66 IEEE TRANSACTIONS ON ELECTRON DEVICES February

Some Studies on a High-Perveance Hollow-Beam Klystron*

E. K. DEMMELt

Summary-The performance of an experimental high-perveance hollow-beam klystron has been investigated. Data of small- and large-signal operation are presented in this paper. For strong magnetic confinement of the beam, it is shown that gap inter- action and gain and large-signal bunching are well predictable by the appropriate theories. A sensitivity of all measurable RF-quan- tities to the level of the focusing field has been studied. Efficiencies are lower than predicted from the measured high degree of bunching, and reflect the effect of potential depression.

INTRODUCTION

I N RECENT years, attention has been given to the use of high-perveance beams in microwave klystrons.' Not only are problems associated with high-voltage

operation effectively reduced, but also, an additional benefit can be derived from the lower beam impedances for the design of wide-band amplifiers.

Questions related to the electron beam and its genera- tion and confinement become increasingly important at higher perveances. As a consequence of potential depres- sion and the associated variation of electron velocities over the cross section of a non-neutralized beam, solid cylindrical beams with perveances in the order of 10 X IOp6 a/v3" are ruled out. The alternative choice, there- fore, is a thin hollow beam very close to the drift tube walls. Potential depression and velocity spread can be kept within tolerable limits, and use can be made of newly developed beam injection schemes' which are naturally adapted to the geometry of the hollow beam. The actual choice of beam dimensions will be a compromise between focusing and alignment requirements, beam sta- bility, and the maximum permissible potential depression and velocity spread.

Although high perveance klystrons promise to gain a sizable part of the power tube market, very little detailed information has been published on the performance of these devices. Design procedures have been widely adopted from, low perveance routines and have proven successful over a wide range of parameters. The results of experi- ments, which are described by this paper, generally con- firm the confidence in established design techniques. Interpretation of those results, which are unusual or un- expected, will be attempted.

* Received September 23, 1963. t Varian Associates, Palo Alto, Calif. W. L. Beaver, "An experimental high-perveance klystron

amplifier," Proc, IEE, B 105, Suppl. No. 12, pp. 821-823; December 1958.

2 G. S. Kino and N. J. Taylor, "The Design and Performance of a Magnetron-Injection Gun," IRE TRANS. ON ELECTRON DE- VICES, vol. ED-9, pp. 1-11; January, 1962.

THE EXPERXMXNTAL TUBE A siu cavity L-band amplifier was built for this in-

vestigation. The emphasis in the design of the device was on versatility rather than optimum performance as an amplifier in order to facilitate the coverage of a wide range of parameters, and to aIlow a variety of small and Large signal experiments.

Fig. 1 is a schematic representation of the test tube. A magnetron injection gun with a 4" tapered cathode (a) in a uniform axial magnetic field produces the hollow beam. The voltage of the experiments was limited by the modulator to the range 30 to 50 kv. An insulated anode (b) was used to vary the perveance between 7 X and I1 X The reduced plasma angle p,1 between successive gap centers as calculated from a laminar flow model covers the range from 80" to 120" for the first three stages, and the range from 40" to 60' for the last two stages, depending on beam parameters.

df

CAVITY NO. * 6 5 4 3 2 I

Fig. 1-Schematic diagram of experimental high perveance klys%ron. (Not drawn to scale.)

The cavities with gridless gaps are equipped with loosely coupled test loops (c). Cavities No. 2, 3 and 4 are tunable over a 15 per cent frequency range by means of tuner rings inside the cavities (d). The beam loaded input cavity was approximately critically coupled to a coaxial line (e). The waveguide output (f) was designed to facilitate a controlled impedance transformation. A careful calibration of cavity parameters allowed the com- putation of induced RF gap voltages and currents from power measurements at the test loops.

