scenario for output pulse shortening in microwave generators driven by relativistic electron beams

246 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 26, NO. 3, JUNE 1998

Scenario for Output Pulse Shortening in MicrowaveGenerators Driven by Relativistic Electron Beams

Nikolay F. Kovalev, Vladislav E. Nechaev, Michael I. Petelin, and Nikolay I. Zaitsev

Abstract—At the present time, microwave generators drivenby high current relativistic electron beams are not baked andsealed, so their inner surfaces are densely covered with moleculesof gas and oil. This allows the production of microwave pulsesof 10�8 s to 10�7 s duration, but not longer.

A microwave pulse termination scenario is speculated asfollows: 1) Electrons oscillating in the strong RF field near themetallic surfaces multiply owing to the secondary emission (themultipactor effect); 2) the multipactor electron bombardmentstimulates desorption of gas molecules from the metallicsurfaces; 3) the gas undergoes avalanche RF breakdown; and4) the resultant plasma stops microwave generation and, sinceelectron-ion recombination is slow, does not allow the RF fieldto revive.

At the gigawatt power level, the characteristic time of such ascenario is much shorter than that of the cathode and collectorplasma expansion and electron beam instabilities.

The energy output parameters of relativistic electronmicrowave generators can be (and usually are) improved athigh pulse repetition rates. A more radical improvement ispossible using the technology typical for high vacuum tubes,i.e., baking and sealing.

Index Terms—Desorption of molecules, microwave pulse short-ening, multipactor, RF breakdown, RF produced plasma.

I. PULSE SHORTENING’S MAIN CAUSE: PLASMA

I T IS well known [1]–[7] that in microwave generatorsand amplifiers driven by high-current relativistic electron

beams the radiated microwave pulse is usually shorter (some-times much shorter) than the voltage-current pulse duration(Fig. 1); the higher the microwave power, the shorter themicrowave pulse. This can be illustrated with a diagram relatedto relativistic BWO’s operating in the TM mode in X-band[1]–[5] (Fig. 2). The radiated energy from all these microwavegenerators is about the same (10–20 J).

There are many causes for the microwave pulse shorteningobserved in different relativistic electron devices (see review[8]). In this paper we will try to analyze asymptotics ofmicrowave generators, where focusing magnetic fields aresufficiently strong to minimize relativistic electron beam in-stabilities and the appearance of a halo around the beam.

To begin, note the hysteresis in Fig. 1. The microwave pulseis appreciably delayed relative to the voltage front and disap-pears long before the voltage goes down. The microwave field

Manuscript received October 17, 1997; revised April 16, 1998. This paperwas presented in part at the International Workshop on High Power MicrowaveGeneration and Pulse Shortening, Edinburgh, U.K., June 1997.

The authors are with the Institute of Applied Physics, Russian Academy ofScience, Nizhny Novgorod, 603600 Russia.

Publisher Item Identifier S 0093-3813(98)04930-3.

Fig. 1. Typical oscillograms of diode voltageU (dashed) and microwaveradiation powerP (solid), ([1, by authors’ agreement]).

Fig. 2. RF pulse duration� versus peak microwave powerP for a set ofX-band BWO’s operating at TM01-mode: 1: [1], 2: [2], 3: [3], 4: [4], 5: [5].

seems to generate its own termination, and this mechanismremains long after the pulse.

Even though the microwave pulse is short, it is much longercompared to any pure electron time, in particular, to the timeof the beam electrons’ transit through the interaction spaceand to the period of electron oscillations in the microwavefield. Therefore, it is reasonable to seek an explanation forpulse shortening in an electron-ion, i.e. plasma process. Theplasma hypothesis [8] explains, in particular, the irreversibilityof microwave termination since the electron-ion recombinationtime is very long compared to the pulse duration.

The plasma may appear in any part of the high powermicrowave tube (Fig. 3), but what kind of plasma is reallyfatal?

