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HDL-TR-2172')February 1990CO

<N Experimental Demonstration of an ElectromagneticallyiPumped Free-Electron Laser with Cyclotron Harmonic

Idlers

by R.Alan Kehs DTJCYuval Carmel #f-k I-ECT EWilliam W. Destler MR 09Victor L. Granatstein

U.S. Army Laboratory CommandHarry Diamond Laboratories

Adelphi, MD 20783-1197

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Adclphi, MD 20783-1145 6.37.3,11 TITLE lirncul Secuity) Classoha lion)

Experimental Demonstration of an Electromagnetically Pumped Free-Electron Laser with Cyclotron Harmonic Iders

'2. PERSONAL AUTI-ORIS)

R. Alan Kehs (HDL). Yuval CarmeI, William Desticr, and Victor L. Granatstein (University of Maryland)

'9 ASTAC (COnu CODE revrs diBJEsTTEiy ar'dinv onV~ revrs ofoc rW&'r adidnif y a,)u

by an intense relativistic electron beamn (625 kV, 2 kA, 100 ns). A grating spectrometer was used to scan the microwavefrequency spectrum from 50 to 130 GHz, and powerful high-frequency radiation was observed in the form of an array ofregularly spaced peaks. The positions of the peaks were observed to Iiary with the magnitude of the axial guide magneticfield in a manner which agrees with the dispersion relationship $,-..- -

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R. Alan Kehs (202) 394-4143 1SLCHD-NW-RS00 Form 1473, JUN 88 Preoi edkorz are o&w~eo SECURITY CLASSIF(CA','N OF TH.S PAGE

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19. Abstract (cont'd) -;' " .-

due to a three-wave FEL inzcraction in which the cyclotron beam waves act as -idlers" where (o,, ) and (a., k_) arethe frequency and wa%e number of scattered and pump %,avesQ ,is the relativistic electron cyclotron frequency, I is theharmonic number, and r, is the axial beam ,elocity. eiietlharmonic numbers l= I and 5 to 14.while sweepingthrough the frequency ranges from 7 to 18 GHi and 50 to 1 i0 GHz. The results exhibitexcellent agrement with a simple

theoretical model of the three-wave interaction. / '

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F ... . .

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Cotet

Page1. Introduction ................................................................ 7

2. Theory..........................................................................................1.1

2.1 Calculation of Expected Frequency Shifts ................................................ 112.2 Frequency Spectra .......................................................................... 20

2.2.1 Magnetostatic Wiggler .............................................................. 202.2.2 Electromagnetic Wi2glcr ........................................................... 21

2.3 The CHARM Interaction ................................................................... 23

3. Experimental Configuration ..................................................................... 23

3.1 Introduction and Outline.................................................................... 233.2 The Intense Relativistic Electron Beam................................................... 243.3 The Backward Wave Oscillator Pump Wave ............................................. 273.4 Support Systems ............................................................................ 293).5 Diagnostics................................................................. . .............. 29

3.5. 1 Beam Diag-nostics ................................................................... 293.5.2 Microwave Diagnostics .............................................................. 323.5.3 Support Systemn Diagnostics........................................................ 35

3.6 Experimental Operation. ................................................................... 35

4. Results and Discussion............................................. -"--........................ 37

4.1 Introduction................................................................................. 374.2 The Measured High-Frequency Spectrm ..........m...................................... 374.3 The EM-Pumped FEL Model ............................................................... )9

4.3.1 Expected Spectrum.................................................................. 394.3.2 Comparison of Theory and Experiment............................................ 424.3.3 Power Estimates ...................... .............................................. 44

4.4 Other Modes................................................................................. 454.4.1 Forward Pump Wave FEL Interactior ............................................. 454.4.2 The CHARM Model ........................................................... 48

4.5 Frequency Scaling .......................................................................... 50

5. Conclusions....................................................................................... 51

References ........................................................ ..................................... 53

3

....- ......-$ - ' - -

Contents (cont'd)Page

Appendix A.-The Dragon REB Generator .......................................................................... 59Appendix B.--The BWO Pump Wave ................................................................................... 63Appendix C.-The Microwave Grating Spectrometer ............................................................ 69

D istribution .................................................................................................................................. 73

Figures

1. Basic magnetostatically pumped free electron laser (FEL) interaction ............................... 82. Basic electromagnetically pumped FEL configuration ........................................................... 113. Wave direction conventions in two-wave electromagnetically pumped FEL

interaction m odel ............................................................................................................ 144. Dispersion diagram for two-wave FEL interaction ............................................................ 165. Stokes diagram of three-wave scattering relationship in electron rest frame with

a space charge idler .......................................................................................................... 186. Idealized dispersion diagram for electromagnetically (EM) pumped FEL with

space charge idler ............................................................................................................ 197. Idealized dispersion diagram for EM-pumped FEL with cyclotron harmonic idlers ...... 208. Plot of interaction frequency versus applied magnetic field for several harmonics

of EM pumped FEL with cyclotron harmonic idlers ....................................................... 229. Basic experimental configuration used for EM pumped FEL experiments ...................... 24

10. Principal wave traffic in the EM-pumped FEL expcriment ............................................... 2511. Idealized electron-beam geometry .................................................................................... 2612. Rippled-wall slow-wave structure ...................................................................................... 2713. P!ot of power versus applied magrnetic field strength for BWO pump wave ..................... 2814. Schematic drawing of applied magnetic field system ......................................................... 2915. Diagnostic positioning on the EM-pumped FEL experiment ........................................... 3016. Detail of D and 13 electron-beam voltage and current probes ............................................ 3017. Typical experimental data showing voltage, current, BWO pump wave,

high-frequency radiation, and witness plate .................................................................. 3218. Idealized electron beam cross section ................................................................................ 3319. Schematic drawing of low-frequency high-power microwave diagnostic system ............. 3420. Measured frequency spectrum from 80 to 120 GHz for an applied field of 9.89 kG ...... 3721. Measured frequency spectrum from 50 to 125 GHz for an applied field of 10.3 kG ...... 3822. Measured frequency spectra from 80 to 125 GHz for applied fields of 9.89 and

10.3 kG showing frequency shift caused by a change in applied field ........................... 3823. Dispersion diagram for EM-pumped FEL with cyclotron harmonic idlers

with theoretical intersection points marked with circles ................................................ 4024. Stokes diagram of three-wave FEL interaction with backward propagating

pump wave, slow cyclotron harmonic wave idler, and scattered radiation along'dow n-shifted" branch .................................................................................................... 42

4

Figures (cont'd)page

25. Dependence of frequency peaks on magnetic field for odd harmonic numbersfrom I through 15 ................................................................................................................. 43

26. Dependence of frequency peaks on magnetic field for even harmonic numbersfrom 4 through 14 ............................................................................................................ 43

27. Illustration of model used to construct crude estimate of high-frequencymicrowave power levels ................................................................................................ 45

28. Low-harmonic interaction frequencies versus applied magnetic field fordown-shifted branches of EM-pumped FEL with cyclotron harmonic idler waves ..... 47

29. Frequency versus applied field for CHARM interaction ................................................... 4930. Low-harmonic interaction frequencies versus applied magnetic field for down-shifted

branches of CHARM and EM-pumped FEL with backward pump wave andcyclotron harm onic idlers ................................................................................................ 49

31. Plot of frequency versus gamma for several interaction models ....................................... 51

Tables

1. Interaction frequencies of an electromagnetically pumped FEL withcyclotron harmonic idlers for an applied field of 10 kG ................................................ 46

2. Interaction frequencies for a cyclotron harmonic auto-resonant maser withan applied field of 10 kG ............................................................................................... 48

5

1. Introduction

In previous experiments Carmel [11 and Denisov f2J have recorded high-frequency microwave radiation that was attributed to a two-stage back-ward-wave oscillator/free-electron laser (FEL), but this report repre-sents the first careful study of the detailed frequency spectrum Dro-duced by such a device. In these experiments, a backward wave os-cillator driven by a high-power relativistic electron beam was used toproduce a high-intensity pulse of microwave radiation that propagatesantiparallel to the electron beam. The ensuing microwave spectrumwas then scanned from 50 to 130 GHz, with the unexpected resultthat the spectrum was composed of an array of regularly spaced peakswhose positions varied with changes in the applied magnetic guide field.The measured data show excellent agreement with a three-wave FELinteraction model utilizing a backward propagating pump wave andcyclotron harmonic idler waves. Although this is primarily an experi-mental report, a brief derivation and discussion of the interaction modelwill be presented.

First, some perspective is provided by a brief review of the classicalFEL (magnetostatic wiggler) and its historical development. This isfollowed by a short description of the electromagnetically pumped FEL.Later sections provide an "in depth" look at the experimental setup, tilebasic theory that was used to describe the interaction, and a completediscussion of the results.

The most basic model of a FEL is a two-wave interaction in whicha transverse, periodic, magnetic field induces oscillations on an intense,energetic electron beam. In the configuration shown in figure 1. anelectron beam is injected along the ---axis so that it vill pass throughthe spatially varying magnetic field generated by the permanent barmagnets labeled N and S. At the point of interaction, the electrons haverandom phase and radiate incoherently. However, a ponderomotiveforce is produced by the action of the induced v. (often called thequiver velocity) and the radiation or scattered wave. That is, from theLorentz force law,

-nd Ie Iv . B, , (1)

where e is the electronic charge, v. is the quivei velocity, and B, isthe magnetic component of the electromagnetic wave. This -i-directed

7

Output

igg'er 8 radatonm~gnets

magneNE

SoentVO N - e-bearn

Injectede-beamr Interaction

lengthI

Figure 1. Basic magnetostatica'ly pumped free electron laser (FEL)interaction.

force acts to push the electrons into axial bunches. The ponderomo-tive force causes some electrons to be accelerated and others to bedecelerated. If the axial velocity v:o is such that more electrons aredecelerated, then the average energy of the electrons decreases and theradiation field is enhanced. Clearly, this process will proceed only whenthe oscillating electrons are properly synchronized with the electromag-netic wave. The synchronism condition also leads to a relation for thefrequency spectrum of the ideal magnetostatic model given by

w = 9(l + 0)y'yck., (2)

where 10 is the normalized axial beam velocity, c is the speed of light,and k,, = 2r/\,, where A, is the magnetic wiggler period. This isequivalent to A = A,/2= (.3)

The above analysis is appropriate for a low-density electron beam inwhich single particle equations can be used to describe the interaction-this is called the Compton regime. For higher density electron beams,collective effects become important and beam waves or "idlers" can par-ticipate in a three-wave interaction-this is called the Raman regime.FEL devices are also categorized by the type and strength of the "wig-gler." Although a magnetostatic wiggler was used in the above example,any field that leads to a transverse velocity modulation of the electronbeam can be used as a wiggler. Several other types of wigglers havebeen proposed-including electrostatic (3], magnetic quadrupole 4-5],and of course the electromagnetic pump wave, which will be discussedmore thoroughly in this report.

8

This classical FEL was first described by Motz in 1951, when heproposed a method for generating high-frequency radiation via the syn-chrotron radiation from electron oscillations in a periodic magnetic field[6). Although Motz conducted several experiments to test his theory[7], the first practical devices to exploit this approach were developedin the late 1950's and early 1960's by R. M. Philips, who called his de-vice the "ubitron" [8-10]. While propagating a 110- to 140-kV electronbeam through a linear wiggler, Phillips was able to generate 1 MW ofpower at 10-percent efficiency by operating the device as an amplifier(gain - 13 dB). Because of strong competition from gyrotrons, ubitronresearch was halted in 1964, but has recently been restarted [11].