The coIIector {g) is insulated from the body of the tube to permit transmission measurements. Special care had to be taken in the design of the collector and the shaping of the magnetic field in the collector region to

196.4 Demmel: A High-Perveance Hollow-Beam Klystron 67

prevent high energy scattered electrons from returning into the interaction region. The stability of the operation of the device was very sensitive to conditions in the col- lector. The magnetic focusing field is produced by a stack of eight solenoids (h). Individual current control of the solenoids allows extensive shaping of the field. The design value of the field is 1200 Gauss a t 50 kv for a beam of microperveance 10.

SMALL SIGNAL PERFORMANCE

Predictions of small signal gain and bandwidth of multi-stage klystron amplifiers rest on the knowledge of such quantities as the electronic gap loading and the transadmittance between pairs of cavities. It has been the purpose of the experiments which are described in this paragraph to test the validity of approximate theoretical expressions for the computation of these R F quantities.

Both quantities, the complex gap loading admittance Y, and the transadmittance \gl-2\, have been derived from single-stage-gain measurements. In the experiments, a small RF signal of constant frequency fo and constant amplitude is applied t o the driver cavity. The resonant frequency f a of the second cavity is varied over its me- chanical tuning range and output power from a weakly coupled test loop is observed. Gap voltages are derived from power measurements at the test loops of the first and second cavity.

The beam-loaded Q of the second cavity is related to the frequency difference Af2 between half power points by Q L = fo/Af2. For Q L << Q,, the unloaded Q of the cavity, the electronic gap loading conductance is given by

The characteristic impedance RJQ, of the cavity was determined by frequency perturbation techniques over the entire tuning range. The imaginary part of Y e is obtained from the difference S f a between drive frequency fa, and the resonant frequency of the second cavity at maximum gain

The transadmittance is derived from the measured voltage gain by

with

I,, = induced RP current in second gap V,,l,2 = RF gap voltages YT, = total admittance at second gap.

At the ((hot” resonance of the second cavity, and for small cavity losses, Y T = G..

A . Conductive Gap Loading Experimental gap loading conductances for a fixed

applied voltage are shown in Fig. 2 over a range of perveance at various levels of the focusing magnetic field. The data are normalized to the DC conductance Go = Io/Va with I, and V , being the DC beam current and the applied voltage. Due to potential depression, the beam voltage decreases with increasing perveance. At micro- perveance 10, the average potential reduction in the gap is approximately 13 per cent.

+I440 G

+I200 G

+960 G 0.24

0.22 i Ge/Go A A - > A n

0.20 - O A

n o - 0 ”

0.18 - 0 __-- _----- - -:-------- --- 0.16 =

0.14 I 6.5 7 8

I ! 1 I I 9 10 I I I2

MlCROPERVEANCE

Fig. 2-Small signal electronic gap loading. V o = 41.5 kv, Parameter: Magnetic field in Gauss - - - Eq. (5).

It is evident from this set of data and others taken at different applied voltages that the level of the magnetic field has a strong effect on the loading. Approximate computations have been made of the loading contribution by interaction with the transverse component of the gap field for finite magnetic fields. The magnitude of this effect is, however, insufficient to explain the observed strong dependence on the magnetic field level. As will be demonstrated by other data in this paper, all measurable RF quantities display a dependence on the magnetic field.

A ballistic expression for the electronic loading by a confined relativistic hollow beam with

2a = inner diameter (= 1.09 inches) 2b = outer diameter ( = 1.25 inches)

is obtained by integration over the contribution of indi- vidual cylindrical current larnella~,~

GB = Io/VB = beam conductance V B = average depressed beam potential in gap

3 G. M. Branch, Jr., “Electron beam coupling in interaction gaps of cylindrical symmetry,” IRE TRANS. ON ELECTRON DEVICES, vol. ED-8, pp. 193-207: May, 1961.

IEEE TRANSACTIONS ON ELECTRON DEVICES February 68

B e = uo - R = M ( r ) =

- w/uo = beam wave number beam velocity (I - u,~/c;)-'" = relativity factor. coupling coeflicient for a thin anular beam of radius r .

For a gridless knife-edge gap4

with

d = gap length (0.875 inches) 2c = drift tube diameter (1.50 inches) Y = P./R.