II. PLASMAS NOT DANGEROUS OREASILY AVOIDABLE

Simple estimates suggest that jointionization of residual gasby a relativistic electron beam (REB) and the RF field in the

0093–3813/98$10.00 1998 IEEE

KOVALEV et al.: SCENARIO FOR OUTPUT PULSE SHORTENING 247

Fig. 3. Cherenkov microwave generator (BWO): 1: cathode, 2: cathodeplasma, 3: solenoid, 4: diaphragm plasma, 5: RF interaction space, 6: REB,7: collector, 8: desorbed neutrals, 9: collector plasma, 10: output window.

interaction space is negligible at standard vacuum conditions.In addition, in a special experiment with an X-band BWO, themicrowave pulse envelope proved to be affected by residualgas breakdown only at gas pressures exceeding 10Torr [9].

In the atmospherebehind thewindow the ionization fre-quency exceeds the electron attachment frequency if the mi-crowave power density is greater than 1 MW/cm[10]. But inorder to reach the critical density, the breakdown plasma needstime. So, for example, in the X-band microwave generators,RF power densities up to 2–3 MW/cmare possible if thepulse length is about 10 ns [11]. Still, higher microwavepower densities can be transmitted through the window if theair is replaced with SF, which can tolerate a power densityup to 5 MW/cm even for microsecond pulses [12]. As forthe vacuum side of the window, in conventional microwaveelectron devices the breakdown occurs at power densities near10 MW/cm [13]. Thus, RF breakdown can be avoided byusing a sufficiently large diameter window.

Much more serious limitations are causedby plasma appear-ing at metallic surfaces of the microwave generator(collector,RF interaction space, diaphragm; see Fig. 3).

III. D ESORPTION OFGASES FROMDIRTY WALLS

It is necessary to emphasize that, to date, in all microwavegenerators driven by high-current relativistic electron beams,high voltage insulators and gaskets made of organic materialswere used. Such systems do not allow baking, so their innersurfaces are characteristically “dirty,” covered with moleculesof gas and oil (up to 10 cm in a monolayer).

During the microwave generator operation, the moleculescan be desorbed owing to wall heating by electrons andto immediate stimulation by electron impact. The desorbedmolecules consist of gas which expands with velocity

cm/s.The gas may be ionized by electrons of the main relativistic

beam, by multipactor electrons and, as a secondary effect,by electrons produced with from ionization. In the resultingplasma the temperature of electrons is usually much higherthan that of ions . Therefore, the quasineutral plasmaexpands with the ambipolar diffusion velocity

(1)

where is average velocity of electrons. In the RF interactionspace and at the collector the parameters are quite differ-ent and, so, plasma generation process need to be analyzedseparately.

IV. PLASMA GENERATION INITIATED BY REB

Thecollector wall bombardmentby the REB (Fig. 3) resultsin gas desorption owing to the wall heating and immediatestimulation by the electron impact.

The heat-stimulated molecular desorption becomes signifi-cant when the wall temperature increase becomes comparableto the absolute room temperature, that is to 300C. Basedon an elementary understanding one can estimate that thecollector temperature rises 100in 100 ns if the current densityis 100 A/cm and in 10 ns if the current density is 1000 A/cm.

The electron impact-stimulated desorption of moleculesis practically inertialess. One electron causes desorption ofat least one molecule for impact energy100 keV andgreater [14]. Therefore, 100 A/cmcurrent produces up to10 molecules/cm in a volume adjacent to the collectorwall, expanding with the thermal velocity of electrons, about10 cm/s.

Usually, the electron impact stimulation prevails over thethermal one, but in a more general case, molecules may bedesorbed owing to a combination of these effects.