Theoretical analyses of FEL configurations began to appear in thelate 1960's and early 1970's (12-16]. These papers featured quantummechanical models to predict that FEL-t'pe devices could be oper-ated as both oscillators and amplifiers at infrared and millimeter wave-lengths; that is, they could "fill the gap" by providing high-powersources in the region between conventional lasers and conventional mi-crowave tubes. Interest in these calculations led researchers at StanfordUniversity to the operation of both a Compton FEL amplifier [17] in1976 and an oscillator (18] in 1977.

Although Compton FEL experiments have been successful in gener-ating respectable power levels at very high frequencies, they are inher-ently low-gain devices which require long (many wiggler period) interac-tion regions and large sophisticated particle accelerators to produce thehigh -1 beams. As a result, researchers began to study millimeter-waveFEL's which operated in the Raman regime, where higher gain andefficiency can be achieved. The first experiments in the Raman regimeused high-power cyclotron maser radiation as tne pump field for theFEL interaction 119]. Initially, a 2-MlV, 30-kA electron beam was usedto generate 1 MW of power in the 400- to 500-pzm range [20]. Later amagnetostatic undulator was used on a 1.2-MV, 25-kA electron beam toproduce -1 MWfV of power at 400 um [21]. Further experiments at theNaval Research Lab (NRL) generated as much as 100 MW of power atfrequencies ranging from 50 to 100 GIIz (22;231. Recently, more sophis-ticated experimental setups [24,25] with better quality electron beamshave begun to show excellent agreement with the more sophisticatedthree-dimensional (261 and nonlinear [27,281 theories that have beendeveloped.

Although difficulties in generating a sufficiently strong pump wavehave kept the electromagnetically pumped FEL in the background, thescheme remains attractive because of the larger frequency shift factor

associated with electromagnetically pumped rather than magnetostati-cally pumped FEL's. That is, for an electromagnetically pumped FEL,

w = 4-y ,, (4)

in the high -t limit where space charge effects have been ignored and w,is the pump frequency. Note that this frequency shift is twice as largeas the factor for the magnetostatically pumped case given in equation

(3).Interest in electromagnetically pumped FEL's has recently been

rekindled by the development of high-power backward wave oscillators(BWO's) [1,29-311. These devices produce an intense electromagneticwave that propagates counter to the electron beam and acts as an elec-tromagnetic pump on the electron beam. In experiments at NRL [1],a 500-MW, 12.5-GHz pump wave was used to produce radiation atfrequencies greater than 140 GIIz via an FEL interaction. Similar ex-periments by Denisov et al. using a 500-MW, 10-GlIz pump and a 600-to 650-keV, 3- to 5-kA electron beam have produced as high as 10 MWat frequencies between 50 and 100 GHz [2,321. This report focuses on adetailed examination of the high-power-microwave frequency spectrumproduced by an electromagnetically pumped FEL.

From the schematic representation shown. in figure 2, we see anelectron beam guided through a slow-wave structure by an applied B..The BWO pump wave grows and interacts with the electron beam untilit reaches the slow-wave structure's beam entrance section which hasa cutoff frequency beyond that of the 8.4-GHz pump wave. The pumpwave is then reflected and propagates back with the electron beamthrough the slow-wave structure. As the electron beam exits the slow-wave structure, the divergence of the axial field causes the beam to-dump" on the side walls while the reflected pump wave continues topropagate to the right, where it passes through a region of high powermicrowave diagnostics that are not shown on the figure. In addition toguiding the electron beam, the applied magnetic field also enables thegrowth of cyclotron waves on the beam, which will play an importantrole in the analysis of the data.

Theoretical models and descriptions of the experiment are intro-duced in section 2. Section 3 provides a, detailed overview of the ex-perimental setup that was used to record the data used in this report.This is followed by a presentation and discussion of the experimen-tal results. The final section summarizes key points, conclusions, andrecommendations for future work.

10

Magnetic field coils

Anular electron edump

beam dump

Waveguide cutoffregion

Figure 2. Basic electromagnetically pumped FEL configuration.

2. Theory

2.1 Calculation of Expected Frequency Shifts

Although a presentation of the full theory of the electromagneticallypumped FEL is beyond the scope of this report, the portions of theoryneeded to predict the simple output spectrum are presented in detail.First. some perspective is provided by a brief review of the "classicaFmagnetosi atic FEL. This is followed by a description of the electromag-netically pumped FEL and, finally, a discussion of some related pro-cesses such as the cyclotron harmonic autoresonant maser (CIIARNI).

The most basic model of a FEL is a two-wave interaction in whicha transverse. periodic, magnetic field induces oscillations on an intense,energetic electron beam. Again, using the configuration shown in fig-ure 1. an electron beam is injected along the --axis so that it will passthrough the spatially varying magnetic field generated by the perma-nent bar magnets labeled N and S. At the point of interaction, theelectrons have random phase and radiate incoherently. However, aponderomotive force is produced by the action of the induced t'. (of-ten called the quiver velocity or wiggler velocity) and the radiation orscattered wave. That is. from the Lorentz force law,

Fpon= -lelvi x B,, (4I)

11

where Ild is the electronic charge, v± is the wiggler velocity, and B, isthe magnetic component of the scattered electromagnetic wave. This--directed force acts to push the electrons into axial bunches. The pon-deromotive force causes some electrons to be accelerated and others tobe decelerated. If the axial veloc:ity of the beam v20 is such that moreelectrons arm deceierated, then the-average energy of the electrons de-creases and the radiation field is enhanced. Clearly, this process willproceed only when the oscillating electrons are properly synchronizedwith the electromagnetic wave. This synchronism condition leads di-rectly to a relation for 'the expected frequency spectrum of the idealmagnetostatic FEL model.

One may evaluate this simple model by approximating the magne-tostatic "pump" field as

B; = B, cos(ktz), (5)

where k, = 2-/L, L is the magnet period, and B, is the magnitude ofthe "pump" field. The equW,'n of motion is given by

-,m, = -IV, x B. - v. x B,. v > V,, (6)c

where -y is the relativistic factor, m is the mass of an electron, and c isthe speed of light. With B_- = 0, this has solution

= =- cos(kz)v.o -.- -Pvo cos(k,,z), (7)

which may be integrated by assuming that ww = k,,v:o and z = v.ot.This yields a form for the wiggler velocity given by

,= .. sin(ww) (S)

The radiation field may be expressed as

B, = B, (sin(k,z - wt)], (9)

where (w,, k,) represents the frequency and wavenumber of the scat-tered wave. The ponderomotive force then becomes

=pond sin(k,:z) sin(kz - wt). (10)

c WwBs

The sine factors that comprise the phase portion of the ponderomotiveforce can now be combined via trigonometric identities to yield a term

12

proportional to cos(k,,z + k.z -wet). Clearly, the ponderomotive forcewill reach a maximum when the phase (?k = k,,,z + kz - wt) - 0. Thephase velocity of the ponderomotive wave can then be written as

VphF k()Vh= T,,, + k,"

Synchronism between the electron beam and the ponderomotiveforce can be achieved when vph ; v.o, the velocity of the electron beam.For a relatively high-frequency wave (wavelength is small compared toexternal boui;daries), one may write w, = kc, where c is the speed oflight. This may be combined with equation (11) to give

k/9 = k,(I - ), (12)

where /= v. 0/c. Noting that -, the relativistic factor, may be ex-pressed as --' = (1 +3)(I - 0), and recalling that A = 2-,/k, one mayrewrite equation (12) as

A, = 2I3(1 +3)" (13)

For 13 - 1, this reduces to the familiar form

A, = (14)92

For an electromagnetic pump, By -+ Bosin(koz-wot), which resultsin a ponderomotive force phase of

qC = k,,z + k,z + wt - wot. (15)

The resulting phase veloci.y is thenWi,, - Wi

Uph = k,,, + k, - Vo. (l.)

Again assuming that w, = kc and now writing that w k, vp, onecan combine to form [33]

= 72(1 + 3)(1 + V,o/vh)w. . (17)

With the usual but not always justifiable assumptions that 3 1 andVph- c, this expression can be further reduced to the familiar

w3 47 y . (2S)

13

A more rigorous derivation of the quiver velocity or wiggler velocityproduced by an ciectromagnetic pump wa,e can be found elsewhere[3.l. 351. As expected, the more rigorous derivation produces an identi-cal reiation for the frequency of the scattered radiation.

These same results may also be reached by modeling the processas Compton scattering in the rest frame of' the electron beam. Thesinusoidally varying magnetostatic pump field of figure 3 will appearas a Doppler-shifted propagating electromagnetic wave in the electronbeam's rest frame. This wave will scatter off the electron beam andbe frequency-shifted a second time by the transformation back to thelaboratory frame of reference.

In the laboratory frame, incoming pump and scattered waves arerepresented by (,, k,,) and (w. k,). In the rest frame of the electronbeam,

and

( -) -, ,). (19)

The overall wave traffic is shown in figure :3. One may 'now constructthe invariant .I-vector as in Jackson [361,

-c = (', k). (.20)

C C

Up-scattered wave

Oow.scattered €,ave xJ , %,-

Pump wave

Electron beam

Figure :3. Wave (Iir,,tui() conventins il two-waveelectromagnetically pimped EL t ineraction model.

i.1

Then with K as the lab frame and K' as the beam frame, one can lookat the waves in the rest frame of the electron beam. That is,

c c cW __ W V.0

! = + ,k3 ), (21)c C c

where v. 0 is the velocity of the electron beam. Now use the Manley-Rowe equations to write

yfkw.j + V.O -)=-(. W'

Vph C

or

W, = 72(l + 0)(1 + V:o/Vph)W ,. (22)

For the static magnetic wiggler case, w,,, - 0 and one uses w., kc toeliminate w, and form

yj(v-kw) = -y(k~c - -v,

which can be combined to form the familiar

A, = -y'( (23)-7 - ( + 9)"*

Since these experiments are generally carried out inside some sort ofwaveguide, the electromagnetic mode w, = kc should be replaced with

k kc 2 + W, (24)

where w. is the effective cutoff frequency c'f the waveguide. This cor-rection will be used in later sections and in all computations.

It is also constructive to consider a gra)hical representation of theFEL interaction. From equation (16) with vph = v:o, the resonancecondition yields

W- = (k, + k,,.) vo. (25)

This resonance condition may then be plotted with the electromagneticwaveguide mode represented by equation (24) to obtain the dispersionrelation shown in figure .1. The two points (w, k) where the electronbeam and the scat tered wave are in phase represent points where energycan be transferred hlom the beam to the wave.

15

This analysis is appropriate for low-density electron beams in whichsingle particle equations can be used to describe the interactions-theCompton operating regime of the FEL. For higher density electronbeams, collective effects become important and beam waves or idlerscan participate in a more complicated three-wave interaction-the Ra-man regime. The FEL described in this report operates in this high-beam-density Raman regime.

The basic approaches used to describe the expected output froma two-wave FEL interaction can be expanded to include the effect ofthe third "idler" wave that participates in the three-wave interactiondescribed in this report.

A high-current electron beam propagating through an axial mag-netic field can support several types of "beam idlers" [37]. The mostimportant types (and the only ones that will be considered in this re-port) are the negative-energy space-charge and cyclotron waves. Theyare called negative energy because they grow in amplitude as energyis lost from the electron beam. They are important because they canact with the pump wave to efficiently couple energy from the electronbeam into "scattered radiation" via a three-wave interaction.