Eq. (4) may be written as

with

G,,,(p) is the electronic gap loading by a solid beam of radius p .

The theoretical curve in Fig. 2 has been obtained from (5) by normalizing to Go and using front and rear radii of the cathode for a and b. The positive slope is caused by increasing potential depression.

The ballistic loading as given by (4) may be considered as the first term of a Taylor series expansion of a more complete description of the electronic loading conductance by We~sel-Berg,~ including the effect of space charge forces.

with

pa = LZ = reduced plasma wave number, and W

UO

ALf@.)l = f @ e + B,) - fCB. - P a ) .

Cambridge University Press, Oxford, England, p. 69; 1948. 4 A. H. W. Beck, "Velocity-Modulated Thermionic Tubes,"

trary, Extended Interaction Fields," Microwave Lab., Stanford 6 T. Wessel-Berg, "A General Theory of Klystrons with Arbi-

University, Stanford, Calif., M. L. Report No. 376; March, 1957.

The dominant contribution of space charge forces to the electronic gap conductance, as given by -the second term of expansion (6), is proportional to wz, and therefore to the perveance. Over the range of gap transit angles of the experiments, d3[Mz(r)]/dp: is a positive quantity. The effect of space charge forces, therefore, is to reduce the loading, as calculated by a ballistic approximation, by a small amount, which is proportional to the per- veance. Application of this correction would reduce the positive slope of the theoretical curve in Fig. 2.

B. Reactive Gap Loading A quantitative evaluation of the imaginary part Be

of the electronic loading admittance has not been at- tempted. Shifts of the resonant frequency of the test cavity produced by reactive beam loading were fractions of a per cent and are not easily measured. However some qualitative statements can be derived from the experiment.

a) For high magnetic fields it was found that

B, > 0 for ped < 1.8

3, < 0 for ped > 1.8.

Thus, the reactive loading reverses its sign for Ped ap- proximately 10 per cent below the transit angle required for maximum conductive loading. This relation is similar to the results of a one-dimensional analysis of beam loading in a constant-field gap, in which case, however, the transit angle for zero reactive loading is T.

b) The reactive gap loading component is also affected by the level of the focusing field. In the range of these experiments (30 kv < V,, < 50 kv) it was found that 3, decreased with decreasing magnetic field. At 35 kv, where for high magnetic fields B, > 0, sufficient decrease of the field reversed the sign of the reactive loading term.

C. Transadmittance Making use of (2 ) , the single-stage transadmittance

lg1-21 has been derived from measured quantities and is shown in Fig. 3. With decreasing magnetic field, an in- crease in transadmittance is seen first which is followed by a sudden decrease. A modest increase is to be expected on the basis of Brewer's space charge wave theory in finite magnetic fields,6 and also as a consequence of a spreading beam. The decrease, however, cannot be ex- plained by known theoretical approaches or by beam imperfections.

For comparison, the transadmittance has been com- puted using only the lowest pair of equally excited space- charge waves;

charge wave propagation," PSOC. IRE, vol. 44, pp. 896-903; July, G. R. Brewer, "Some effects of magnetic field strength on space

1956.

Dernmel: A High-Perveance Hollow-Beam Klystron

3'61 4 1440 G

-0- 1200 G

4 960 t 3.2

2.2 ":. 10 I I I2

i

MICROQERVEANCE

Fig. 3-Small signal transadmittance of single klystron stage. T T o = 41.5 kv, Parameter: Magnetic field in Gauss - - - Eq. (7) .

with

= relativisticly corrected reduced pIasma frequency

5 = plasma frequency 27r F = space charge reduction factor7

= mean square coupling coefficient.

From the results of Fig. 3, it may be concluded that the simple expression of (7) predicts the transadmittance of a strongly confined beam sufficiently close for most practical requirements.