The gas composed of desorbed molecules is ionized first bythe REB, and at a subsequent stage by electrons oscillating inthe RF field. The second process, the RF gas breakdown, isavalanche in character: the electron density increases exponen-tially in time and saturates only when the plasma frequency

approaches the RF frequency.Usually in the collector region, which is much wider than

the RF interaction space, the RF field is relatively small,10V/cm for an X-band oscillator. In the plasma near the collector,the thermal velocity of electrons is close to their RF oscillationvelocity. So, according to (1), the collector plasma expansionis relatively slow, 10 cm/s, and only sometimes causes adistortion of the output wave pattern.

In the microwave generators under consideration, a partof the REB can bombard not only the collector, but othersurfaces. At the cold cathode, the REB is emitted froma dense plasma which is time dependent. The higher themagnetic field used to transport the REB, the less is theplasma transverse expansion velocity: beginning with1 Tthis velocity decreases below cm/s [15]. However, aperipheral part of the REB expands faster then the cathodeplasma owing to:

• the diocotron instability;• transverse defocusing by the RF field [8];• reflection of electrons from the collector;• reflection of electrons from a virtual cathode which occurs

for a low energy fraction of the spent REB transported tothe collector not sufficiently close to the metallic wall.

In a number of experiments [8], [16] the above effectswere found to cause a heavy electron bombardment of thediaphragm (cutoff neck) and the slow wave structure (Fig. 3),which produces a plasma in the RF interaction space and,finally, results in pulse shortening.

Note that some of these effects can be excluded or weakenedby a proper tapering of the wall profile, combined with a deepmagnetic decompression of the spent REB in the collectorregion. In the optimized configurations, the wall bombardment


Fig. 4. Configuration of fields and REB in the RF interaction space:H0:guiding magnetic field,E0: REB electric field.

Fig. 5. Functional relationships in plasma generation process near dirty wallof RF interaction space.

by electrons can be reduced and, so, the microwave pulse canbe lengthened by use of a sufficiently high magnetic field.

However, in microwave generators of gigawatt power thepulse lengthening with the increase of the magnetic fieldencounters a saturation. For instance, Fig. 2 shows that theplasma preceding the microwave pulse is too weak to preventthe generation of a very high RF power. On the other hand,the rise time of the REB-produced plasma should be com-mensurable with the part of the voltage-current pulse durationpreceding the RF pulse end and, so, is much longer than thehind front of the RF pulse. Thus, it is evident that the RFpulse shown in Fig. 1 is shortened by an effect not related tothe bombardment of walls by the REB or its halo.

V. PLASMA GENERATION INITIATED BY MULTIPACTOR

Plasma generation in the RF interaction space (Fig. 4) in theabsence of REB bombardment may be envisaged in connectionwith the diagram shown in Fig. 5. The primary reason for theprocess seems to be themultipactor which is described asfollows [17]: a cloud of electrons driven by and oscillatingin synchronism (resonance) with an RF field builds itself upby secondary emission resulting from electron impact witha surface. A number of theoretical and experimental studiesdevoted to the “classical” multipactor between two metal wallswhen motion is perpendicular to the metal surface revealed thatit is a rather delicate, weak effect. In this case, the secondaryemission yield only slightly exceeds 1 within a relativelynarrow band of electron energies, from 50 eV to 2500 eV[18]. However:

• the multipactor can develop near a single metal wall ifthere is a force returning electrons to the wall [19], [20];such a force may be provided by the static magnetic fieldused to transport the REB and/or the static electric fieldproduced by the REB;

• if the electron incidence to the surface is oblique, thesecondary emission yieldexceeds 1 at electron energies

Fig. 6. Disposition of desorbed molecular layer (�M), multipactor electronsand plasma (�p) near discharge surface.

Fig. 7. Plasma density versus product of RF durationt and desorptionprobability g for various RF fields, E! . 1: 200 kV/cm; 2: 300 kV/cm; 3:400 kV/cm; 4: 500 kV/cm.

up to tens of kilovolts (including a rather broad energyinterval where ) [18].