In the following approach adapted from Marshall (38), the three-wave FEL is studied in the rest frame of the electron beam by con-sidering the interaction of the pump wave (w',, k,,), the scattered wave-

ws=ww+kwVl +ksVI

kOown.sh ,ll - .

Figure 4. Dispersion diagram for two-wave FEL interaction.

16

(P, ks), and the beat or idler wave (w!, k!). The idler arises from theponderomotive bunching of the electrons via the force term given by

ee[ ' w') x B'(w )], (26)

where the primes indicate the shift to the clecton-beam rest frame. Theinteraction occurs at ,J - w', leading to

I I I

andk "=k,,, k. (27)

for the idler frequency and wavenumber. The idler or "beat" waveis always present, but the interaction is enhanced whenever ;4 corre-sponds to a "natural" resonant frequency of the system; i.e., w, = w(.or w' = P', where C4' and Q' represent the beam plasma frequency andelectron cyclotron frequency in the rest frame of the electron beam.The three-wave interaction w' =J - w, is referred to as "stimulatedRaman scattering." This effect is shown graphically in figure 5. Theparallelogram relating the three waves follows from equation (28):

and

= k +(2)

It should be remembered that this model is somewhat oversimplified.involving uncoupled modes of the system. The actual situation is farmore complicated when mode coupling occurs.

One can also study the effect of idler, by their influence on the beamresonance condition. Based on equation (2$). there will be an additionalshift in the frequency, so that the resonance rondition becomes

,.:, - .', = k,x 1 + k,3 1 - -'tdkr, (29)

The derivation of similar relations is described in more detail in thereferences [39].

For the space charge idler, the relation becomes

w, -w,,. k,,. vl + k,' u - ,-6. (30)

where -b is the plasma frequency of the electron beam and the +1-signs represent the positive/negative-energy space charge waves whichare als discussed in detail by Johnson (391. This effect has recently

17

been the subject of careful study in a series of Raman regime experi-ments at the Massachusetts Institute of Technology [2-5.401.

A typical dispersion relation foi a Rainan-regimce FEb with spacecharge idlers is shown in figure 6. The wave of interest is the slowor negat ive-energy space charge wave because it is able to grow by"feeding" from the electron beam's kinetic energy. Note that two inter-sections or operating points are possile which yield both an up-shiftedan(] a down-shifted frequency. Although (in a classic FEL) one is gener-ally interested in the up-shifted frequency, the down-shifted frequencyis also present [25.10].

Although frequency shifts in Raman FEI1 experiments have beenLraced to cyclotron wave idlers [41-13], the observation of cyclotronwave harmonics as idlers is new .11.Their effect is similar to the spacecharge waves with a resonance condition now given by

-W~ k,,c 0- + +3 '11 + (31)

where Do is the effective relativistic electron cyclotron frequency and t

is the integer harmonic number.

Pump

Scattered wave

WX Stokes- Anti-StokesIdler

Figure 5. Stokes dJiagramn of thrce-wave scatterig relationship inielectron, rest frame with a space charge idler.

18

The idealized dispersion relatio: for the electromagnetically pumpedFEL with cyclotron harmonic idlers is shown in figure 7. There aretwo allowed interaction frequencies for each harmonic number: an '-up-shifted' frequency and a "down-shifted" frequency. Actually, both in-teraction frequencies are generally higher than the pump frequency, butconvention refers to the higher as up-shifted and the lower as down-shifted. In figure 7, the up-shifted interaction frequencies are markedwith squares while the lower down-shifted interaction frequencies aremarked with circles. in either case, the interaction would be expectedto produce a spectrum of regularly spaced peaks. In the next section,these predicted frequency spectra are examined in more detail, withemphasis on their dependence on the applied axial magnetic field.

Cyclotron .'OS2kS,2.,CO2wave idler

Fast space-charge . Cyclotronwaeilrwave idler

Slow space-charge wave idler

"- Oown-shit

-- kw - A

Figure 6. I(Iealized dispersion diagram for electromagnetically

(EM, pumped FEL with space charge idler.

19

WS

7

-

:,z ks

Figure 7. Idealized dispersion diagram for EM pumped FEL with

cyclotron harmonic idlers.

2.2 Frequency Spectra

In order to facilitate the calculation of the frequency spectra in differentphysical situations, a result will be derived in terms of an effective k,that will be designated krff. Plots of the spectra from appropriatephysical situations will be used to analyze the experimental results in alater section. In the equations that follow, Oil = v:o/c and -1F"2 = 1 - 2

will be used to emphasize the difference between 911 and Pph.

2.2.1 Magnelostatic WViggler

For the case of the magnetostatic wiggler, it is appropriate to use equa-tion (25) with w, = 0 and k,, = keff. This can be combined withequation (21) to yield

W, lckfi7I 2 1 ,ll ,- ) 2 ], (32)

20

which is the normal result for a magnetostatic pump wave. Note thatthe +/- signs represent the up/down-shifted branches of the interac-tion. that is, the square/circle points in figure 6.

2.2.2 Electromagnetic Wiggler

In order to cast the electromagnetic wiggler in terms of keji, it is usefulto define i3h =_ -w/k' c, where the minus sign indicates that the pumpis a backward propagating wave. This can be used in conjunction withequation (25) to produce

S[I A] (33)

which may be used in equation (32) to produce a spectrum given by

Note that when the waveguide effects are ignored (w, = 0), equation(34) reduces to the familiar result given by equation (22). These formu-las must now be further "corrected" to include the effects of the beamidlers.

For space charge waves, the effective k, is given by

ke %C -= [ + Ah] 13' (35)

where the +/- signs represent Lhe fast/slow, positiv e/negative-cnergyspace charge waves. In actual practice, only the slow. negative-energywave can help to couple the beam's kinetic energy into electromagneticradiation.

For cyclotron harmonic idlers, the effective k, is given by

,.= f [I + , (36)

which results in a frequency spectrum represented by

21I) + c [1 (37)

21

377CFTTT7 M- ,WWO' 'M T-,77 V-71 T. 77517777r", -

Alt hough they were in~clude(] in thle calculations, thle wavcguide cffects(wyc) are generally unnoticeable at high frequencies (C > .1); however.they miodify the filial totern) by

AlI -oil W.(1 + 91119p ) 2]1/2 (38)

It is important to note that equation (37) gives the expected frequencyspcctra versus app~lied mnagnetic field for four situations of interest: a"b~ackward"' propagating pumpl wave, up or down shifted, and "for-ward" proIpagat~ing punip wave, upl or down shifted. The forward pumnpsituation miust, be conside-red b~ecause (as we see in the next section)in the actual experiment, thle M3VO punip wave reflects off a section ofwvaveguide beyond cutoff (near thle dliode) and] travels back through thleslow-wave sticture before finally exiting the systemi.

A graphical representation of equation, (37) is provided in figureS. If a value is chosen for thle applied magnetic field, a whole spec-trumn of regularly sjpced p~eaks should be produced by the interaction.Althoughi some of the even harmonics were omnitted from thle plot inorder to reduce overcrowding, all hiarmionics should be present in anyspectrumn which canl he rnodel,. by equation (37).

180 I

15 1 010

404

120

60 20 30 4

AooI,d ax~i guide magnetic field (kG)

Figure 8. Plot of interaction frequenicy versu1s

aplied( inanetic fieio for several hiarmionicsof EM-pumiped FEL with cyclotron harmocnicidiv'rs.

2.3 The CHARM Interaction

In the previous section, cyclotron harmonic waves were considered idlersin a three-wave FEL interaction. The possibility also exists that theobserved spectrum of regularly spaced high-frequency peaks may bedue directly to the cyclotron waves-with no FEL type of interaction.

The cyclotron autoresonant maser (CARM) is a well known pro-ducer of high-power microwave radiation (45, .161. The term "CIIARM"was coined to describe harmonic radiation from the basic CARM pro-cess. Although the history and detailed theory of the CHIARM lie be-yon-l the scope of this report, it is necessary to consider the frequencyspectrum of such a device in order to help prove that the proper modelhas been chosen to explain the experimental data.

The simplest approach is to begin with equation (37) in the previoussection. If the FEL term is deleted and the "idler" term is retained,the effective k, is given by

ke f = tool, (39)

which yields a properly Doppler-shifted frequency spectrum of

Clearly this relation leads to the same spacing between peaks, and athigh frequencies where CPO > w,,[1 + illI 3phl, the FEL and CIARMspectra will be virtually identical-except for a relatively small fre-quency shift. lowever, at low frequencies (f = I or 2), the frequencydifference is significant and the differences are readily apparent. In alater section. the ee differences are more fully explored when the actualexperhnental data are presented.

3. Experimental Configuration

This section provides an overview of the basic experimental setup, fol-lowed by a detailed look at the major individual components and thediagnostics used to measure ard record the data.

3.1 Introduction ard Outline

The basic experimental configuration is shown in figure 9. An intenserelativistic electron beam (650 kV, 2 kA, 100 ns) is produced by driving

23

M7 ,

an annular, field-emission cathode with the Dragon pulse generator.'rile axial magnetic field then guides the beam through the foilless anodeand slow-wave structure to the beam dump region. The rippled-wallslow-wave structure allows the beam to couple kinetic energy into thestructure's TAol backward propagating mode at 8.A GIz, providingthe pump wave for the FEb interaction.

In the principal mode of operation illustrated in figure 10, the back-ward pump wave grows in strength and drives the FEL interaction asit propagates towards the "cutoff" region. The scattered radiation fol-lows the same path, except that its reflection from the cutoff region isnot as complete as for the lower frequency pump wave. Thus it is thereflected waves that finally reach the microwave diagnostics region. Ina later section, it is also shown that the reflected waves do not interactwith the electron beam.

3.2 The Intense Relativistic Electron Beam

The intense relativistic electron beam used in these experiments is pro-duced by an annular field-emission cathode driven by the Dragon pulsegenerator [471. In the Dragon machine, a capacitive energy store is res-onantly discharged through a voltage step-up transformer to a coaxial,water dielectric, transmission line. When the voltage on the transmis-sion line reaches its peak, a self-breaking switch feeds the stored energyto the diode. A more detailed description of the Dragon pulser is givenin appendix A.

Magnetc I eld soleno d

k3',," ;4, / ." , > " , " ""/,," 5'u

MW A/2 i Picillp N~n

7Couglinghoie TO~;mee

diagnostics

Anode Wavegubde slow Wave i'ufrure

Figure 9. Masic experimetal configuration used for EM-pumpedFEL experiments.

1

7,

Reflected pump wave

Backward pump wave

I \..',J-.A.,r Scattered wave

* Reflected scattered wave

Electron beam

Cutoff IDansiregitonf Slow-wave structure Oiagnosticre gion region

I -

Figure 10. Principal wave traffic in the EM-pumped FELexperiment.

'Ihe Dragon pulser is tuned to deliver a relatively flat 100-ns-widevoltage pulse across the anode-cathode gap. This pulse is measured by a

capacitive voltage probe, and a self-magnetic field current probe, whichare located along the cathode shank, about 30 cm from the anode-cathode gap. It is important to remember that the measured voltageis not equal to the kinetic energy of the electrons. Although this wouldbe true for a single electron, the situation is different for an intenseelectron beam. In the dense beam case, electrons will split their energybetween kinetic energy and seit-field energy. Thus. the space charge orself-field energy must be subtracted from the accelerating potential inorder to determine the electron beam's kinetic energy.