LARGE SIGNAL ELECTRONIC GAP LOADING

In the preceding section, it was demonstrated that linear theories predict to a satisfactory degree the small signal behavior of a strongly focused, high perveance beam. The onset of nonlinearities has been studied in gap loading experiments. Using the same techniques as de- scribed for small signal measurement, the data of Fig. 4 have been obtained. Although it was chosen to present the data as the real and imaginary part of a large signal gap loading admittance, it must be realized that the particular experimental procedure might have strongly effected the results. This possibility is suggested by an increasing asymmetry of the cavity response with in- creasing signal level, indicating a dependence of the loading admittance on the phase of the gap voltage with respect

G. ;!I. Branch and T. G. Mihran, "Plasma frequency reduction factors, IRE TRANS. ON ELECTRON DEVICES, vol. ED-2, pp. 3-11; ApriI, 1955.

0 . 4 4 ~

o'41 0.3

/ ___--- -_--

69

-0. I I I ! -0.16 0 0.2 0.4 0.6 0 8 1.0 1.2 1.4 1.6 IS

v29 / VB

Fig. 4-''IAarge Signal Electronic Gap Loading" measured with premodulated beam. V, = 46 kv, pe l = 1.6, high magnetic field. - - _ Ballistic loading of a constant field gap after Wessel-Berg: A: pel = ~ / 2 ; B: @,I = 3/47r; C: 8.1 = T.

to the driving current. Large signal loading by an un- modulated beam might differ considerably from the experi- mental curves in Fig. 4.

For gaps with constant RF fields, Wessel-13ergS has calculated ballistic large signal loading conductances. FOP comparison, his results for three different transit angles are also plotted in Fig. 4. The degree to which the dis- crepancy is caused hy inadequacy of the experimental precedure has not been determined.

LARGE SIGNAL BUNCHING

High efficiency operation of a klystron amplifier, as of any other velocity modulated device, is associated with a high degree of bunching of the electron beam. To measure the degree of maximum obtainable hunching, the ratio of the saturated RF current amplitude in the funda- mental frequency t o twice the DC current in the beam is used. This ratio 1m/21!210 is called the "bunching efficiency".

Experiments to measure the bunching eficiency of a two or more cavity section of the klystron were performed by modulating the beam at the input gap with drive power adjusted t o produce saturation a t one of the

lators with Constant RF-Field," Norwegian Defense Res. Estab., 8 T. Wessel-Berg, "Large Signal Analysis of Monotron Qscil-

Division €or Radar, Technical Note No. 1; June, 1960.

70 IEEE TRANSACTIONS ON ELECTRON DEVICES February

following gaps. The impedance of the test cavity was reduced to the lowest possible level by detuning in order to avoid voltage saturation effects. Knowing the param- eters of the cavities and test loops, RF gap voltages and induced RF currents were again derived from power measurements. Application of a mean coupling coeffi- cient yielded the fundamental component of the R F cur- rent in the beam. The mean coupling coefficient, which is assumed t o be appropriate for a saturated beam, is given by

a=--- J b M(r) r dr. bz - a2 (8)

For a thin hollow beam, it differs very little from (?C?i)l”.

A. Two-Cavity Experiments Bunching efficiencies of a two-cavity section of the

tube are plotted in Fig. 5 vs perveance. The applied voltage was kept constant and the experiment repeated for several levels of magnetic field. The dependence of bunching efficiency on the magnetic field level is clearly reflected.

B. Multi-Cavity Experiments Data of Fig. 6 were obtained from two three-cavity

experiments at somewhat different perveances. The resonant frequency of the center cavity is varied with a corresponding change of magnitude and phase of its impedance. The focusing field was chosen sufficiently high, therefore avoiding the previously observed de- terioration in bunching efficiency. Normalized RF beam currents a t the center cavity which were required for saturation at the third gap are also shown.

Bunching enhancement by inductively loading the pen- ultimate gap in multi-cavity tubes (fZ > f o in Fig. 6 ) has long been known and made use of. However, in the case of Fig. 6, this enhancement is small, and decreases with an increase in perveance and therefore with an in- crease of p,1 between cavities. p,1, as derived from a con- fined beam model, is in excess of 90” for both perveances.

