerably be-yond the capabilities of conventional machining and turningtechnologies. Therefore, new, high precision methods be-come paramount to reliably and repeatedly shape and as-semble electromagnetic wave circuits for miniature, micro-fabricated vacuum electronic devices, or �-VEDs, suitablefor THz regime applications.

FIG. 2. �Color online� Magnetic field and electron beam current densityrequirements for a 100 W millimeter-wave traveling wave tube obtained bythree different scalings of the device parameters with frequency from atypical 5 GHz device to 200 GHz. The dashed �red� lines are the magneticfield and the solid �black� lines are the current density. The dotted black lineindicates the nominal maximum solenoidal magnetic field ��10 kG� avail-able from practical permanent magnet configurations.



Recent research has pioneered the adaptation of1-micron-precise lithographic fabrication methods to�-VEDs.41,71–74 Advances in high-speed mechanical machin-ing, microelectric-discharge-machining �micro-EDM�, andlaser micromachining have also proven valuable to reliableprecise fabrication of high power mmw devices.41,71,75–78

Indeed, for compact high-power-density sources nearf =100 GHz where dimensional tolerances are �15 �m, thefabrication choices appear to include wire-EDM �Ref. 79�high-speed small-bit machining,80 laser micromachining,79

and Si DRIE.81 X-ray LIGA has also proven viable as afabrication method for research prototypes,73 but is perceivedto be significantly limited by its requirement for a high-brightness x-ray lithography facility. Early efforts were hope-ful that a diversity of fabrication technologies would alsoprove viable for �VEDs at f �100 GHz, providing the re-searcher or engineer with an array of options. The fabricationmethods researched have included x-ray LIGA, ultravioletLIGA, polymer micromolding, deep reactive ion etching�DRIE� of Si, micro-EDM, and laser micromachining.41

However, recent experience is converging on micro-EDMand Si DRIE for two main reasons. Micro-EDM is appealingbecause of its ability to work with bulk, high-conductivitycopper, which is important for thermal stability with highpower density sources.71 Si DRIE appears to most reliablyproduce the highest precision structures, again in a bulkstructural material, with mature “tools” that are available andaffordable for many institutions, including academic, govern-ment laboratory, and commercial vendors. In fact, the recentbreakthrough realization of an efficient, 670 GHz regenera-tive TWT oscillator36 was based on the successful adaptationof pioneering research of Si DRIE-fabricated folded-waveguide TWT oscillators first described in Ref. 72.

In summary, micro-EDM and Si DRIE appear to cur-rently offer some of the best prospects for THz-regime�VED circuit fabrication. However, there appear to be manypromising alternatives for electromagnetic circuits and eachnew concept requires customized research to find a viablefabrication and assembly procedure. In addition, research isneeded for other components, such as miniature vacuumwindows, as well as new, high precision assembly methodsto achieve exact alignment between circuits, cathodes, col-lectors, and focusing magnets.

B. High current electron beams

As discussed earlier, increasing the power of compactTHz-regime �VEDs implies high density electron beams.This presents a number of challenges, which, along with thedifficulties for precision fabrication of the miniature circuits,have been responsible for the lack of sources in the THz gap.

1. Magnetic focusing of dense beam spacecharge

An instructive approach to understanding the electronbeam physics challenges of high power THz-regime �VEDsis to start with typical parameters for a conventional, 100 W,5 GHz microwave TWT and scale the dimensions to producea 100 W, 200 GHz TWT, just crossing into the THz gap for

powerful compact sources �see Fig. 1�. Taking illustrativeparameters of the XWING TWT �Refs. 82 and 83� of 2.5 kV,0.2 A, and 20 A /cm2 and scaling at constant voltage to200 GHz, the reduction of 40� in the wavelength translatesinto a current density of 32 kA /cm2. The minimum magneticfield required for focusing the space charge repulsion forcesin this beam is that which satisfies Brillouin equilibrium,84

�c2 � 2�p

2 �4a�

or

B�kG� � 1.5�J�A/cm2��V�eV��1/4 , �4b�

where �c is the electron cyclotron frequency for magneticflux density B, �p=�ne2 /m�0 is the beam plasma frequencyfor electron density n, electron charge magnitude e and elec-tron mass m, J is the beam current density and V is the beamenergy �in eV� or voltage �in V�. Given that the maximumcompact magnetic field achievable in a compact configura-tion with permanent magnets36,85 is �1 T or 10 kG, it isstraightforward to deduce that the constant-voltage scaled100 W, 200 GHz TWT is impractical, as illustrated in Fig. 2.

Perhaps the next option is to reattempt the scaled design,but allowing for a higher beam energy. ChoosingV=20 keV to maintain a compact size and minimize highvoltage insulation challenges, yields a scaled current densityof 4 kA /cm2 and requires a minimum magnetic focusingfield of �0.8 T, as shown in Fig. 2. Although the magneticfield requirement is within achievable limits, minimally scal-loping electron beams require higher-than-Brillouin mini-mum magnetic fields. Moreover, this scaling does not pro-vide any margin to increase the frequency further beyond200 GHz.