From Gauss's law and the simple beam model shown in figure 11,the self-electric field can be written as

IoEr for r,.-r>ri, (41)2.ov_.r

25

________. .t .X ..~ .2 .C ...A .r .. ' . . .1....

f I

rbr

tFigure 11. Idealized electron-beam geometry.

where Io is the beam current, v.. is the beam's axial velocity, co is thefree space permittivity, and r is the radial measurement position. Notethat E, = 0 for r < r,. Integrating E, from the beam to the wall yields

o (42)laV:I(r0 /r,)'

where r, and r, arc the radii of the wall and the beam. The conservationof energy gives

?- )'c 2 = (-p - )wc 2 - c6", (43)

where (' - I)ic 2 is the kinetic energy of the beam. (70 - I)m 2c isthe accelerating potential, e6,, is the space charge energy, and -y is thestandard relativistic factor y = (1 - 32) -

1/ 2.

For the experiments described in this report, the space charge de-pression represents the principal correction needed to extract the beamparameters -1 and i3 from the accelerating potential. One should alsoaote that the space charge depression is min;mized when the beampro[)agtes near the outer wall. Taking r, equal to the average radiusof the ripples in the slow-wave structure yicld a correction of approx-imately 75 kV.

26

In order to analyze the FEL interaction and differentiate betweenFEL effects and those arising from cyclotron maser type interactions,the beam's perpendicular energy must be estimated. The principalsource of this energy is the E x B drift [36] given by

ErV0 =

Here B. represents the applied axial field, and E, is provided by eitherthe angled electric field lines in the diode, the beam self-fields, or the E,fields associated with the TMol pump wave. For an applied field of 10kG. and typical beam parameters, the E x B drift in the diode and fromself-fields yields a maximum drift velocity of /.3 < 0.05. From estimatesof the electric field component of the TMol wave (481, dq3e, < 0.02. Anexperimentally measured upper limit of )3. < 0.05 was obtained bymethods more fully described in the diagnostic section.

3.3 The Backward Wave Oscillator Pump Wave

The backward wave oscillator (BWO) used in these experiments is aphysically simple device in which an intense relativistic electron beamis passed through a rippled-wall type of slow-wave structure as shownin figure 12. The slow-wave structure interacts with the beam in sucha way that some of the beam's kinetic energy is coupled into the prop-agating electromagnetic modes of the slow-wave structure. This is ac-coniplished through the growth of negative-energy space charge waveson the beam. The mode, frequency, and intensity of the generatedmicrowave radiation are determined by the geometry of the slow-wavestructure, the electron beam, and the applied magnetic guide field.

Magnetic field coils

Anua lcinSlow-wave structure Beamii'beam dump

Waveguide cutoff-region

..... ....

Figure 12. Rippled-wall slow-wave structure.

27

An important feature of 13W0 operation is the dependence of thcpower on the applied axial magnetic field. The characteristic field sigf-nature shown in figure 13 has been observed by several experimentaltcais [2, :31, 32, .19, .50]. The dip in the output power is due to theresonant reradiation into fast cyclotron waves on the electron beam[32].

Comparisons of the electromagnetic wiggler with its magnetostaticcounterpart. are facilitated b~y expressing the strength of the magneticfield comp~onenit of the pump wave in gauss (C). A simple estimate ismadle ly noting that the 50-MWf, TM01 pumip wave must flow throughat corrugatedl-wall wvaveguidc with r,,,, ;z 0.5 in. Fromi the Poyntingvector with sinusoidal1 time variation 1361,

P./A =IRC(Er x HI-). (5

Assuming that P is constant over an area A and

with B = pH., one finds that

For thie above parameters, 13 : 300 G. A more dletailed exposition ofthe 13W0O pumip wave geiierator is found in applendlix B3.

70-

60 BWO pump power vs applied B3

.40L

0 I0j

10

0 '3 10 15 20Applied axial magnetic field jkGl

Figinre 13. Plot of i)ower ve'rsus appfiediiiagm-iei fiold streiigtx fov [3XV ()pin p

28

3.4 Support Systems

A\ backgroundI vacuum pressuic of -1 XI106 lorr was maintaine(l iiihe lbeaml propagation sect ions of the exp~eriment by a standlardI 6-inl.

diffuision pumrp.The fielhl-cinission diodle andI slow-wave strmetutre are immnersed inl

an aplied axial magnetic gu~ide fieldl. A\ I -i-lona solenoi(l was usedI to

Iprodtilce fieldIs 111 to 2:3 kC onl axis. Energy for the coil was storedl in acap~acitor bank C. as shown inl figure 1-1. When lte capacitor bank wasfully chargedI (and the D~ragon pulser was also reatly). switch Si wasclosedl an(l coil 1, was energize(l. When the current inl the coil reachedits p~eak. tilie switch 52 was clsd-'rwbrin lte circulit. This(gives the magnetic lieldI more time to (liffuse in to t lie beaml pal i s a 11(1

lpre'v'nts 1lv s"10tem f oirn -ringin g" wvhich dlecreases the l ifetimues of Ithe

energy'" storage cap~acitors.

3.5 Diagnostics

The dliagnostics usedl onl this experinten t fall into t It ree basic cat egoiie"':elect ronl-bea i lia gno~i ics. microwave (liagnost ics. an1(1 stipport 5stemvi

(liagnost ics. This sect ion focusevs on tIlie actial physical quta itit ies tlia(

werie meastiredI andI the pat aineters that cali be inferred from them.Figmre 15: shows thle posit ions of tilie different diagnlostics tisedl in : tisexperiment.

B-. Iam Diayno,,Iir,

Informnat ion a hoithle elect ron b~eami is providled by b aii(l b priobe,that are located onI tilie cat hode stalk -3t cml fronm tile aiiodo-calb Iodtal Tlli, places themil jw-t ill'ide' the illaamw.ic gulii'e lvd whichlt!

14)~e h~e O 11),t'idilive 1) plobo frnh -I rax Cl" 1,10 bi I) dW

S,Capacitor Solenoidbank S2 LCT__

Figitre 1.1. Si 1 niati H drawing ef app inigliletic,fiel s5t(eili.

29u

Not to scale

Low frequency MWcoupling hole

Air

VacuumCathode High-

_7 frequencyhorn

S Witnress plate

Figtire 15. Diagnostic Positionilg 0on tHe EINI-pminpedl FELeXipQIrtmnlCt.

Copper

Cathode stalk

Figurve 1G. Detaill of a ~id 13 elve ti-onl- boa volt lage and( curr-ent.

:30

The D probe is a cylindrical capacitive divider whose output isproportional to the time derivative of the voltage pulse traveling downthe transmission line formed by the cathode stalk and the 6-in. outerdiameter (01)) vacuum hardware. The pickoff is a thin, 1-in.-widepiece of copper tape insulated from the vacuum wall by a 0.125-in.-thick piece of Teflon. The copper tape is "terminated" in 10 Q. byfour .50-Q resistors and the 50-D signal cable that are evenly spacedaround the circumference of the cylinder. The signal is then fed intoa passive analog integrator and stored on a computer disk via a fastsignal digitizer. Careful calibration of the probe yielded a sensitivity of-177 kV per volt of input when the probe was connected to an integratorwith a :3-lis time constant.

The current probe. which is also shown in figure 16, consists ofa small loop which is aligned to intercept the self-Bo of the currentflowing down the cathode stalk. The probe is formed by breaking thecontinuitv of the loop. then connecting a piece of coaxial cable acrossthe .break." Since the voltage induced into the cable is proportional tothe time derivative of the current, the output of this probe must alsobe integated. Careful calibration of this probe yielded a sensitivity of7.9 k:\/V when the probe was operated into a 3-Is integrator. Sometypical voltage and current traces are shown in figure 17.

More information about the beam can also be obtained by exami-nation of witness plates that were placed as shown in figure 15. Thetime-integrated position of the beam is etched directlv on the plates.Typical values for :hese experiments were a beam inner diameter (11))of 1.6.5 cm and an OD of 1.8.5 cm. The width of tlie beam fixes anupper limit on the amount of perpendicular energy possessed by thebeam. \n electron with transverse energy will gyrate in the appliedmagnetic field with a gyroradius given 1w

= (IS)

where 90 is the nonrelativistic electron cyclotron frequency. As indi-cated in figure 18. the maximum value for r. is one-half the beam thick-ness or ,-1 am. For an a)plied magnetic field of 10 kG and = 1.9.equation (.1S) yields a maximum value for 3. of 0.05. A photographof one of lite actual targets is shown in figure 17. in principle, one Coildalso consider the beam a rigid rotor. In this case r, 0.9 cm (max)

and equation (18) yields a value of 0. 15 for 3 _L!

31

/

(a) M (b) kA

0 0

1900

380-

570 - 1.6

0 100 200 ns 0 100 200 ns

(C) (d)

0 20 40 60 80 ns 100 200 300 400 ns

(a)

Figure 17. Typical ixi)rinilntal data showing (a) voltage.

(b) current,. (c) BNWO ptImp wave. (d) high-froquencyradiation and (e) witnless plate.

11. ;. 1 c/rnl-arr 1 )amno'I.c,

11) I lhese xperinii'ills, high.-poWer microw ave radiation was mneasur(e(I

in Ihe freq(iency ranges from 7 to IS GlIz and from 50 to 1:30 G;ly.,licrowaves ini he low ralge (7 to IS ClIz) were st ii(liod via the coupling

hole shiowin in lig'ire 15 while the high range was collectcd with the

horn--also shown in figure 15.

:32

____________-9, __

Figure 18. Idealized electron beam cross section.

The detection methods for the low-frequency microwaves are illus-trated in figure 19. A small aperture in the side of the vacuum cylinderallows some of the igh-power microwave radiation to enter a sectionof \'R-90 (X-band) rectangular waveguide which carries the signal tothe rf-shielded data collection room. A 20-dB waveguide directionalcoupler then splits part of the signal into a "'prompt* path and a sec-tion of coiled dispersive waveguide. Vaveguide-to-coaxial adapters wereused to brinz boih the prompt and dispersed qi-nals into coaxial cable.C',xld ,eupler, were then u,,ed to further -plitI the si,,nak for analyzis.

An array of bandpass and low-pass filters was used to isolate and,study different portions of the frequency spectrum from 7 to 12.4 Cliz.Iligher frequency high-pass filters were constructed with sections of\W1-62 waveguide (f = 9.486 Cllz) and WR-42 waveguide (f =1.1.0.17 G'Iz). The WR-90 wa'eguide has a cutoff frequency of 6.5.57Gllz. The filters were especially useful for identifying peaks in thedispersed signals.

In addition to the standard dispersion line and filter techniques.microwave mixers "II1 were also used to study the frequency spectrum of

the oberved radiation. As indicated in figure 19. a known. convenient

3:3

Electromagnetic

RadiationCoiled dispersive

Coupling hole waveguide

Attenua or

< 'Detector Atnao

P"I oscilloscop~e

Figure 19. Schematic drawing of low-frequency high-powermicrowave diagnostic system.

frequency is applied to the local oscillator (LO) input, and the differencefrequency between the LO and rf appears at the intermediate frequency(IF) port an,' is recorded directly on a fast oscilloscope. By changingthe LO and observing the corresponding change in the IF, one canaccurately determine the rf input frequency-especially if one is. ableto Fourier analyze the IF signal.

All waveguide runs and components were easily calibrated from 7 toIS GIz with a network analyzer system. The coupling holes that fedthe \VR-90 waveguide could not be calibrated by such simple means.