Data of Fig. 7 were obtained at the fifth cavity which, for the beam parameters of this experiment, was separated from its penultimate cavity by a reduced plasma angle of only 47’. The bunching enhancement, with respect to operation with synchronous tuning of the penultimate cavity, is as great as 40 per cent. In a variety of tests involving the same number of cavities it was seen that the bunching efficiency was only little affected by the tuning of the third cavity, provided it was not tuned below the signal frequency. A capacitive loading of the third cavity, however, caused a significant reduction in maximum bunching efficiency, as is seen in Fig. 7.

C. Summary of Bunching Experiments Bunching efficiencies, as obtained from a large number

of tests, are summarized in Fig. 8. All data represented by‘this diagram were taken at high magnetic field levels

and cover the voltage and perveance range specified for this tube. Bunching eEciency is plotted vs the reduced plasma angle between the test cavity and its respective penultimate cavity. In this representation, it was found that voltage and perveance produced only a minor spread of the experimental points of which the curves of Fig. 8 are the averages. This emphasizes the relative importance of the small signal space charge parameter pal for the final bunching stage.

Single stage experiments were only performed in the range of large p,1. A speculative extension to lower p,1 suggests optimum bunching efficiencies of approximately 0.58 as are predicted by Webster’s bunching theory. Multi-cavity experiments covered a wide range of large p,1 and a narrower range of small p,1. Multi-cavity data which were obtained with synchronous tuning of the penultimate cavity exhibit a similar dependence on p,1 as single-stage data. This is to be expected since, due to the high impedance a t the penultimate gap for syn- chronous tuning, large signal bunching takes place only in the last stage. However, the magnitude of bunching efficiency in this mode of operation is reduced from the genuine two-gap case by approximately 10 per cent. This corresponds in magnitude to the R F current required to drive the penultimate cavity, and therefore suggests that the difference reflects the effect of feed-through terms in current due to bunching before the penultimate cavity. Bunching enhancement by means of inductively loaded buncher cavities becomes increasingly effective for re- duced &I.

A detailed theoretical study of bunching phenomena for two and multiple gap klystrons with solid cylindrical beams of low and moderate perveances has been published by S. E. Webber.g,lo,ll

As has been pointed out, a comparison of different beam geometries with Webber’s results requires a new interpretation of the parameter yb.lo For the cylindrical solid beam, an approximate relationship between yb and the space charge reduction factor F has been given by Tien, et 511.’’

F = w,/w, = rl + (2/yb)2~-11/2.

A comparison of different geometries should be made on the basis of an equal value of F . Typically F is 0.16 for this tube, therefore data presented in this paper should compare with data for yb = 0.3 for solid cylindrical beams. Webber’s curves for rb = 0.4 are closest, and agree- ment with experimental data is indeed very satisfactory.

klystron,” IRE TRANS. ON ELECTRON DEVICES, vol. ED-5, pp. * S. E. Webber, “Ballistic analysis of a two-cavity finite beam

98-108; April, 1958. 10 S. E. Webber, “Large signal analysis of the multi-cavity

klystron,” IRE TRANS. ON ELECTRON DEVICES, vol. ED-5, pp. 306-315; October, 1958.

traveling-wave amplifiers,” PROC. IRE, vol. 43, pp. 260-277; 11 P. Tien, L. Walker and V. Wolontis, “A large signal theory of

March, 1955. 12 S. E. Webber, “Some calculations on the large signal energy

exchange mechanism in linear beam tubes,” IRE TRANS. ON ELEC- TRON DEVICES, vol. 7, pp. 154-162; July, 1960.

1964 Demmel: A High-Perveance Hollow-Beam Klystron

-+-- 1200 G

IO80 G

-43- 960 G

MICROPERVEANCE

Fig. 5-Bunching efficiency of single klystron st,age. V o = 41.5 kv. Parameter: Magnetic field in Gauss.