The next option follows from recognizing that the origi-nal device82,83 dimensions at 5 GHz were intentionally small,in order to achieve exceptionally high gain and efficiency ina relatively short circuit. Relaxing these dimensions by afactor of 5 still fulfills the criterion for transverse dimensionsof approximately 0.1�0, but now produces J=160 A /cm2

and B=1.6 kG for the scaled 200 GHz, 100 W design, bothof which are well within demonstrated technology capabili-ties.

2. High current cathodes

The previous discussion indicates the importance of gen-erating and transporting high current and high current den-sity electron beams for higher power VED sources. In fact,this is an issue for both HPM and mmw-to-THz devices.Since the electron beam starts with the cathode, we will like-wise first examine the limits on performance and physicalunderstanding of high current density cathodes to generatethese beams. Producing an electron beam requires deliveringenough energy to electrons within the surface of a solid toenable their escape of the binding forces into the vacuum.The foundations of theoretical understanding of this processbegan in the early 1900s with models developed by Richard-son, Dushman, Laue, Fowler, and Nordheim.86 The mecha-nisms used to realize vacuum emission include thermionic,



field emission, photoemission, and secondary electron emis-sion. Most cathodes for microwave generation devices ex-ploit one of the first two, although many FELs rely on pho-toemission and magnetrons and crossed-field devices usesecondary electron emission.86,87

Most of the applications envisioned for sources fillingthe THz gap call for long pulse or continuous electron beamemission, whereas the traditional HPM application of elec-tronic attack is addressed by short pulse emission ��1 �s� atlow duty cycle.20,21,88 For continuous or “dc” electron beams,the highest demonstrated current density of �650 A /cm2

was achieved with a gated Spindt field emitter array �FEA�,89

although the highest demonstrated current density by a gatedFEA in an actual microwave device90,91 remains less than20 A /cm2. The reason for this large difference will be dis-cussed shortly. For thermionic emission, the highest currentdensity with dc operation in a device is �100 A /cm2, inTHz regime BWOs.92 However, this results in short cathodelifetimes of less than 500 h. For longer-lived thermioniccathodes, the highest emitted dc current densities93 are�10 A /cm2. Pulsed current emission from thermionic cath-odes has been reported of �100 A /cm2 for novel scandatecathodes,94 but their use in microwave sources has not yetbeen reported. For pulsed emission for HPM applications,several recent cathodes have emerged as providing high cur-rent density emission from cathodes with mechanically andthermally robust construction. These include CsI-coatedgraphite fiber cathodes,88,95 laser micro-textured aluminumcathodes,96,97 and micro-textured-HfO-film-coated metalliccathodes.98 The first two have demonstrated emission currentdensities �1 kA /cm2 while the third has demonstrated a cur-rent density of �80 A /cm2 through the mechanism of triplepoint emission.

In addition to impressive experimental advances in highcurrent density cathodes, there have been significant ad-vances in the theoretical understanding of cathode physics.Whereas previously it had been necessary to model thermi-onic, field, and photoemission cathodes with separate treat-ments, a recently developed combined treatment improvesour understanding of the common physics underlying eachphenomenon.99 Another persistent challenge has been to ex-plain high surface field enhancement factors inferred fromexperimental measurements of field emission cathodes. Insome cases, part of the answer appears to be an inaccuratelylarge assumed value for the cathode’s surface work function,resulting from the difficulty of making a self-consistent, insitu determination of the correct value.100 Another importantstep has been the determination that microscopic protrusionsdecorating the top of a macroscopic protrusion on a cathodewill produce a composite field enhancement greater than�proportional to the product of� each of the individual fea-tures’ field enhancement factors.101 In this way, the field en-hancement observed from a knife-edge or other intentionallytextured surface typically will exceed, by a considerableamount, the value calculated for the measured shape of themacroscopic surface features. Recent analyses of triple pointemission102 reveal that this method of producing electronshas more to do with secondary electron emission from di-electric surfaces than it does with field enhancement, as had

been previously assumed. Recent computational modelingcalculations are helping to understand the copious electronemission and significant reduction of turn-on electric fieldobserved with CsI coatings of graphite-fiber-on-graphitecathodes. Using ab initio computational models, it has re-cently been shown that very thin, partial monolayer films ofCsI reduce the work function of graphite by over a factor of3, thereby reducing the turn-on electric field by nearly anorder of magnitude.103

One of the persistent hopes for FEA cathodes has beenthe desire to exploit demonstrated high-current-density emis-sion capabilities89 for generating microwave or THz-regimeradiation with higher efficiency and/or higher power. Recentanalytic and computational studies help to explain the reasonwhy after more than a decade that this objective still remainselusive. The essence of the challenge is the relatively highelectric fields required with extremely dense electron beams.The Child–Langmuir Law104,105 serves as a useful guide,

J�A/cm2� = �eu � 2.33 � 10−6V3/2

d2 , �5�

even for more complicated situations involving nonplanarcathodes or gated operation of field emitters. In Eq. �5�, �e isthe absolute magnitude of the electron density, u is the beamvelocity, and d is the distance between the cathode and an-ode. Near the cathode, the beam velocity is small, the beamdensity is large, and a large anode-cathode voltage, V, isrequired to overcome the large space charge depression thatresults at the cathode. The resulting high electric fieldstresses on the cathode and anode can lead to breakdown andarcing in long-pulse or dc electron guns that are designedwith overly ambitious cathode emission current density. Tounderstand how it was possible to achieve the impressivedemonstration of �650 A /cm2 from a Spindt FEA �Ref. 86�,one must note that this experiment involved a relativelysmall cathode area of approximately 400 �m2. Recentcomputational106 and analytic107 studies have revealed thatwhen the cathode emitting area is much smaller than theeffective cathode-anode spacing, then it is much easier toachieve very high emission current densities without exceed-ing cathode-anode breakdown voltage limits. In particular, asthe radius R of a circular cathode emitting area decreases atfixed anode-cathode gap distance d, the space charge limitedcurrent for a given anode-cathode voltage increases accord-ing to106,107