Since the hole coupling is highly mode sensitive, a TMo mode launcherwas constructed (52]. The need to physically tune the mode launcher re-stricted the range of frequencies over which it could be swept. However.excellent data were obtained near S.A GlIz, die operating frequency ofthe BWO pump wave.

Measurements of the high-frequency microwave spectrum were madefrom .50 to 130 GlIz. For these measurements, a small horn (area ,-0.88cm2) was placed just behind (,-2.5 cm away) the polyethylene windowthat provided the vacuum-to-air interface in the experiment. The out-

3.1

T -17--~' -.7T7',r -M. '.1" 77____ _____M__W

put of the horn was fed into tile microwave grating spectrometer [531which acts like a l)andpass filter. 3y changing the grating angle andusing different gratings, it was possible to study -frequency windows"from 50 to 1:30 Gllz. Crystal detectors were mounted directly on thespectrometer, and their detected output was fed back to the shield(eddata room where it was recorded on a fast oscilloscope. Some typicaltraces for the B\VO pump wave and the high-frequency radiation areshown in figure 17. The spectrometer is descril)ed in more detail inappen(ix C.

-;.5.o/ Support Syslcm Diagnoslics

In addit ion to such obvious Irai,,. ,z as vacuum pressure and machinecharging voltage, two other eil, Irical signals are routinely recorded oneach shot: magnetic field and the voltage on the Dragon machine'scharge line.

A single-loop pickup coil located just outside the vacuum cylindernear the diode is used to generate a signal proportional to tile timederivative of the applied magnetic guide field. This signal is fed intoa digitizer and integrated numerically. A small correction factor isapplied to account for tie diffusion time of the magnetic field into thereg'ion traversed by the electron beam.

The charge line voltage is monitored by a self-integrating b probe(.5-11 that is also fed into a digitizer in the computer data acquisitionsystemIl.

3.6 Experimental Operation

Before the experiment-described in this report bcgan, the Dragon ma-chine was tined to provide relatively flat voltage and current pulses..\lthoulh ,one minor re-tuning was required in tile later stages ofIhe experiment, tie voltage and current traces were very rel)roducil)lethroughout the experiment. Despite considerable variation in signalamplitude (factors of 2 to 5 were not uncommon) on a shot-to-shotbasis, the positions of the frequency peaks were quite reproducible-to

1.5 (llz, the resolving power of the spectrometer. In fact, the generalexperimental procedure was to scan frequency ranges from low to highand then back to low to ensure that the frequency peaks were repro-ducible. It was also possible to reproduce the same peaks on a day-to-day basis.

:35

52 7", '17-I7 7 m.-v 17 7-17 - X:' ., ,.

- -~ i~.J~s4~~~< - --

Studies were also conducted on the magnetic field. system [55] toensure that the field emission diode and the slow-wave structure wouldreside in the flat-field region of the solenoid. These studies also quan-tified the relation between the field monitor pickup loop outside thevacuum cylinder and the actual field inside the slow-wave structure.Shot-to-shot reproducibility of the magnetic field system was excellent;the only problems came from the transient digitizers that.were used torecord the dat-a signals. Frequent air-conditioning problems and a hot-ter than normal summer often resulted in equipment overheating whichcaused baselines to drift, affecting the integration of the 1 magneticfield monitor.

The stainless-steel cathode and carbon anode were periodically in-spected, but no damage or significant deterioration was evident. Theanode and cathode were approximately 2000 shots "old" by the con-clusion of the experimental period.

Four Tektronix 7612 transient digitizers [56] were used to record themagnetic field signal, the voltage on the Dragon charge line, and thevoltage and current on the cathode stalk. A DEC PDP-I 1/34 computerwas then used to store the data on removable disk cartridges and finallyon tape. This system allowed convenient examination and later storageof the slower data signals without the costs and troubles of recordingthem on film.

Three Tektronix 710.1 oscilloscopes (1-GlIz bandwidth) [56] wereused to record the faster microwave signals. This limited the amountof data that could be recorded on any given shot but still providedenough flexibility so that the lower frequency (7 to 20 GIz) signalscould be thoroughly studied.

The high-power-microwave output from the experiment leaves thevacuum cylinder (after passing the coupling hole) by passing througha polyethylene window and then into a mini anechoic chamber. Af-ter app)roximately 1500 microwave shots, souni discoloration is evidenton the polyethylene window, but it does not appear to have had anysignificant impact on the experiment. The mini anechoic chamber notonly eliminates any safety problems that might be caused by high levelsof nonionizing radiation, but also reduces the noise level at the high-frequency spectrometer.

36

-,R; W, 1 77 7 g UV V T-- 11 !77M4 .MCI

4. Results and Discussion

4.1 Introduction

The high-frequency spectrum from 50 to 130 GI'z is composed of anarray of regularly spaced peaks. The frequencies of the peaks and theirvariation with the strength of the axial magnetic guide field indicatethat the spectrum is due to a three-wave FEL interaction in which cy-clotron harmonic beam waves act as "idlers." A detailed examination oflow-frequency, low-harmonic-number data will be used to demonstratethat tile emission spectrum is due to an FEL interaction and not to aCIIARNI interaction. This is important because of the close similaritybetween the FEL and CHARM spectra-especially at high frequencies

The raw data are presented in the next section, followed by a com-parison of the data with the model of an electromagnetically pumpedFEL with cyclotron harmonic idlers. The last sections provide a morecomplete justification for choosing the FEL rather than tile CIIARMas the interaction model that best describes the experimental results.

4.2 The Measured High-Frequency Spectrum

The experimental procedure was to select a value for the magneticguide field, and then use the grating spectrometer to sweep throughthe frequency range appropriate to the particular grating and detector.This process yielded tables of power versus frequency for different valuesof applied magnetic field. The electron-beam parameters were heldconstant throughout tile experiment. Some typical power spectra areshown in figures 20 through 22.

Gamma

~0706 9 89 K Gauss

S05. 04,

z ; I I

80 85 90 95 100 I0" 110 115 120Frequency (GHzl

Figure 20. Moeasured frequency spectrum

from 80 to 120 GHz for an applied fieldof 9.89 kG.

37

0.9

0.8

S0.706"= 1.9

n = -1= 05 Bz = 10.3kG

o 0.4 xI 0.3

0.2 Lo.1 x

50 60 70 80 90 100 110 120 130

Frequency [GHz

Figure 21. Measured freqiency spectrum from 50 to

125 GIz for an applied field of 10.3 kG.

0.9- I =1.90.81 n,

C [S0.7

0.6 tj ,9.89 kG0.6 .1 t

S0.4 -1 ~10.31 kGD 0.3

o 0.2I

80 85 90 95 100 105 110 115 120

Frequency (GHzj

Figure 22. Measutred frequency spectra from 80 to

125 GHz for applied fields of 9.89 and 10.3 kG showing

frequency shift caused by a change in applied field.

, :,-,. -., ., ,. - -, -- .-,..:,,' J- y ... .- - . : : - z, : : : .= . K.

Figure 20 shows the simple set of regularly spaced peaks presentbetween 80 and 120 G!z for an applied magnetic field of 9.89 kG. Thedata have been normalized to the highest peak present in the frequencyrange.

In figure 21, two measured spectra have been joined together. Al-though the same magnitude of magnetic field was applied in both cabes,different gratings and detectors were required to cover the two contigu-ous frequency ranges. Also, both data sets were normalized separately.This is the reason for the "hump" in relative magnitude at approxi-mately 82 Gllz. In general, the power decreases monotonically as thefrequency increases.

In figure 22 the spectra corresponding to two different values ofmagnetic field are plotted on the same axes. It can be clearly seenthat the entire frequency spectrum is shifted when the magnitude ofthe guide field is changed. The data sets were normalized separatelyeven though the same diagnostic components were used in both cases.Although not shown in this section, spectra were also measured forseveral other values of the magnetic field, including 11.4, 19.4, and 20.3kG. Regularly spaced peaks were always present.

4.3 The EM-Pumped FEL Model

In this section the experimental data are compared to the theoreticalmodel of the electromagnetically pumped FEL with cyclotron harmonicidlers that was developed in the last section.

,.:3. 1 Expcelcd Spechruni

Th'i frequency ;pectrw;n was expressed in section 2 by equation (37).For the data presented in the previous section, the minimum frequencywas 50 GlIz and waveguide effects can be ignored. Equation (37) canthen be reducel and cast in terms of frequencies to become

f = ,f,(I + Al + l)

where f, and f,,, are the frequencies of the scattered and pump wavesand f, is the relativistic electron cyclotron frequency.

The dispersion diagram for the model is shown in figure 23. Notethat the interaction sites of interest lie along the "down shifted" branch.

39

.........

The lines representing the different resonance conditions for each har-monic (labeled C = I through 12) will move up and down as the mag-netic field, and hence f, is changed. Recall in equation (49) that apositive value for 6;,;i represents a backward propagating wave. Thespacing of the frequency peak: indicates that the down-shifted branchwill best match the experimental data; thus the minus sign must befavored in the last factor. The formula for the frequency peaks as afunction of magnetic guide field is then

2cj( [f (I 3:i) (50)

The following parameters were used in the above expression:"7jj 11.9,il "0.S5,f S , .4 GItz ,

)3ph - 1.054,and of course f¢ is 2.8/-y11 (GHz/kG).

y= 1.9 14 /12 X0

180

' 140

1 80 -

S 60404

208-20 -o 0 1 0

60

Wave number [1/cm]

Figure 23. Dispersion diagram for EM-pumped FELwith cyclotron harmnoiic idlers with theoreticalintersection points marked with circles.

4

- ~*'*' .*,- *.*- -\7

It should be noted that equation (50) can also be reached directly viathe appropriate Stokes diagram shown in figure 24 and the conservationequations. From the conservation of energy,

WW = Wi + W3, (51)

and from the conservation of momentum,

k, = ki + k,. (52)

The dispersion relation of a slow, negative-energy cyclotron harmonicwave is given by

wi = ki .v - MtO. (53)

For v = v1i5, equations (53) and (51) may be combined to yield therelation

w, = w,, - ki. v + O (54)

orW3 = W - (k.,, - k).v + O. (55)

However, from the Stokes diagram in figure 24, both the pump waveand the down-shifted branch ef the scattered radiation are backwardpropagating. Thus, equation (55) becomes

w, = w, + (kw - k,)vii + MO, (56)

Where k, wl/c and kw = wwIVph. Substituting for k, and kw leads to

w'(1 + il) = w(1 + Ill/.iph) + O, (57)

or

which is identical to equation (50).

WM ,1

0

2 k 2c2 + 2

(ws, ks) ~co

(w, kw) C

Figure 24. Stokes diagram of three-wave FEL int.erac tioli with

backward propagating pump wave, slow cyclotron harmouic wave

idler. and svaltrvuld radiation along 'dIown- ishiteld" branch.

;.3.2 (omparison of "lTz uiry and I..'Xprim r Ii

ihe ('xN'lent nl mat ch bet ween i hex pert ilivilt al (ata and the predic ions

of le simple io(el rel)resente('(I by equation (50) is shown gralphicallyin figures 25 and 26. In these figures, crosses are used to denote Ihel)ositions of1 tile inmeasill'(d peaks on lie theoretical scales. hle evveanid odd harmnis were plotted seIaIately it) iev('ent (rowding oll Olilegrapis.