In real microwave generators (Figs. 3 and 4) there is a widevariety of local configurations favorable for combinations ofthe two mentioned effects [21], which makes the multipactora rather robust phenomenon. At the primary stage of themultipactor, the number of electrons in the bunch oscillatingnear the wall grows exponentially. But after a few tens of RFperiods the bunch is saturated because the Coulomb interactionof electrons shifts them out of the resonant RF phase. Atsaturation, the electric field produced by the oscillating bunch

is small compared to the main RF field (e.g., if ,then in strong magnetic field [17], and,accordingly, the number of electrons per square centimeterof the oscillating multipactor bunch is cm ).Therefore, the multipactor cannot interfere with the microwavegeneration (amplification) process immediately.

However, the multipactor electrons stimulate desorption ofmolecules from the “dirty” metallic surface. These moleculescomprise a gas that is ionized by multipactor electrons and,as a secondary effect, by electrons from the resulting plasma.The plasma electrons, in turn, oscillating in the strong RF field,interact with the metal surface, producing secondary electrons,and causing desorption of molecules from the “dirty” wall thatare subsequently ionized.

The desorption of gas is described by the equation

(2)

where and are the gas molecular density and plasmaelectron density, respectively, is RF period, is angle


TABLE IBREAKDOWN CHARACTERISTICS FOR X-BAND BWO

between magnetic field and discharge surface, andis thenumber of desorbed molecules per number of impact electrons.If the gas molecules absorbed at the metal surface comprise amonolayer with cm , the desorption probabilitygrows from molecule/electron at electron energiesof 100 eV [22] to molecules/electron at electronenergies of 100 keV [14]. At intermediate energies there areno experimental data published.

Since the thermal velocity, , is relatively small, thedesorbed gas is confined to a thin layer near themetal surface (Fig. 6).

The gas ionization is described by the equation

(3)

where is the ionization cross section due to plasma elec-tron with average velocity . The valueof reaches a maximum of cm /s atelectron energies of several keV, and then slowly decreases.The ionization with cross section is caused by secondaryelectron bunches produced in the multipactor process. Theymove with increasing velocity from the metal surface, andtheir energies do not exceed keV within the molecularlayer. The ionization cross section has a broad maximum at

cm within 100–1000 eV energy range. Therefore,the value of may be regarded as fixed ( cm ).Returning toward the surface, electrons have energies aboutsome tens keV, so their ionization action is negligible. Inthe plasma, the thermal velocity of electrons is comparablewith their oscillatory velocity, the temperature of electrons ismuch higher than that of ions and the plasma expands with theambipolar diffusion velocity (1). Therefore, the plasma layeris much thicker than the gas layer (Fig. 6).

The process, described by the system of “feedback” (2),(3), with an initial condition of develops (Fig. 7)in three stages:

• in the first stage, terms with on the right-hand sideof (2) and (3) are negligible and the plasma densitygrows proportionally with time;

• during the second stage, the term with on right-handside of (2) is still negligible and the plasma densitygrows exponentially;

• during the final stage, terms with become negligiblecompared to those with in (2) and (3), soand the plasma density grows in an explosive manner,proportionally to which tends to infinity at afinite time .

If all of the coefficients in (2) and (3) are assumed constant,the dependence of the plasma density on time takes the form

(4)

Accordingly, the “explosion” time is

(5)

Of course, (3) and (4) become invalid a little before the“explosion” moment , when the plasma density reaches thevalue critical for the operating frequency (see Fig. 7). Sucha plasma changes the electrodynamic configuration of the RFinteraction space and makes the microwave generator inoper-able. When the RF field disappears, the plasma recombinesonly after s.

The above assumptions and equations may be applied tothe set of X-band BWO’s described in [1]–[5]. Relevantestimates (in which the angle is taken 45) are presentedin Table I. Microwave pulse shortening in experiments [1]–[5](see Fig. 2) may be explained with the above “theory” (see thelast line of Table I) if the probability of molecular desorptioncaused by the electron bombardment of the “dirty” wall isassumed to increase slowly from0.03 to 0.1, when theRF field grows within the interval of consideration. Theseestimates of are in rough agreement with those previouslypublished [14], [22].