J2D � J1D � 1 +d

4R� . �6�

Thus, to achieve the 650 A /cm2 emission from a cathodelarge enough to produce adequate total currents for highpower, compact, THz regime radiation would require muchhigher anode-cathode voltages than were needed in the ex-periments of Ref. 86, probably exceeding thresholds atwhich arcing and breakdown would occur. On the otherhand, microwave-frequency HPM devices are designed tooperate with high voltages and short pulse lengths, allowingthem to operate their cathodes at very high space-charge-limited current regimes. This allows them to exploit the very



high current density emission levels that field emission cath-odes are, in principle, capable of. Given this capability ofextracting very high field emission current densities usinghigh electric fields in HPM devices, a recent study108 hasquantitatively examined how space charge depression of thesurface electric field affects the emitted current density offield emission cathodes. The results support the conclusionthat for an idealized planar diode configuration, the fieldemission current density will be less than �i.e., upper-bounded by� the classic Child–Langmuir space charge limit.However, for sufficiently large surface electric field, result-ing, for example, from sharp surface features that enhancethe local electric field by factors of �10 or more, the ob-served field emission currents may be indistinguishably closeto the Child–Langmuir space charge limit.

Given these physical considerations and contrasts, wecan conclude that while both HPM and compact high powermmw-to-THz VED sources call for high current density elec-tron beams, the approaches are likely to be complementary.With HPM devices, short pulses of high voltage electronbeams will be used to extract �1 kA /cm2 electron currentdensities from field emission cathodes. In contrast, for com-pact, high power, long-lived mmw-to-THz sources, the morelikely approach will require cathode emission current densi-ties of 10 A /cm2 or less and to use magnetic and electro-static field compression to realize beam current densities�100 A /cm2. In fact, this is exactly the approach used in thehighest power density �most compact� source of �100 GHzradiation to date, the extended interaction klystron,93 wherean emitted current density of 10 A /cm2 is aggressively andprecisely compressed to beam current density in excess of500 A /cm2. It should be noted, however, that even10 A /cm2 is a relatively high emission current density thatcan stress existing cathode technologies, leading to shortcathode lifetimes. One interesting innovation currently beingresearched is a type of reservoir cathode, made from a sin-tered assembly of tungsten wires with controlled porosity.109

If successful, this cathode would enable high current densityemission �J�10 A /cm2� with significantly longer lifetimesthan conventional dispenser cathodes69 emitting at these highcurrent densities. Advancing the physical understanding andperformance of high current cathodes remains a priority forlong-lived, high-power-density vacuum electronic radiationsources.

In addition to benefiting from high current density emis-sion, most HPM and high power THz regime VEDs alsorequire uniform emission from the cathode. Nonuniformemission produces high emittance electron beams, which, aswe shall discuss, are problematic for beam confinement inhigh power, compact THz-regime VEDs. It has been a per-sistent challenge for field emission cathodes, and recent in-vestigations have emphasized modified configurations toachieve highly uniform emission from field emitter arraycathodes.110 Nonuniform emission can also reduce the effi-ciency, or reduce the power-handling capacity of spent-beamcollectors of high power mmw gyrotrons.111,112 Thesegyrotrons are a crucial technology for fusion research plasmaheating and nonlethal antipersonnel21 systems and in bothcases, a high premium is placed on maximizing efficiency.

Recent studies have revealed that the current emitted fromhigh power gyrotron cathodes can be very nonuniform. Forexample, the emitted current can vary by as much as 60%around the circumference of the cathode.111 There are severalhypotheses explaining the cause of this undesirable nonuni-form cathode emission111,113 but they share a common indict-ment of imprecise machining and/or fabrication of the cath-ode surface. Experiments are currently underway to evaluatealternative cathode fabrication procedures to see if this bothisolates the cause and provides a solution to the problem.17

3. Dense beam impact physics

Based on the above discussion, compact, high powersources of mmw-to-THz radiation and HPM sources share aneed for very high current density electron beams. We nowexamine another challenge associated with high density elec-tron beams: The effects of electron beam impact on collec-tors and electromagnetic circuit walls which are kept in closeproximity for strong beam-wave interaction.

Electron impact on collectors and structure surfaces canproduce secondary electrons, device heating, and form plas-mas on the collector or anode, leading to decreased effi-ciency or pulse shortening.47 Primary or secondary electronsthat are reflected back into the electromagnetic interactioncircuit can alter the beam-wave interaction and reduce thedevice efficiency and linearity.114 This has motivated re-examinations of the phenomenon of secondary electronemission.115 One key finding of this recent work is that thesecondary electron yield is time-dependent, with an evolu-tion time scale of minutes to hours during continuous beambombardment. The evidence strongly implicates the role ofmere monolayer films of gaseous or hydrocarbon adsorbates,consistent with findings reported elsewhere.116 This is alsoconsistent with the ab initio cathode studies103 that illustratethe importance of monolayer or partial monolayer adsorbatefilms on the surface binding energy of low energy electrons.