12

180- = 1.9 +Experimental

160 n = -1 -Theory

q140 -1

S120S100 j- 4-----

.80L-----

LL60 _____________5

Applie

Apidaxial magnetic field [kG]

Figure 25. Dependence of frequency peaks on magneticfield for odId hiarmonic niumbers from I. thiroughi 15 withicrosses marking positions of measured peaks.

t180 y 1.9, n = 1 + Experimental

160 -Theory

''140- 14-

( 120 .- ... ....... . 12 -

o100-- - -- -0C 8

S80 80*

IL -40 L =4-

20-09.5 10 10.5 11 11.5

Applied axial magnetic field [kG]

Figure 26. Depenrdence of frequtency peaks on magneticfield for even hiarmionic numbers 4 throuigh 14 withi crossesmarking positions of measuired peaks.

The two most convincing aspects of the fit between theory and ex-periment are the peak spacing and magnetic field dependence. Peaksrepresenting harmonic numbers e = 1 and f = .5 through 1-1 cal beclearly identified on the figures. Data showing the change in frequencycorresponding to changes in the applied magvetic guide field also fit wellinto both figures 25 and 26. This variation in frequency with magneticguide field is especially important because it not only eliminiates severalprospective mechanisms for high-frequency-microwave production butalso eliminates the possibility that the peaks were due to iesonances inthe diagnostic system.

..3..3 Powr .Estimales

For the high frequencies. the signal strength times the detector sensi-tivity times the in-line attenuation yields a level for the peak powecrentering the pickup horn (shown in fig. 1.5 and 27) that feeds the grat-itug spectrometer and hence the rest of the high-frequency detectionsystem. For the t = 9 peak at 82 GIlz, this calculation gives a re-sult of approximately 20 XV at the pickup horn (0.9-crn2 cross-sectionalarea). Although this is a very small fraction of the total power (at82 GIlN) produced in the experiment, realistic measurements would re-quire mode and radiation pattern information that is beyond the scopeof this report. Ilowever, a crude estimate can be made by consideringthe idealized iodel shown in figure 27. Here the actual radiation source

in the cylindrical waveguide has been replaced by a "point source" lo-cated at the center of the end of the guide. This yields a geometricattemation factor of -4100, which would imply a power of --90 kW inthe waveguide (at 82 Gllz). This estimate could be considerably higheror lower, depending on the actual radiation pattern.

The low-frequency measurenents were based on energy coupledthrol, a hole in thw -ide of the cylindrical waveguide. as (!'. i.-,,ed

iu section 3.5.2. For the 8.i.1-(1iz pIump wave. nalmbliguous power

levels of 50 .XX\V were roi tinely measured. Ilowever, the other, 'low"frequency peak occurred at -..16.5 Gliz. In this case, mode uncertaintyprecludes anly sinple estimate of the power. The best guess is to assumethat power drops by -10 to 15 percent each time tire mode numl)er isincreased. Then working back from the high-frequency estimate at 82Gll (f = 9). one can crudely determine that 200 to 300 k\V should befound at 16.5 (llz for the = I harmonic.

II

Point source High frequencypick-up horn

Figure 27. Illustration of miodel used to construct crude estimateof high-frequency mnicrowave power levels.

4.4 Othier tModels

Although the experimental data clearly fit the down-shifted branch ofthe backward w.ave electromagnetically puimped FEL model, it mustalso be showvn that othicr competing dtories are inappropriate. ieprincipal contenders are the forwvard pumnp wave FEL interaction andthe CHIAR.M. Models based onl the excitation of higheir order modesin the 13W0 canl easily be dismissed by, considecring the experimentalfrequency shift versus magnetic field. The high-order BWVO modesare solely a function of the geomctry and (10 not depend onl applIied1i'agnel ic livld -t rvii' h. InI hlenext sect ions. the possibility of a forwardpuimip wave i nE raci ion or a C'1 HRM is ('on,,iderev in More det ail.

I.. Forivard Pump 11"are EEL Interaction

Thle op~eration of the experiment is such that the "normal" backwardpropagating puimp wave passes through the slow-wave structure (as infig. 10), reflects from a section of waveguidle beyond cutoff, and again

pa~sses through thle slow-wave st ructuire-t his time moving with ileelectron beam. Clearly, anl interaction is theoretically possible, and thespectra caii be computed from eqluation (:37) or (419) with 3 ;, -3ph

07 T7,7- PF"'~ff 7,771r. -'15 2-'T7'WrM"

Although equation (.37) will be usedl in all calcnlatiouis (becaulse wave-giii(Ie effects mlay. not always be ignorable). equation (19) is easier to"look at" anid it contains the samne basic 1)hsics-except for the wave-

gulid~e effects. Table I contains thle up- aiid (lown-shifted interact ion

frequencies for both forward and b~ackwa rd pumip waves. Clearly. thlemevasure(I spectra are not dueI( to any inuteract ion based Onl thle uij-shiftedlb~ranclh of eil her thle forward or backwardl pumip waves. As a result, onlylie (lown-shlift ed bra ndies will be considered fromi this point onwardl.

Table 1. Interaotioui frequiencies (in gigahortz) of an electroinag-netically pmpedI FEL with cyclotron harnionic idllers for anl aip-plie(l fil of 1t) kG

I B~ackward pump B~ackward pump Forward pump Forward pumpup-shifted down-shifted up-shifted down-shiftcd

1 199.0 17.0 107.7 10.42 297.7 24.7 206.9 17.63 396.3 32.5 305.6 25.3

494.8 40.4 404.2 33.25 5933 48.3 502.7 41.06 691.8 56.2 601.2 48.97 790.2 64.,. 699.7 56.98 888.7 72.1 798.1 64.89 987.1 80).1 896.6 72.2

10 1085 88.0 995.0 80.711 11,4 96.0 1003 88.612 1282 103.9 7192 96.613 1381 111.9 1290 104.5141 1479 119.8 1389 112.515 1578 127.8 1487 120.5

At high frequencies (I > -1). the spacing between thle peaks and thlemlagnlet-ic fielil dependence is vi rt ually identical for botll the forwardanld backward pu np waves- when viewed locally. Whien data are taken

ia WIde raw-c,. of n-nie ihed. idont ifyino iev peaks with Iipecihucmode ininberi beconies very difficult . This is comlplicated by tile factt hat even t holgli the luaruniic niumhers ar d' (ifferent, tilie forwa rd andbackward p(Inui mnodels predict almiost identical sp~ect ra. However, thes4i at ion is signlicil ly11% different at lower frequencies (C < :3). Theforward wave model predicts interactions at both 1i0A.. and 17.6 GINz.while. thle backward wave mlodel predicts only a single interact ion at 17

lz. Careful study of Owe frequency range froin 7 to 20 GIN revealedpeaks at only 8A GINl (Ilite puimp frequency) andl 16.5 Gil%. There wasno0 mw1rowave power (let ected ili the frequency range near 10.1 C liz. Avaplhi(al rep~resent at ion of the low hanomiic interact ion frequencies is

17776-1 t T7

given in figuEv 28, where the ]one experiment ally ob)served frequency isdlenotedl by the circled cross. The I = 0 (no idler) interaction was alsoabsent.

in addition, there was no clear evidence of thc three-wave FELwith space charge idler that was briefly dIiscussed in section 2.2. Theinteract ion frequency for the down-shift ed branch was -6.5 G lIN, whichis below the cutoff frequency of the waveguide used to transport thlemicrowave signals and] it was therefore not detectable. The up-shiftedinteraction frequnicy should have produced a peak at -. 80 GINz thatwould not change with the applied magnetic field, but no such peak wasobserved in the 1ff spectrum. Thus. the electromagnetically pumped17iji, with space charge idlers dlid not produce observable power in theseexp~eriment s.

20

S 15

CL-

10 t= akwv

6 8 10 12 14 16

Applied axial magnetic field (kG)Figure 28. Low- harmionic interact ion frequtencivs vei's'is appliednlagn('ic field for (IowiI-shiftedl branches of EM-pumiped FEL withcyclotron harmonic idler waves.

17

4.4.2 The CHIARM Model

The expected frequency spectrum from a CHARM interaction wasshown in section 2.3 to be given by equation (40). Table 2 showssome interaction frequencies predicted by equation (40) with similarfrcquencies representing the do\wn-shifted backward EM-pumpcd FELinteraction. Once again, the down-shiftcd branch of the CIIARM in-teraction predicts a high-frequency spectrum quite similar to that ofthe FEI,. In fact, figure 29 shows the measured data on a plot of theinteraction frequencies generated by the CHARM model via equation(40). However, there are once again significant differences in the lowfrequency (C < 3) spectrum. These differences are clearly seen in figure:30 in which the down-shifted spectra are plotted for the CHARM andbackward pump wave FEL interaction. The solid lines represent thc-orN' and the crosses denote experimentally measured peaks. A carefulsearch of the microwave spectrum was able to detect power only at thesingle frequency marked by the circled cross. The CHARIM model failsto adequately predict the measured frequency spectrum.

Table 2. Interactioui frequencies (in gigahertz)for a cyclotron harmonic anto-resonant maserwith an applied field of 10 kG

ltannonic CHARM CHARMI up-shifted down-shifted

1 94 12.52 195 18.13 294 25.34 393 32.95 491 40.76 590 48.57 688 56.48 787 (4.39 886 72.2

10 984 80.1II 1082 88.012 1181 95.913 1279 103.914 1378 111.815 1476 119.8

.48

- - ~~S -

180

16051 9 15

120

9.1000 1 1

Ao~lied magnetic field (kG)Figure 29J. Frequency versus ipplied field for CHARMiniteraction with experimcental datai points reprcsciitedby crosses.

25

10 -Theory

SExperiment

6 8 10 12 14 16Applied magnetic field (kr1)

Figure 30. Low- harmnonic interaction frequeicieSversus appliedl maignetic field for down-shiftedbrainches of CHARM and ELM-pumiped FEL withbaickwaird pim-tp waive and cyclotron hairmionic idlers.

77 1, M 7V -V~~9 I VM T

In addition to the poor match between low-frequency predictionsand experimental measurements, the CHARM model is inappropriatefor another reason-insufficient O.L. In order to drive the CHARMinstability, a large amount of perpendicular energy is required in theelectron beam. In fact, the resonance point occurs when /-y = i/[.15, 461. For the parameters of this experiment, flj. 0.5 would berequired. However, the witness plate measurements of the electronbeam (sect. 3.5.1) showed a measured value of nPj. < 0.05, which ismuch less than the perpendicular energy needed to efficiently drive theCHARM interaction.

In a pure CHARM device, there are no rippled walls. The inter-action is driven by O.L and the applied magnetic field. When a thinfoil was inserted into the slow-wave structure (effectively eliminatingthe corrugations), all microwave radiation ceased-both high and lowfrequency. This supports the assertion that the observed microwavespectrum was due to a non-ChIARM type of process. Thus, all evi-dence points to the backward-wave electromagnetically pumped FELwith cyclotron harmonic idlers as the model that best explains themeasured data.

4.5 Frequency Scaling

An interesting feature of this novel FEL mechanism is its frequencyscaling with -y, as shown in figure 31. Also shown in the figure are theup-shifted (+) and down-shifted (-) frequency conversion factors formagnetostatically (labeled SM) and electromagneticaIy (labeled EM)pumped FEL's with space charge wave idlers. Note that the behaviorpredicted for a down-shifted electromagnetically pumped FEL with acyclotron harmonic idler (labeled CI in fig. 31) is dramatically differ-ent from the behavior of the other FE, mechanisms since the outputfrequency (ecreases with increasing 1 . The ligure shows the specilicscaling law for harmonic number t = 10, but the behavior is typicalfor all harmonic numbers. It can easily be understood by referring toequation (.19). There DO is the relativistic electron cyclotron frequencywhich decreases with increasing -/, and the term tf, is dominant. Re-call that -,2(1 - j 11) = (1 + fill)- ' - 2. Note also that it is possibleto tune the frequency of the FEl by varying either the axial magneticguide field or -'.