A rather convincing illustration to the above scenario ispresented in the paper [1] describing an experiment with avariation of electrical regimes in one microwave generatorwith fixed geometrical parameters. Fig. 6 of that paper showsthat the microwave pulse duration is inverse proportional tothe output power.

However, further studies would be helpful for additionalverification of the above theoretical model.


VI. M ICROWAVE GENERATION PECULIARITIES WITH

COLLECTOR IN THE RF INTERACTION SPACE

The above analysis concerns microwave generators drivenby electron beams propagating through an RF interactionspace. However, some microwave generators (the magnetron,the MILO, the grid vircator, the Reltron, etc.) operate with aprinciple that implies the bombardment of the RF interactionspace walls by the primary electron beam, which causes muchmore intense desorption of molecules than the multipactorelectrons. The primary beam bombardment not only accel-erates plasma development, but, as an example, in X-bandmagnetrons the anode segments become severely deformedafter 100 pulses of 10 ns duration.

Nevertheless, at relatively low frequencies the microwavegenerators with a collector in the RF interaction space canproduce relatively high powers in relatively long pulses [23].

VII. M ETHODS TO IMPROVE ENERGETIC PARAMETERS

A method to make the microwave pulse longer and morestable rests with pulse repetitive operation. In an experimentalradar using a transmitter based on an X-band 0.5 GW 5 nsBWO [24], after the initial system switching on, the firstmicrowave pulses have20% scatter of amplitudes, but thenafter 1000 pulses the scatter reduces to1%.

And, of course, the most radical enhancement of energeticparameters of relativistic electron microwave devices may beachieved with the traditional high-vacuum technology includ-ing baking and sealing.

ACKNOWLEDGMENT

The authors are grateful to Dr. E. B. Abubakirov, Dr. F. J.Agee, Dr. J. P. Brasil, Dr. G. Caryotakis, Dr. Y. Carmel, Dr.G. Faillon, Dr. E. V. Ilyakov, Dr. I. S. Kulagin, Dr. D. Parkes,and Dr. E. Schamiloglu for useful discussions, to referees fortheir valuable comments, and to Dr. J. Gaudet for his help inediting this paper.

REFERENCES

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[2] Yu. F. Bondar, S. I. Zavorotny, A. L. Ipatov, N. I. Karbushev, and N.F. Kovalev, “Study of microwave radiation of relativistic carcinotron,”Kratkie Soobshcheniya po Fizike, no. 2, pp. 3–7, 1982 (in Russian).

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[10] A. D. Mc. Donald,Microwave Breakdown in Gases. New York: Wiley,1966.

[11] Y. Saito, “Surface breakdown phenomena in alumina RF windows,”in Proc. SPIE XVI Int. Symp. Discharges and Electrical Insulation inVacuum, Moscow-St. Peterburg, Russia, 1994, vol. 2259, pp. 512–517.

[12] Yu. P. Raizer,Gas Discharge Physics. Berlin, Germany: Springer, 1991.[13] G. Faillon, private communication.[14] R. E. Clausing, “Release of gas from surfaces by energetic electrons,”

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accelerators,”IEEE Trans. Plasma Sci., vol. 19, pp. 683–689, Oct. 1991.[16] O. T. Loza, P. S. Strelkov, and S. N. Voronkov, “Plasma in high-power

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[17] A. F. Aleksandrov, L. G. Blyachman, S. Yu. Galuso, and V. E. Nechaev,“Near-wall secondary-emission RF discharge in high power electronics,”in Relativistic High-Frequency Electronics. Issue 3, Gorky, Russia: IAP,pp. 219–240, 1983 (in Russian).

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[20] L. G. Blyachnan and V. E. Nechaev, “Near-wall secondary-emission RFdischarge in an insulating magnetic field,”Zh.T.F., vol. 54, no. 11, pp.2163–2168, 1984 (in Russian).