Meanwhile, the high power densities in the electronbeams of HPM and compact mmw-to-THz high powersources pose special challenges for dramatic and potentiallydestructive surface heating. In HPM devices, dense beamimpact on the anode or collector surfaces leads to release ofadsorbed gases111,117 and ultimately plasma production thatlimit the achievable operating pulse length.47,118 In compactmmw-to-THz high power sources, dense beam impact on thecircuit or collector can lead to irreparable, single-shot dam-age, even with short pulses during initial device testing.

The issue is quantitatively understood by estimating theheating of a surface due to volumetric energy deposition byelectron beam impact. To simplify the calculation withoutsacrificing significant quantitative accuracy, a beam with asquare cross-sectional area of 2Rb�2Rb is assumed, as de-picted in Fig. 3. It is assumed that the beam electrons deposittheir energy uniformly in a volume with the same area as thebeam and over a depth determined by the electron stoppingrange119 in the material of interest. Generally, these stoppingranges are quite shallow, ranging from 0.4 to 300 �m forincident electron energies between 10 and 500 keV, allow-



ing for the formation of large thermal gradients inside theimpact surface with high power density electron beams.

For approximate estimates with such large thermal gra-dients, radiative heat dissipation is neglected in comparisonwith thermal conduction. The justification for this can beunderstood by recognizing that the radiative heat flux will beupper-bounded by the radiation rate of a blackbody surface,or

Prad PBB = SBT4, �7�

where SB=5.7�10−12 W /cm2 /K4 is the Stefan–Boltzmannconstant. Restricting our interest to temperatures less than orequal to the melting temperature of copper, which occurs atT�1080 °C yields Prad15 W /cm2. In contrast, we are in-terested in understanding the effect of surface impact bydense electron beams transporting energy fluxes in excess ofhundreds of kW /cm2. Therefore, we choose to ignore thesmall corrections associated with radiative heat dissipation.

To estimate the peak surface temperatures, we solve thetime-dependent thermal diffusion equation with volumetricheat sources, assuming thermal diffusivities that are indepen-dent of temperature and space. Solution of the heat transferequation using these approximations is straightforwardly ac-complished using a Green’s function method120 and the resultcan be expressed as

T�0,0,0,t� =VJ

d�mcp�

0

t

d erf� tr

4��2

erf� tz

4� ,

�8�

where tr= Rb2 / D , tz= d2 / D , D= K / �mcp , �m is the mass den-

sity, cp is the specific heat, K is the thermal conductivity ofthe target material, and erf is the error function.

Sample calculations with Eq. �8� for various candidateconductor materials confirms the fact that copper representsthe best material choice. Although other refractory materialssuch as tungsten or molybdenum can tolerate significantlyhigher temperature without melting, this advantage is morethan offset by copper’s superior thermal conduction proper-ties. This theoretical result is supported by many empirical

observations, including Refs. 117 and 121. Figure 4 illus-trates two illustrative quantitative results obtained with thisapproximate model.

The first result observed in Fig. 4 is an estimate of thetheoretical maximum surface temperature �at x=y=z=0� fora 1 �s pulse as a function of the incident beam energy, as-suming a current density of 330 A /cm2. Also shown in Fig.4 is the energy flux, in J /cm2 that results in short-pulse,single-event melting, again as a function of incident beamenergy. In general, the conclusion is that for beam voltagesbetween 1 and 500 kV, electron beam impact energy fluxdensities of 1–20 J /cm2 are sufficient to melt copper �orother� surfaces in �1 �s. This theoretical estimate is in goodagreement with experience obtained with electron beam ab-lation, for example.122 Correspondingly, electron beams withpower flux densities of 1–20 MW /cm2 represent a high riskof single-event surface melting within pulse lengths of 1 �s.

A vivid illustration of the challenge this poses �and onesolution� for high power mmw and THz VEDs is the 1 kW,94 GHz �w-band� klystron development program at the Stan-ford Linear Accelerator Center �SLAC�. The first approachinvolved a permanent-periodic-magnet �PPM� focused roundor pencil electron beam.123 It required the propagation of a110 kV, 2.4 A, 0.25 mm radius electron beam through anelectromagnetic circuit consisting of an array of microfabri-cated klystron cavities. Using the best available numericalmodeling tools and methods at the time, the magnetic focus-ing optics nevertheless included an unanticipated small quad-rupole leakage field error near the exit of the circuit. As aresult, beam interception occurred over an impact area of�1 mm2 with a power density of �1 MW /cm2. As shown inFig. 5, the single-event damage threshold was indeed ex-ceeded in a single 5 �s pulse, and the circuit was irreparablydamaged.

Electron beam optics design codes have improved sig-nificantly, and it is likely that the same result would beavoided upon a second try. However, this points out the ab-sence of margin for error arising when VED designs arechosen around beam power densities of 1 MW /cm2 or

FIG. 3. Illustration of the idealized configuration assumed for estimating therapid temperature rise of conducting circuit or collector surfaces due toimpact by a high-power-density electron beam.