50

7 7 71 '4 7-

104

4

................

2

10 - SM+

c2.,

;. 4

10 I

24 6 8 10

Gamma

Figure 31. Plot of frequency versus gamma for several interaction

models.

5. Conclusions

Although the concept of using an electromagnetic wave to pump a FELtype of interaction has been demonstrated previously (1, 2, 20, 44], thee'periments discussed in this report represent the first careful study .of a significant portion of the frequency spectrum produced by suchd(evices. In fact, the spectrum was resolved from 7 to 20 Gllz and from50 to 130 GIlz. Quite unexpectedly, the spectrum was found to be Icomposed of an array of regularly spaced peaks.

Several interaction mechanisms were used to model the experimen-tally measured frequency spectrum. The most successful were thedown-shifted branches of the CHARM and FEL with cyclotron har-monic idlers. The CHARM model was dismissed because it did notadequately predict the low-frequency portion of the spectrum and thebeam did not appear to possess a sufficient amount of perpendicular en-ergy. The lone remaining candidate model was the electromagneticallypumped FEL with cyclotron harmonic idlers.

51

A three-wave FEIL interaction with a cyclotron idler wave has beenrel)orted [,11-43], but the experiments reported here represent tie firsttime that cyclotron harmonic idler waves have been observed. The ac-tual implementation of the experiment allowed both forward and back-ward waves to interact with the electron beam. Optimistically, thisprovided Ilhe opportunity to study both the forward an( backward in-teract ions. Fort unately, the differences in the spectra predicted by thetwo models were sufficiently distinct so that the forward pump wavemodel could )e eliminated in favor of tie b)ackward-wave-driven inter-action. Thus, it has been demonstrated that backward electromagneticwave pumping in the presence of an axial magnetic guide field produceda three-wave FEL interaction via cyclotron, harmonic idler waves.

The production of this coherent, powerful, high-frequency microwaveradiation was achieved with relatively modest magnetic-field and clec-tron-beam parameters. This FEL mechanism also features continuoustunability by varying either the applied magnetic guide field or y.

At the point where 3. z 6 kG, the beam is not stable and the powerin the pump wave drops to zero-as suggested in figure 13. As a result,10'kG was chosen as the basic operating point; it is not too high and thebeam is stable and a healthy pump wave is produced. The presenceof high-frequency stop-bands in tie rippled wall slow-wave structurecould also account for some of the amplitude variation with increasingharmonic number that is present in figures 21 and 99.

Tie wide range of frequencies accessible through this mechanismand its demonstrated tunability provide the basis for a wide range of ap- -ji-plications. Some prospective uses would include spectroscopy, chemicalreaction and process control, and laser isotope separation, in additionto tie more "classical" applications such as remote sensing of the at-mosl)here, high-resolution radars, plasma heating, particle acceleration,and laser surgery. A more extensive discussion of FEL applications isgiven by. Marshall [3S]. V)

This experiment rei)resented a venture into unexplore(d areas ofphysics, and it was not always possible to be prepared for some of tieresults that were discovered. However, the experience gained in thisseries of experiments does provide some basis for structuring futirestudies.

In particular, the region between the slow-wave structure and the re-flecting waveguide beyond cutoff should be extended to provide a longerinteraction region that would give some of the instabilities more timeto grow and possibly lead to higher output powers. Some sort of mode

52

selective device such as a Bragg cavity [57] could also be introduced tohelp maximize the power in some selected frequency range. It shouldalso be possible to replace the waveguide cutoff region with a couplingcavity that. would extract the pump wave rather than reflecting it backthrough the interaction region. This would eliminate the distraction ofbeing always forced to look for forward wave interactions, and it couldalso lead to more efficient extraction of the power in the pump wave.The possibilities for operating the device as an amplifier should also beinvestigated.

In the diagnostic area, there are many opportunities for furtherstudy. The gap in the frequency measurements between the high andlow ranges should be closed so that the gamut of peaks can be studied.A more comprehensive survey of the lower frequency range should beundertaken with axial horns replacing the radial coupling holes. As di-agnostic sophistication grows, mode and radiation pattern informationshould be recorded, and of course the search should be renewed for theinteraction frequencies on the up-shifted branch.

Finally it should be noted that (for the present) this is the onlyknown area of FEL research in which there is more experimental thantheoretical activity.

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541

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22. R. 11. Jackson, S. 11. Gold, R. K. Parker, 11. P. Freund, P. C.Efthimnion, V. L. Gfanatstein, MN. Hlerndon, A. X. Kinkcad, J. E.Nosakowski, and T. J. 1(wan, Design and operation of a collectivemillimeter-wave free-electron laser, IEEE J. Quanuin Electron.QE-19 (1983), 3,16.

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241. T. J. Orzechowski, B. R. Anderson, J. C. Clark, WV. NM. Fawley,A. C. Paul. D. Prosnitz, E. T. Scharlemann, and S. NM. Yarema,Hligh-efficiency extraction of microwave radiation from a taperedwiggler free electon laser, Phys. Rev. Left. 57(17) (27 October1986), 2172.

25. J. Fajans, Radiation measurements of an intermediate energyEEL, Phi.D. thesis, MIT (1985).

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41. P. C. Efthimnion and S.P. Schlesinger, Stimulated Raman scat-tcring by an intense relativistic electron beam in a long rippledmnagnetic field. Phys. Rev. A 16(2) (1977), 633.

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4-1. R. A. Kehis. Y. Carmel, WV. WV. Destler, and V. L. Granatstcin.Experimental demonstration of an electromagnetically-pumipedFEL with cyclotron harmonic idlers. Plzys. Rev. Lett. 60 (4) (2.5JIanuary 1988).

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-0

53. J. Fisher, D. A. B~oyd, A. Cavallo, and J. Becnson. Ten-channelgrating polychromiator for electron cyclotron emission plasma di-agnostics, IRev. Sci. hzslrurn. 54(9) (1983), 1085.

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58

Appendix A.-The Dragon REB Generator

This appendix describes the operation of the Dragon relativistic electron-beam generator that was used to provide the electron beam used inthe experiments described in te main body of this report. The ba-sic Dragon generator is shown schematically in figure A-I. After theprimary capacitors, C1, have been fully charged. switch S, is triggeredand the energy stored in Ct moves through the transformer to a trans-

mission line represented by C2. When the voltage on C2 reaches itsmaximum, switch S2 closes (self-breaks). and tl,e energy on transmis-sion line C, flows into the electron-beam diode, producing the intenserelativistic electron beam used in the experiments. By properly tuningthe LC circuits on the primary and secondary windings of the trans-

former, one can achieve the "dual resonance" operating mode in whichall the energy stored in the primary capacitor bank will appear on the

transmission line. C2. A tuning ind'bctor, L. is used to help ensuredual-resonance operation. The tuning inductor also helps to protectthe transformer from potent;ally dangerous high-voltage spikes.

Main capacitor bank (C1) Tuning inductor (Lt) PFL-50-ns water

rimary switch (Si) transmission line (C2),/ /MN Resistive shunt

Transformer Secondary Diodeswitch (S2) isolation section

Figure A-1. Schematic (Irawing of Dragon relativistic electron-beam generator.

59

77 T

Figure A-2 shows a more graphic view of tile Dragon system. Tilecapacitor bank lives in an isolation box that can be filled with Freon foradditional insulation. The capacitor bank is connected directly to tileprimary of the step-up transformer through the primary switch. Theoutput of the transformer is coupled through the tuning inductor to a6.5-SI water-filled transmission line which is used as a pulse forming line(PFL). A self-breaking secondary switch connects the PFL to a sectionof time-isolation transmission line which feeds the diode. The diodeconsists of a variable-impedance dummy load, an axial insulator stack,and a standard anode-cathode gap electron-beam diode. The remainderof this appendix describes some of the major individual components inmore detail.

The primary capacitor bank consists of eight 1.85-pF high-voltagecapacitors. When charged to 50 kV, thuse capacitors store 18.5 k-Jof energy. In the actual operating configuration. four capacitors arecharged to +50 kV and four are charged to -50 kV. Their connectionto the primary of the transformer is shown in figure A-3.

A split single-turn primary (isolated from the secondary) was usedin place of the more conventional autotransformer. This allowed theminimization of insulation, volume, and power supply requirements.Also in this configuration, the highest voltage with respect to ground(outside the transformer) is 50 kV, which can be easily insulated with-Mlar and Freon gas. The capacitor cases remain at ground duringdischarge.

PRIMARY SWITCH. TRANSFORMER ISOLATION DUMMY LOAD

S "PFL SECTION L /INSULATOR

UNING INDUCTOR SECONDARY SWITCHCAPACITOR BANK

Figure A-2. Graphical representation of Dragon relativistic electrou-beam generator.

60

- -[- - -

Primary switch

Primary winding

Secondary windingHigh-voltage plate

7Acrylic stabGround plate

Primarycapacitorbanks

Figure A-3. Idealized (Irawig of Dragonvoltage step-tip tranisforiier.

TIhe voltage step-up transformer is designed to work in the dualreoance mode (1 ,21. WVhen this condition is satisfied, all of the energy

storedl in the primary capacitor bank will periodically appear on thePIFh. The conditions for dual resonance are achieved by (1) setting

k0. 6, (A - 1)VI(0 2 + LO)

where k is the coupling constant and .11 is the mutual inductance, and(2) Setting

LiC, =L 2C2. (A -2)

The secondarv on the Dragon transformer currently contains 31 turns.The P"'l byrpeen d1 C., in fig'iire A. I k a wvat er- filled transinis-

~ion linew withI it elect rical len gil of 50) ts. The outeIr and i Inner il-eters are 2.3.5 and 9 in., whticht results in a characteristic impedance of6.3 Q.. The 23-ns isolation section separates (by .16 ns) the main pulseinitiatedl by thle secondary switch closure from any post pulse due toreflection at a mismatched load. Thte isolation section also serves as acapacitive divider to suppress any prepuilse on the diode.

The pulse forming line is terminated with a dummy load shunted bytlte anode-catltode diode. This disk-shaped load p~rov'ides an approxi-_mately matched termination to tite 6,.5-P PFL. With this dummry load

61

77-7............................................

the high-impedance diode has a niniscule efict on the voltage drivingthe diode. 13, :ause of the relatively large size of the geometry, alu-minum electrodes were used with sodium thiosulfate as the electrolyte.The solution is continuously circulated to the outside world, where itsconcentration can be easily adjusted as necessary.

The operation of the Dragon machine is described in more detail byKehs [31 and Shpilman [2].

References

1. G. J. Rohwein, A three megavolt transformer for PFL charging,IEEE Trans. NS-26 (1979), .1211.

2. A. Shpilman, Design considerations, implementation, and testingof a transformer powered pulse generator, MS thesis, Universityof .MD (198:3).

3. R. A. Kehs. C. A. lluttlin, A. Bromborsky, B. G. Ruth. S. E.Graybill, A. Shpilman, and M. J. Rhee, DRAGON, a low imped-ance megavolt modulator for performing relativistic electron beamexperiments, Proc. 161h Power Modulator Symposium, Rossalyn,VA (1984).