------l

/DRIVE FREQUENCY

I220 IPEQ I x ) O 1340 1380 1420 1 9 6 0

CAVITY N0.4 FREQUENCY IMC)

Fig. 7-Bunching efficiency of 5-cavity klystron section. V O = 45 kv, K = 7.7 Micropervennce &14-a = 47".

.--C K.7.55 KT6, BqL=92'

& Ks9.62 II IO". BqL=104.

l lEO 1220 1260 1300 1340 1380 1420 1460

CAVITY NO.2 FREQUENCY ( M e )

Fig. 6-Bunching efficiency of 3-cavity klystron section. V O = 40 kv. Parameter: Perveance.

0.8 I I I I I I I

\

MULTICAVITY KLYSTRON

PENULTIMATE CAVITY W I T H OPT. TUNING OF

0.6 TWO CAVITY KLYSTRONd

0.5

0 . 4 1

--__ -- \ -- .\ -_ --.

MULTICAVITY KLYSTRON W I T H SYNC TUNING OF PENULTIMATE CAVITY

0.3 30 _1 40 50 60 70 80 SO IO0 110

8, L (degrees)

Fig. %-Dependence of bunching efficiency on reduced plasma angle 6.1 between penultimate and test cavity.

_ _ - _ speculatian. average of experiments,

7 2 IEEE TRANSACTIONS ON ELECTRON DEVICES February

EFFICIENCY The output efficiency of a klystron depends on a large

number of parameters, some related to the output gap, others to the characteristics of the bunched beam driving it. Bunching efficiencies, which were investigated in the preceding paragraph, may only be regarded as upper limits never exceeded by the output efficiency. S t ~ d i e s ~ ' ~ ~ ' ' ~ of the effect of velocity distribution in the bunches and of space charge forces in the output gap indicate the com- plexity of the problem.

The information related to the energy conversion process in output gaps, which was obtained from experiments in this program, is rather limited. The design of the tube and the frequency limitations of the driver did not permit variation of the penultimate gap impedance over a large range. The low impedance of the penultimate gap resulted in a high degree of bunching a t this gap for saturation of the output. It is believed that the efficiency of this tube has suffered from nonoptimized bunching conditions.

Two major observations were made. First, the efficiency of the device was very sensitive t o the shape of the mag- netic field, and second, maximum efficiencies occurred a t normalized RF output gap voltages considerably below those commonly observed in low perveance tubes.

Fig. 9 illustrates the dependence of efficiency on mag- netic field shape. Curve A was taken with a uniform flat magnetic field, whereas in curve B, the magnetic field shape was optimized for each applied voltage. While the drive power is optimized for each point, tuning of the tube, perveance and output gap impedance were kept constant. A large number of tests, both in the small and large signal region, were subsequently carried out to systematically investigate the nature of the observed efficiency improvement by field shaping. The main ob- stacle in analyzing these data was that due to the thickness of the individual solenoids, variation of one solenoid cur- rent resulted in field changes which generally extended over more than one klystron stage.

It was found that for optimum efficiency, the shape of the focusing field was strongly related t o the impedances of the buncher cavities; in particular, it was related to the impedance of the fourth cavity which precedes the fixed tuned penultimate cavity. The intergap spacing between the fourth and the penultimate cavity was, how- ever, the region most effected by field shaping. In addi- tion, the results of small signal gain measurements between these cavities suggest that the beam follows the curved flux lines. For a thin hollow beam, even small changes in the spacing between drift tube walls and beam boundary will modify the space charge forces ~onsiderably.~ The efficiency improvement by means of shaped magnetic fields (Fig. 9) has therefore been interpreted as an optimi- zation of reduced intergap plasma drift angles for given cavity impedances. Efficiencies as high as those with the optimized magnetic field shapes of Fig. 9 were obtained with straight magnetic fields and a different impedance

--+-FLAT F I E L D 1440G

- O P T I M I Z E D F I E L D S H A P E

0.40

0.24 1 I 1 I I I I I 1 34 36 38 40 42 44 46 48 50 52

DRIFT TUBE VOLTAGE (Kv)

Fig. 9-Efficiency for flat (Curve A) and optimized (Curve B) magnetic field shape. K = 8 microperveance. Output resist- ance = 555 Q.

of the fourth cavity. In comparing performance for dif- ferent magnetic fields, only those shapes have been used which provided equal average fields over the length of the output gap, and therefore, minimum perturbation of the output gap coupling coefficient.