FIG. 4. �Color online� Calculated peak surface temperature vs beam voltage�circles and solid blue line� in copper after 1 �s of impact by an illustrative330 A /cm2 electron beam using the approximate model described in thetext. Also shown is the calculated energy flux vs beam voltage �squares anddashed red line� for which melting is predicted in 1 �s or less.



greater. In the meantime, the SLAC 94 GHz klystron sourceprogram adopted an entirely different approach which will bediscussed shortly.

4. Another look at magnetic focusing: Emittance

Having identified the risk to compact, high power mmw-to-THz regime VEDs of circuit interception by high currentdensity electron beams, it is prudent to re-examine the con-ditions required for robust confinement of the electronbeams. The prior discussion emphasized only the effect ofspace charge confinement. However, one should also con-sider the effect of electron transverse or thermal energy,sometimes characterized by the beam’s emittance �. As dis-cussed in Ref. 84, beam emittance acts as a transverse pres-sure gradient force due to random thermal transverse kineticenergy in the beam electrons. To account for this additionaldefocusing force, Eq. �4a� should be amended as84,124,125

�c2 � 2�p

2 + 2u

a2 �2

�2. �9�

In the above equation, a is the beam radius and u is the beamvelocity. In Fig. 6 we have recalculated the magnetic fieldthat would be required to focus the electron beam for the100 W, 20 kV TWT with beam radius a�0.1�0 of Fig. 2which was scaled from 5 GHz to 200 GHz. This time, how-ever, it was assumed that the electron beam’s emittance wasequal to 3 mm mrad, a value typical of a well-designed elec-tron gun.126 Below 50 GHz, the effect of this emittance isnegligible compared to space charge defocusing forces, butabove 100 GHz, the emittance term dominates and extrapo-lates to impractically large magnetic fields, i.e., B�10 kG,above 200 GHz. The fact that emittance determines the fo-cusing requirements for THz regime VEDs instead of spacecharge has been observed elsewhere, including Ref. 127.

It is common to describe the nonlaminarity of conven-tional microwave tube electron beams using emittance.128

However, emittance is an inconvenient parameter for inter-device comparisons because the value of � in a beam is afunction of the beam voltage, which one may wish to use as

a design variable. One alternative is to utilize the beam-voltage-independent normalized emittance,84 �n=��, where� is the normalized velocity, �=u /c, � is the relativisticenergy parameter, �=1 /�1−�2, and c is the speed of light.This is generally the preferred electron beam nonlaminarityparameter in accelerator and FEL literature, for example. Ofcourse, for nonrelativistic electron beams, �n��. Anothergood alternative is to re-express Eq. �9� in terms of anequivalent transverse beam temperature,84 kT�,

�c2 � 2�p

2 + 8kT�

ma2 � , �10�

where �2= �kT� /eV�a2. The effective beam temperature willbe a function of several influences, including the physics ofthe electron emission from the cathode �especially from thecathode edges129�, cathode surface roughness,130 and themagnetic and electrostatic optics that guide and compress theelectron beam from the cathode into the electromagnetic cir-cuit. To illustrate the quantitative relationships, for a 20 kVbeam with a radius of 0.15 mm and an emittance of3 mm mrad, the normalized emittance is �n=0.84 mm mrad,and the equivalent transverse beam temperature iskT��8 eV.

Figure 7 shows the minimum �Brillouin� magnetic fieldrequired to confine our canonical 100 W TWT’s 20 kV,a=0.1�0 5-to-200 GHz scaled electron beam for transversebeam temperatures varying between 0 and 10 eV. Lookingat Fig. 7, it is important to remember that robust focusing isnecessary to avoid dense beam interception, and that robustfocusing requires a magnetic field higher than the minimumBrillouin focusing field.69 From this, we can infer from Fig.7 that high power density mmw-to-THz VED sources willrequire submillimeter-sized beams with low-transverse-temperature, e.g., kT�� 1 eV. We can appreciate the chal-lenge this poses given that for thermionic cathodes, surfaceroughness130 alone may contribute several eVs to kT�.Hence, future research will need to emphasize not only high

FIG. 5. �Color online� Illustration of final 1 kW, 94 GHz klystrino finalcavity aperture before �left� and after �right� impact by a 3 �s electron beamwith �1 MW /cm2 �printed with permission, G. Scheitrum �2007��.

FIG. 6. �Color online� Magnetic field required to focus the 20 kV,increased-radius version of the scaled 100 W traveling wave tube of Fig. 2.The dashed �red� line shows the required magnetic field to confine the elec-tron beam space charge. The solid �red� shows the required magnetic fieldneeded to confine both the space charge and the kinetic pressure associatedwith nonzero emittance.



current density, long-lived cathodes, but also cathodes andbeams with low-emittance or transverse temperature. Also, itwill be important to develop cathodes amenable to micron-precise alignment and integration with the electromagneticinteraction circuit and magnetic focusing fields. This presentsan interesting dilemma with FEA cathodes. On the one hand,the fact that FEA cathodes are photolithographically micro-fabricated allows for straightforward introduction of align-ment features and precise assembly procedures that may notbe possible with conventionally fabricated, miniature thermi-onic cathodes. On the other hand, FEA cathode emissionleads to very high beam emittance. Recently developed, low-gate-voltage FEA cathodes,91 for example, appear to gener-ate electron beams with relatively high characteristic trans-verse equivalent temperatures131 of kT��10 eV.