62

Appendix B.-The BWO Pump Wave

B-i Introduction

The backward wave oscillator (BWO) used in these experiments is aphysically simple device in which an intense relativistic electron beam(IREB) is passed through a rippled wall type of slow-wave structure asshown in figure B-1. The beam interacts with the slow-wave struciurein such a way that some of the beam's kinetic energy is coupled into thepropagating electromagnetic modes of the slow-wave structure. This isaccomplished through the growth of negative-energy space charge waveson the IREB. The mode, frequency, and intensity of the generatedmicrowave radiation are determined by the geometry of the slow-wavestructure and the electron beam.

Since the electron beam is discussed in section 3.2 (in the mainbody of text), the following sections present the slow-wave structureand describe how ;t was used to couple the beam's kinetic energy intothe propagating T.1!o mode in the structure.

B-2 The Physical Picture

The slow-wave structure used in these experiments is the rippled wallwaveguide shown in figure 13-1. This type of structure was chosen be-caue it k less 'uZceptible to the high field breakdown problems foundin such conventional devices as the helix- and iris-loaded waveguides.Physically, the actual device was constructed by plating a thin layer ofcopper onto an aluminum mandrel that was machined to the desiredinner dimensions of the slow-wave structure on a numerically controlledlathe. The copper-plated aluminum piece was then cast in an epoxysupport structure and the aluminum was etched away with a sodiumhydroxide solution, leaving the finished slow-wave structure. The phys-ical dimensions of the structure were chosen to match those of Bondar

63

T~ V, 77 77 -M7, - 11 7 ,77 " f

i-

et al. [1] so that analysis techniques (2] could be checked with resultsreported by Bondar et al. [1].

R=0.59+0.16 sin (9.5'6z) IR.z in inchesl

(086- - -06575'

0I0" ,41L 050"

:- - 0.50- 3.00.

Figure B-1. Rippled wall slow-wave structure.

B-3 The Empty-Waveguide Dispersion Relation

In order to analyze the effect of the slow-wave structure on the electronbeam, one must first determine which modes and frequencies are ableto propagate in the structure. Since the electron beam is primarilydirected in the ^ direction and is axiaily symmetric, one anticipatescoupling of beam energy to the TMo0 modes of the structure. TheMaxwell equations can be solved for an infinitely long structure with theripple given in figure B-1. The results are summarized in the dispersionrelation shown in figure B-2. Note the small extent of the pass bands,which indicates that Idwldk.I < c everywhere within the pass band,implying large E. fields and good coupling to space charge waves. Thenext step is to plot the space charge wave dispersion relation

= - 2.n IL). (B - 1)

(where vii is the beam axial velocity, n is the spatial harmonic, and Lis the ripple period in the slow-wave structure) on the same axes as theempty structure dispersion relation.

64

skim. ,77r" - 77% IT" - -- -.

t . . - - ' . .

'477

20.0

17.5 -

N 15.0-

12.5-

2 10.0-

0 7.5LU

L. 5.0

2.5

0.0 I I I I

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

k (cm- 1j

Figure 3-2. Empty-waveguide dispersion diagram for

low-order TMon modes.

B-4 Beam Dispersion Relation

Tile addition of the space charge waves to the empty waveguide dis-persion relation results in the plot shown in figure B-3. The spacecharge waves which propagate at the beam velocity are the source ofthe energy that couples into the structure's propagating electronag-netic modes and drives the BWO interaction. The operating frequencyof the BWO is well approximated by the intersection of the n = -1 spa-tial harmonic of the space charge wave with the n = 0 spatial harmonic(-r < k.L < ,) of tile empty waveguide mode (i.e., the TMol mode).Note that this point is equivalent to the operating point determinedby the intersection of the n = 0 spatial harmonic (r < kL < 3-r)of the empty waveguide mode in tile sense that tile frequency, fields,and beam quantities associated with each operating point are identi-cal. However, the phase velocity of tile BWO wave is different at eachoperating point.

65

___________-___-___________,_,,_______________________ -_"_________

20.0

17.5 :

% 15.0- TMO2,

12.5

10.0 -

w

-2.0 -,.5 -1 0 -0.5 0.0 0.5 1.0 1.5 2.0

k 1cm-11

Figure B-3. Empty-waveguide dispersion diagram withsuperimposed ideal beam waves added.

Also note that two axially propagating space charge waves are sup-ported by the electron beam [3): fast (Vph > vii) and slow (vpa < vii)

space charge waves. The actual dispersion relation is approximated by

w = Vll(k - 2 /it/L) ± w6 , (B -. 2)

where wb is the beam electron plasma frequency. Thus, the plot infigure B-3 is valid only when wb is small.

The intersection point of the space charge wave line with the peri-odic electromagnetic wave dispersion relation is the operating point Gt.the device. The full beam dispersion relation easily yields the possiblefrequencies and modes of operation. Note that the intersection pointin figure B-3 lies on a portion of tLe electromagnetic wave dispersionrelation where dw/dk < 0, which implies a backward propagating wave.

The above discussion of dispersion relalions is highly idealized. Inact ual practice', coupling between the space charge and electromagneticwaves results in a far more complicated region of intersection (4,5] inwhich the actual operating point will be complex-with the imaginaryportion representing the growth rate of the instability. An "in depth"discussion ii beyond the scope of this report, although moie detailedexpositions are found elsewhere [.1-61.

66

I "" +- ' ,' " " . .. . " " , ' : •'° ' " '+ ' " +"'-": 5" °''

:" ' . .. .--' -,

References

1. Yu. F. Bondar et al., Measurements of RF emission from a car-cinotron with a relativistic electron beam, Sot'. J. ,-lasmla Phys.9(2) (1983), 223.

2. A. Bromborsky and B. C. Ruth, Calculation of the TA! 0 ,, (lisper-sion relations in a corrugated cylindrical waveguide, IEEE Trans.MTT-32(6) (1984).

3. C. C. .Johnson, Field and IWave Elect rodyna mics, McG raw- Hill,NY (1965).

4. .1 A. Swegle, J. WV. Poukey. and G. T. Leifeste, Backward waveoscillators with rippled wall resonators: Analytic theory and nu-mierical simulation, Phys. Fluids 28(9) (1985), 2S82.

5- R. J. Briggs, Electron Stream Interaction with Plasmas, MITPress, Cambridge, MNA (1964).

6. J. A. Swegle, Approximate treatment near resonance of backvardand traveling wave tubes in the Compton regime, Phys. Fluids28(12) (19S5), 3696.

67

Appendix C.-The Microwave Grating Spectrometer

The spectrometer used in these experiments was the prototype of a sys-

tem that was designed by the University of Maryland's Lab for PlasmaFusion Energy Studies for measuring the electron cyclotron emission

from tokamak plasmas [1]. It is similar to the microwave spectrome-

ters used by other researchers in the high-power, high-frequency reigme

[2-4]. The operational frequency range was extended from the original

design of 90 to 140 GlIz to 50 to 200 GHz by the construction of addi-

tional gratings. A detailed description of scattering from a diffractiongrating [5-7] is beyond the scope of this report; however, the elementary

theory and operation are developed and discussed in this appendix.

A schematic drawing of the spectrometer configuation is shown in

figure C-I. The microwave radiation enters via the input horn andilluminates the mirror MI which deflects the radiation through a lens

and onto the grating. The scattered radiation from the grating then re-

flects off mirror M2 and into the pickup horn which feeds the microwave

detector.

The effective scattering by the grating is given by the conditionfor constructive interference. If each grating line is considered a pointsource, then by equating the wave path lengths as shown in figure C-

2. the familiar form for the constructive interference condition may beeasily expressed as

d(sin 10, - sin 0,) = A. (C - 1)

where d is the spacing between adjacent gratings and A is the wave-

length of the wave under consideration. The local convention has been

to describe the configuratior in a state in which beth the incident and

reflected rays are on the same side of the norma" to the grating. Thus,the condition for constructive interference becomes

d(sin. 9i + sin 0,) = A. (C - 2)

69

1;;,..7.

With this convention, the useful range of grating angles, Di (for reason-ably flat frequency response), is approximately -2' to +80.

Note that in figure C-i, the angle 0, -Oi = a = constant. One mayeliminate 0, in favor of a to obtain

sin Oi + sin(a + OD) = A/d. (C - 3)

The substitution A = c/f and judicious use of half-angle formulas maybe combined with equation (C-3) to reach

S .[c/fd 1,(C40,= -' + arcsn [2c 2) (C-4)

which gives the grating angle 0, needed to detect a given input fre-quency, f. This formula was used to build the tables of 0, for variousvalues of f and d that were used to set the spectrometer for the desiredfrequency measurements.

The initial setup of the spectrometer was facilitated by the use ofa small Ite-Ne laser that was mounted in place of the microwave inputhorn. The relative zero angle on the angular scale (attached to thegrating) was determined by the position at which a mirror on the surfaceof the grating reflected the laser beam straight back along its originalpath. Actually, the laser was slightly tilted so that the reflected beamdid not reenter the source. The grating (with mirror) was then rotateduntil the laser beam struct, the center of the receiving horn, providinga measure of the angle a/2 in figure C-i. In actual practice, the mirroris attached to the nongeating side of the grating piate, and the zeroangle must be "corrected" by 180'.

Further calibratijn was achieved by launching a known microwavesignal into the sp'ctrometer and viewing the detcctor output as a func-tion of grating angle. The results indicated that equation (C-4) is ahighly accurate predictor of spectrometer operation. The F\VIIM ofthe detector signal divided by the base frequency gave Af/f - 0.02,which is close io the resolving power quoted by Fisher (1]. The linewidth ,.of the input "calibration" signal was not known.

The gra: ing ;pect roineter was a reliable "work horse" that provi(dedno surprises and always functioned as predicted by the simple modelsdescribed above.

C

70

M M-

/ ........

D e te c to r R e e v n

horn

Receaving

Mirror

Millimeter Wave ________

Radiation Mro

Figure C-1. Schiezativ clrawiiig of grating spectrometer.

d Grating surface

d(sin 0,-sin 01)=X

I'igture C-2. Simp jle ino)dPI of comlitioil for coilstructivetuiterfermiee froiui a (liff'ractiozi gratiing.

71

References

1. J. Fisher, D. A. Boyd, A. Cavallo, and J. Benson, Ten-channelgrating polychromator for electron cyclotron emission plasma di-agnostics, Rev. Sci. hstrum. 54(9) (1983), 1083.

2. W. NI. Bollen, R. 11. Jackson, D. J. Sullivan, and D. E. Voss, Agrating spectrometer for millimeter waves, Proc. IEEE Int. Conf.on Plasma Sci., San Diego, CA (1983).

3. J. A. Pasour and S. P. Schlesinger, Nfultichanne! grating spec-trometer for millimeter waves, Rev. Sci. Instrum. 48(10) (1977),1355.

4. R. M. Gilgenbach, T. C. Nhrshall, and S. P. Schlesinger, Spec-tral properties of stimulated Rainan radiation from an intenserelativistic electron beam. Phys. Fluids 22(.5) (1979), 971.

5. D. Maystre. Rigorous vector theories of diffraction gratings, inProgress in Optics, vol 21, ed by E. Wolf, North-Holland PhysicsPub, Amsterdam (198,1).

6. E. G. Loewen. M. Neviere, and D. Maystre, Grating efficiencytheory as it applies to blazed and holographic gratings, Appl.Opt. 16(10) (1977). 2711.

7. M1. Born and E. Wolf. Principlez of Optics, 6th ed, PergamonPress (1980).

72

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