[21] , “Near-surface secondary emission vacuum RF discharge inmagnetic insulation conditions,” inProc. SPIE XVI Int. Symp. onDischarges and Electrical Insulation in Vacuum, Moscow-St. Petersburg,Russia, 1994, vol. 2259, pp. 534–537.

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[23] J. Benford, “Magnetrons and other crossed-field devices,” inHigh PowerMicrowave Generation and Applications, E. Sindoni and C. Wharton,Eds. Bologna, Italy: SIF, 1992, pp. 299–307.

[24] G. Mesyats, M. Petelin, M. Osipov, B. Wardrop, C. Clutterbuck, andD. Clunie, “Experimental high power, short-pulse radar,” inProc. 4thMicrowave RF Conf., London, U.K., 1996, pp. 11–17.

Nikolay F. Kovalev was born in Russia on February27, 1943. He has been with the University of NizhnyNovgorod, Nizhny Novgorod, Russia, as a Professorsince 1996, and also with the Institute of Ap-plied Physics (IAP), Russian Academy of Sciences,Nizhny Novgorod, as a Head of Laboratory.

His field of scientific interest is the high powermicrowave electronics and applied electrodynamics.

Vladislav E. Nechaev was born in 1933 inGorky, USSR (now Nizhny Novgorod, Russia).He graduated from Gorky State University in 1955.He received the Ph.D. degree in 1964 and the Sci.D.degree in 1992.

He worked at the Radio-Physical ResearchInstitute and since 1977 at the Institute of AppliedPhysics (IAP), Russian Academy of Sciences,Nizhny Novgorod, Russia, as a Senior Researcher.His field of scientific interest is the high powerelectronics: intense relativistic electron beams,

cross-field electron devices, secondary emission RF discharge (multipactor)and breakdowns.


Michael I. Petelin was born on March 7, 1937. In1959 he graduated from the University of NizhnyNovgorod, Russia.

For several periods of time he worked at theUniversity of Nizhny Novgorod (presently as aProfessor), and also at the Radio-Physical ResearchInstitute and later at the Institute of Applied Physics(IAP), Russian Academy of Sciences, Nizhny Nov-gorod (presently as a Head of Division). In 1997,he was a visiting professor at the University ofCalifornia, Davis, and simultaneously a visiting

scientist at Stanford Linear Accelerator Center, Stanford, CA. His field ofactivity is the high power microwave electronics and its applications to plasmaphysics, radar, and accelerations.

Dr. Petelin was awarded with the State Prize of the USSR in 1967 for studyof the stimulated cyclotron radiation of relativistic electrons, which resultedin elaboration of the gyrotron. In 1996, he received the K. J. Button Medaland Prize for contribution in the millimeter and IR waves. He is a memberof Russian Nuclear Society and of the councils “Physical Electronics” and“Plasma Physics” of the Russian Academy of Sciences.

Nikolay I. Zaitsev was born on June 6, 1944.He received the Ph.D. degree from the Instituteof Applied Physics (IAP), Russian Academy ofSciences, Nizhny Novgorod, Russia, in 1983.

He was an Engineer and a Senior Engineer atthe Research Radiophysical Institute, Gorky, USSR(now Nizhny Novgorod). Since 1977, he has beenwith the IAP. He was a Researcher at IAP and iscurrently a Senior Researcher. He was also DeputyHead of the Relativistic Microwave Electronics Di-vision and Chief Engineer of the Department of

Plasma Physics and High-Power Electronics. Since 1977, he has been Leaderof the research group. Until 1973, he was connected with problems of formingthe helical electron beams and of generating the power radiation of millimeterand submillimeter wavelength. Since 1974, he has worked with relativistichigh-current microwave electronics. He gives significant consideration to theproblem of limitation of pulse power and duration in relativistic sources ofelectromagnetic radiation.

scenario for output pulse shortening in microwave generators driven by relativistic electron beams

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