For completeness, it is noted that electron microscopesprovide the lowest emittance electron beams, with normal-ized emittances �n�10−3 mm mrad. This, however, isachieved only with extremely small transverse beam andcathode radii �1 �m�, very low total current, and signifi-cant electron gun volume devoted to elaborate, high-orderelectron-optics-correcting lens systems. With similar sacri-fices on volume and supporting systems requirements, verylow emittance electron beams, �n�10−1 mm mrad can alsobe produced using intense rf electric field-assisted photo-emission and needle cathodes.132 However, neither of theseapproaches appear to be realistic electron beam source alter-natives for compact and mobile THz-regime VEDs.

III. THE DISTRIBUTED ELECTRON BEAMALTERNATIVE

Even with extremely low-emittance cathodes, the resultsof Fig. 7 suggest that approaches relying on scaling lowerfrequency architectures to high frequencies by reducing thelateral beam and circuit dimensions may be impracticalabove a few hundred GHz. An alternative approach that hasattracted significant recent interest80,133,134 is to recognize

that as the frequency increases, it is only necessary to reduceone lateral dimension commensurate with the shrinkingwavelength, allowing the other lateral dimension to remainlarge. This approach exploits distributed electron beams,such as sheet beams135,136 or arrays of multiple beams thatprovide large electron currents for high power mmw-to-THzradiation generation, while keeping the electron current den-sity low.

The idea of sheet beams is not new, but for many yearsthey were avoided because of their vulnerability to curling,filamentation, and breakup via diocotron instability in uni-form magnetic focusing fields.137,138 An illustration of thephenomenon is provided in Fig. 8�a�. However, during thelate 1980s and 1990s experimental and theoretical studiesidentified stable alternatives using periodic magnetic fields tofocus sheet beams,135,139,140 as illustrated in Fig. 8�b�. Sev-eral of these studies136,140 established alternatives for focus-ing the beam in the wide transverse dimension as well as thenarrow dimension.

With the recent interest in compact high power sourcesof mmw and THz radiation, researchers are taking a newinterest in distributed beam devices.107,133,134 In particular,considerable progress has been recently made towards a1 kW, 94 GHz klystron source by abandoning the pencilbeam architecture of the klystrino123 in favor of a sheet-beamconfiguration.80 Using offset pole-piece, periodic-cusped-

FIG. 7. �Color online� The minimum required magnetic focusing field toconfine the illustrative 100 W, 20 kV, increased radius TWT �of Fig. 2�scaled from 5 GHz to 1000 GHz for different values of transverse beamtemperature.

FIG. 8. Results of particle-in-cell simulations of a sheet electron beam fo-cused by �a� a solenoidal, and �b� a periodic-cusped �or planar PPM� mag-netic field with a 3 mm magnet period. For this example, the beam voltagewas 10 kV, and the current density was 90.9 A /cm2. The magnetic fieldstrength was 1200 G in both cases. The intervals between frames are givenin multiples of the characteristic 3 mm magnetic period length along thepropagation dimension. The solenoidal-focused beam exhibits diocotron in-stability, whereas the periodically focused beam is stable. �Reprinted withpermission from Figs. 8�b� and 8�c� of Ref. 136. Copyright 1999, AmericanInstitute of Physics.�



magnetic focusing,140 researchers have demonstrated over90% beam transmission of a 74 kV, 3 A beam without anycircuit damage,80 i.e., below the single short-pulse damagethreshold.

Of course, it is still possible to use uniform, or solenoi-dal magnetic field focusing of distributed beams, providedthat the device length is less than the distance over whichbeam curling, filamentation, or emittance growth occurs dueto diocotron instability. We know that the instability growthrate scales with the time scale,140–143

t� �a

vE�B� a

B

E�

�c

�p2 . �11�

Therefore, the risk of beam distortion or interception is low-est for large magnetic fields and low beam charge densities.More detailed analyses have been conducted using particle-in-cell simulations, including startup from noise and bench-marking against non-neutral plasma �Penning trap�experiments.143,144 However, various specific factors willcontribute to the growth rate of the instability in a particularsheet beam VED configuration, including conducting wall�image charge� stabilization, finite temperature effects, low-level plasma stabilization, initial beam uniformity and align-ment, beam density bunching due to beam-wave interactions,etc. Therefore, as a practical matter there is still room for amore precise quantitative knowledge, obtained from experi-ments and simulations of the “safe” propagation distance forsheet electron beams in high power THz regime VEDs. Itshould also be noted that theoretical studies suggest that edgedistortion effects of sheet beams in solenoidal magneticfields may, in some cases, be ameliorated using electrostaticelectrodes.145 This approach deserves more careful scrutinyin experiments or design analyses, to determine for whichsituations the improvements in sheet beam transport justifythe added complexity of additional high-voltage electrode�and bias power supplies� in the beam transport and interac-tion channel.