The data of Fig. 9 was obtained with a fixed output impedance of 555 Q. Efficiency improvements were ex- pected by increasing this impedance, and therefore in- creasing the relative gap voltage to levels commonly ob- served in low-perveance tubes at high-efficiency operation. These attempts failed, and maximum efficiencies always occurred a t gap voltages less than the applied voltage. From the trend of the optimized curve of Fig. 9, it is expected that further increases in applied voltage would only insignificantly raise the efficiency and relative gap voltage.

Unfavorable velocity distributions in the bunches are recognized as limiting the gap voltage for optimum effi- ciencies. There exists, however, a fundamental reason why high-perveance beams should yield lower efficiencies than low-perveance beams.

The potential depression of the investigated beam was calculated to be typically 6 per cent below applied po- tential in the drift tube region, and 10 per cent average in the gap region. These calculations were done for a beam which is uniform in axial direction. Certainly this assumption is still valid for small signal operation. How- ever, for large degrees of bunching, the bulk of the charge which in the unmodulated condition occupied the region of one electronic wavelength, is now compressed into a much shorter region, perhaps one half to one third of an electronic wavelength depending on the bunching effi-

1964 Demmel: A High-Perveance Hollow-Beam Klystron 73

ciency. In a magnetically confined beam, this compression will be accompanied by a corresponding increase in po- tential depression a t the expense of kinetic energy. The field energy cannot be recovered in the output gap and is converted into impact energy in the collector. The amount of potential energy will even increase as the bunch is slowed down in the output gap. It is therefore con- ceivable that the optimum efficiency of this device is reduced by approximately 20 t o 30 per cent of the effi- ciency of an optimized low perveance design where po- tential depression is not a very important consideration.

CONCLUSION

Experimental data which have been presented in this paper encourage the designer of high-perveance hollow- beam klystrons to use the familiar tools of space-charge wave and ballistic theories to predict small signal per- formance and large signal bunching, provided a strong confining magnetic field is used. In the described tube, the minimum field for predictable performance was found to be about 30 per cent above the design value. The efficiency of the experimental tube was below expectations based on the high degree of obtainable bunching. A qualitative argument has been produced relating reduced efficiencies t o potential depression in heavily bunched high perveance beams. Nevertheless, observed efficiencies in excess of 40 per cent qualify high-perveance designs for many applications.

It was found that all measurable RF quantities dis- played a reproducible dependence on the magnitude of

the focusing field. In an effort to interpret this effect, the theories of space-charge wave propagation in finite magnetic fields and coupling to transverse fields in grid- less gaps have been considered. No agreement between the predictions of these theories and experimental data was found. Reduced beam transmission, unavoidable in some of the experiments, showed no correlation t o the observed effects.

It is suggested that the investigated beam was not in a state of laminar equilibrium for most experimental condi- tions. Energy in cycloidal motion will reduce the longi- tudinal velocity of the beam. In devices utilizing pre- dominantly longitudinal interaction and bunching, this should produce observable effects on RF performance. Quantitative conclusions about the energy in transverse motion can be drawn from RF measurements and will be discussed in a forthcoming paper.13

ACKNOWLEDGMENT The author is greatly indebted to Dr. L. A. MacKenzie

of Cornell University for his contributions to this work during his association with the project. The support of these investigations by the M. I. T. Lincoln Laboratories and the continual interest to Dr. G. Guernsey is gratefully acknowledged. Dr. W. Beaver, while supervising this work, has given a generous amount of help and many valuable suggestions.

13 E. K. De?rnel, “RF-Diagnosis of Magnetron-Gun Injected Hollow Beams, presented at 1963 Electron Devices Meeting, Washington, D. C.