IV. SUMMARY AND REMAINING CHALLENGES

Impressive advances have been achieved in both funda-mental and applied research of issues critical to advancingthe power of vacuum electronic sources in two categories ofdevices: those intended for short-pulse HPM applicationsand those required for mmw, and THz applications requiringcompact high average power sources. Examining the rangeof this research spanning three orders of magnitude in fre-quency, one can identify both common challenges as well ascontrasts. Both, for example, have high electromagneticpower density issues, but rf breakdown, a problem forf �100 GHz, is not a concern for the foreseeable future forcompact high power sources above 100 GHz. Both will ben-efit from further research of electron-surface interactionphysics, for an understanding of beam impact, surface heat-ing and adsorbed gas atom release, secondary electron emis-sion, and high current density �J�10 A /cm2�, long-livedcathodes.

Meanwhile, for f �100 GHz, new methods for highlyprecise circuit fabrication are being investigated, with micro-

EDM and DRIE looking best above 200 GHz while EDMand high-speed mechanical machining look attractive forf �100 GHz. Beyond mere circuit fabrication, however, in-tegral components such as low-reflectivity, ultrahigh-vacuumwindows, input-output coupling structures, and high-gain an-tennas become much more difficult to fabricate and assemblefor compact sources with f �100 GHz, and new researchwill be needed to address this. In spite of space charge de-pression limits on usable cathode current densities and re-maining concerns for cathode lifetime, the need for highlyprecise alignment during fabrication, may still favor theeventual adoption of FEAs over miniature thermionic cath-odes. Both HPM and compact high average power mmw-to-THz sources face challenges with the impact of high-power-density electron beams on anode, collector, or circuit walls.For HPM devices, the solutions will probably need to em-phasize surface conditioning and surface coatings to delaythe release of adsorbed gas atoms. For mmw-to-THz devices,some of the most promising approaches include low emit-tance, distributed electron beams to enable robust magneticconfinement with B10 kG fields.

As mentioned, the FEA cathode holds particular interestfor such high frequency devices. Lifetime limits due to arc-ing at the cathode are being addressed by a combination ofcareful electron gun design, high vacuum control, carefulconditioning protocols, and redesign for low gate voltageoperation.91 This last feature, which promises to dramaticallyincrease FEA cathode lifetimes, appears to exacerbate thehigh beam emittance associated with single-gate-electrodeFEA cathodes. However, exciting possibilities for ultralow-emittance electron beams include FEA cathodes that includean integral, additional focus electrode to achieve equivalenttransverse beam temperatures146–148 of kT��1 eV. Other in-teresting approaches include beam cooling techniques thatreduce high emittance in the narrow dimension of a sheetbeam in exchange for increased emittance in the other, lesscritical wide dimension or by increasing the thermal spreadin the longitudinal degree of freedom.149

Figure 9 shows the impact that realization of a distrib-uted beam device with 10 A /cm2 and an effective transversetemperature of 1 eV would have on the required magneticfocusing field for our canonical example of the compact highpower TWT scaled from 5 GHz up to 1 THz, using a beamhalf-thickness �narrow dimension� of a=0.05�0. Comparingand contrasting Fig. 9 with Fig. 2 illustrates the dramaticmagnetic focusing field reductions to be gained from low-emittance sheet electron beams in narrow transport channels.

From Fig. 9, we see that a transverse beam temperatureof 10 eV leads to unacceptably large magnetic focusingfields for frequencies above �400 GHz, especially when oneallows for an extra margin of B�1.5–2.0�Bmin for robustfocusing. However, achieving a 10 A /cm2 sheet beam withkT��1 eV leaves plenty of margin for strong magnetic fieldfocusing and interception-free beam confinement. In fact, thecriterion of Eq. �10� for beam confinement applies equallywell to solenoidal or periodic magnetic field focusing, wherein the latter case one substitutes the rms magnetic field in-tensity for the calculation of the electron cyclotron fre-quency. The significance of this in the context of Fig. 9 is



that compact periodic magnetic focusing configurations us-ing permanent magnets are generally unable to achieve the10 kG magnetic flux densities that “permanent magnet sole-noids” are capable of. Maximum magnetic flux densities aremore likely limited to �4–5 kG due to mutual demagneti-zation, although further studies of planar periodic configura-tions may be needed to determine the precise limits. In anycase, Fig. 9 indicates that the combination of moderate cur-rent density sheet beams with low-emittance cathodes wouldallow for stable sheet beam confinement with periodic mag-netic focusing, well into the THz regime of frequencies.

There are still a large number of topics requiring furtherstudy. The full complement of possible electromagnetic cir-cuits has yet to be investigated for compatibility with theneeds of compact, high power VED sources. As discussedabove, there is still a great deal of additional study needed onlong-lived, low work-function, uniformly emitting, low-emittance, high current density cathodes. Recognizing thatpermanent magnet solenoids may be easier to assemble thanperiodic magnet focusing configurations, careful experimen-tal studies are needed to obtain quantitatively precise knowl-edge of the onset distances for significant distortion of dis-tributed �sheet, multi-� beams due to diocotron instabilitywith aggressive benchmarking for computational designtools. Innovations are needed for providing mode control andcompact input and output coupling in overmoded electro-magnetic circuits compatible with distributed electronbeams.

Finally, fundamental research questions remain regard-ing the physics of Ohmic current losses in electromagneticcircuit walls at frequencies above 100 GHz. For frequenciesbelow 100 GHz, probably the most important characteristicof an efficient VEDs waveguide circuit is a strong beam-wave coupling or high interaction impedance.9,69 Above100 GHz, however, the circuit’s Ohmic losses become equalin importance or even more important than the interaction

impedance. Therefore, accurate knowledge of the effectivehigh frequency or rf conductivity of bulk metal and metalfilm surfaces is crucial for successful design and fabricationof waveguide components and VED sources of THz regimeradiation.

Below 30 GHz, where the skin depth is on the order ofmicrons or greater, the effective rf conductivity of metals andmetal films is generally considered to be well understood andequal to bulk material values. In the millimeter-wave rangebetween 30 and 100 GHz, there is ample experimental datato show there is a significant decrease in the effective rfconductivity of metal surfaces. This is generally attributed toincreasing sensitivity to enhanced electron scattering fromsurface microroughness41,150,151 as the skin depths becomesmaller than one micron, �1 �m. In the THz regime, how-ever, there are only sparse experimental data attempting tomeasure the pure material intrinsic rf conductivity and theresults are in significant disagreement.152–155 For example,the question of whether the intrinsic conductivity is anoma-lously smaller than or simply equivalent to the classicalvalue at THz frequencies is a topic of current controversy,with experimental and theoretical data and arguments sup-porting both views.152–159 There have been attempts to de-velop analytic theories for the intrinsic surface resistance, butthey all necessarily make simplifying assumptions. Mean-while, there is no fundamental theoretical model for the ef-fect of surface conditions on the surface resistance at THzfrequencies. Similarly, there are no systematic experimentalstudies of the effects of realistic surface conditions such asroughness or polycrystalline microstructure, on rf surfaceconductivity at THz frequencies. This gap in knowledgehandicaps the systematic design of advanced THz regimedevices, forcing researchers to adopt a trial-and-error ap-proach, guessing at the Ohmic losses to be expected prior tofabricating and testing a device.

Prospects for addressing these and other challenges forincreasing the power of compact VED sources are very posi-tive, owing to the successful emergence of powerful compu-tational modeling codes. In fact, many of the advances in thelast 10 years in high power VED sources owe partial or fullcredit to the accurate, predictive capabilities of these codes.An extremely important factor in the reliability and accuracyof these codes has been a persistent and aggressive attentionto detailed experimental benchmarking. The list of codes andmodeling capabilities used on a regular basis in the researchand design of high power microwave-to-THz regime VEDsis very large. Even a summary discussion is beyond thescope of this paper, but two recent, comprehensive reviewsinclude Refs. 160 and 161. The general categories of codesthat have been crucial in advancing the power and perfor-mance of high power microwave-to-THz-regime VEDs in-clude 3D electromagnetic codes �static and time-dependent�,3D electron optics �trajectory� codes, 3D particle-in-cellcodes, 3D thermomechanical codes, and 3D ab initio codesfor modeling surface physics. It would also be remiss not toacknowledge that many of these codes now available todaywere not a result of mere chance, but rather owe their genesisto the persistent investment and leadership of particular in-dividuals and institutions.160,161

FIG. 9. �Color online� Minimum magnetic field required vs frequency toconfine a 20 kV, 10 A /cm2 sheet electron beam in a transport channelwhose narrow dimension scales as �0.1�0 for two values of transversekinetic temperature.



V. CONCLUSIONS

There are many potential applications for compactsources of high power mmw-to-THz frequency electromag-netic radiation, including high resolution radar, high data ratecommunications, concealed weapon or threat detection, re-mote high resolution imaging, chemical spectroscopy, deepspace research and communications, and biomedical diag-nostics. Vacuum electronic sources have intrinsic advantagesfor compact high power sources at high frequencies from100 GHz to �1 THz. However, there are still unsolved chal-lenges associated with high power density that are similar tochallenges facing lower frequency, short-pulse HPM sources.In particular, to advance both types of sources will requirestructures and strategies to handle higher power densities andhigh current electron beam generation and confinement.

Recent research breakthroughs include novel methods toprecisely fabricate miniature electromagnetic circuits, under-standing rf breakdown, new high current density cathodesand improved understanding of cathode emission physics.Remaining challenges include delaying rf breakdown forHPM sources, innovating compact mmw-to-THz circuit con-figurations that are precisely dimensioned yet able to handlehigh average power, improving the lifetime of long-lived,low-emittance, uniformly emitting, high current density cath-odes, and advances in the confinement and impact manage-ment of compact, high power electron beams. Prospects forsolutions to these and other challenges are positive, owing tothe emergence of powerful three-dimensional computationalmodels for electromagnetics, beam optics, beam-wave inter-actions and particle kinetics, and surface physics.

ACKNOWLEDGMENTS

There are literally over 100 colleagues and studentswhose generous intellectual and supportive contributionsmade this paper possible. It is therefore, unfortunately, notpossible to mention each one individually. Many of themhave participated or collaborated with two United States De-partment of Defense Multidisciplinary University ResearchInitiative Consortia Programs: 1999–2004, Innovative Micro-wave Vacuum Electronics and 2004–2009, Nanophysics ofCathodes and Breakdown. These consortia programs wereadministered by the United States �U.S.� Air Force Office ofScientific Research �AFOSR�. In addition to the AFOSR, theauthor is grateful for generous financial support of his ownrecent research contributions by the U.S. Army Research Of-fice, the University of Wisconsin, Northrop Grumman Cor-poration, and L3-Communications, Electron Devices Divi-sion.

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