a method of improving the - dticvoltage on second electrode of a two-electrode collector 35 - v -...

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A METHOD OF IMPROVING THE EFFICIENCY OF KLYSTRONS

By

Riebard II. Winkler

Technical Report P revered under C'f;; ; if Naval Research Contract

HfiHii 251*1 •MR 07? S(Slk

jttirrtly •uppwfed fc» »«..« y,s. Army Signii Corps,

rtte U.S. Air Fc.ce, attd the U.S. Navy

(Clike cf Naval Reeearch)

MX. Report No. 235 May, 1954

I W. W. BAHSSN LABOIUTOHFES OF PHYSICS „,_,_ "*tuu ( . STANlfySB UNIVERSITY 'tilfmM

STANFORD, CAM?• >r.P(iA " *** •-

THIS REPORT HAS BEEN DELIMITED

AND CLEARED FOR PUBLIC RELEASE

UNDER DOD DIRECTIVE 5200,20 AND

NO RESTRICTIONS ARE IMPOSED UPON

ITS USE AND DISCLOSURE,

DISTRIBUTION STATEMENT A

APPROVED FOR PUBLIC RELEASE;

DISTRIBUTION UNLIMITED.

r Microwave Laboratory

• W. W. Hansen Laboratories

Stanford University

A METHOD OF IMPROVING- THE

EFFICIENCY OF KLYSTRONS

Richard H. Winkier

Technical Report

May 1, 195^

Prepared under Office of Naval Research Contract . N6onr k.3123 (NR 073 361) J » Jointly supported by the U-S. Array Signal Corps,

the U.S. Air Force, and the U.S. Navy (Office of Naval Research)

M.L. Report No. 235

Stanford, Cai^ornia

4 I

The research reported in this document

was supported jointly "by the TJ. S. Army

Signal Corps, the U. S. Air Force, and the

U. S. Navy (Office of Naval Research),

L

- iii -

L .

•

r LIST OF FIGURES

6.7. Collector efficiency and current transmission vs collector voltage ...... 34

6.80 Collector efficiency and current transmission vs voltage on second electrode of a two-electrode collector 35

- V -

•

Page

2.1. Exit velocity and output gap efficiency vs gap spacing for a gridded klystron 5

2.2. Output gap exit velocity vs time 7

2.3. D-e beam-spreading curves 9

3.1. Recaptured power vs collector voltage for a single electrode collector 12

3.2. Electron current per increment of electron velocity vs electron velocity 13

4.1. Collector electrode shapes , ..... 17

5.1. Klystron assembly drawing * . . 20

5-2. Collector chamber equipotential plot 22

5.3. Collector assembly drawing . 24

6.1. Circuit diagram 27

6.2. R-f power output, r-f power gain, and efficiency vs beam voltage ..... 28

6.3. R-f power output and r-f power gain vs r.--f power input 29

6.4. Current transmission vs r-f power input 30

6.5. Current transmission vs collector voltage 32

6.6. Collector efficiency and current transmission vs collector voltage > • . • 33

I 6.9. Collector efficiency and current transmission vs voltage on first electrode of a two-electrode collector 36

i

J

TABLE OP CONTENTS

Page

I. Introduction . 1

II. Study of r-f structure ..... 3

III. General discussion of collecting devices .... 10

IV. Collecting and velocity-sorting devices 15

V. Description of collector 19

VI. Experimental data 25

VII. Possible improvements kO

VIII. Circuit considerations . . 42

IX. Conclusions 4j

Appendix 44

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A.l.

Page Collector efficiency and current transmission vs voltage on first electrode of a two-electrode collector 37

Single-electrode collectors ..... kl

Construction for determining electron exit potential and time of exit for electrons passing through gridded gaps 45

1

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V

NOMENCLATURE

a = «= electron acceleration

d distance between entrance and exit plane

time

* . time at crossing entrance plane

dz u = -*£• electron velocity

•> u0 input velocity of electron at entrance plane

u0

u2

z distance from entrance plane

ood D <m -— normalized distance between entrance and exit plane

peak r-f gap voltage between entrance and exit plane

0 V0= •^STm Potential corresponding to input velocity uQ

Y normalized distance

(DZ Z = -— normalized distance from entrance plane u0 V

a = •»— normalized gap voltage v0

<D frequency

- vii -

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j

ACKNOWLEDGMENT

The author wishes to acknowledge the help of

Professor E. L. Glnzton, Director of the Microwave Laboratory,

whose faith and enthusiasm contributed greatly toward the com-

pletion of the project? and the author wishes to thank the

many members of the Laboratory staff who have helped with the

construction of the apparatus described in the present report.

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- viii -

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I. INTRODUCTION

A klystron ^s essentially a device for converting one

form of electric power into another form. In particular, one j

is usually converting d-c or pulsed d-c power to a-c power ,

whose frequency is In the thousands of megacycles per second.

The klystron is composed of three physically distinct

structures: first, an electron gun which converts the d-c

power represented by electrons flowing in a pair of wires,

with a potential between the wires, tr an electron beam In

which the power is represented by the kinetic energy of the

electrons; second, an r-f structure which extracts some frac-

tion of the kinetic energy in the form of radio-frequency

electric power; and third, a collector for dissipating the

remaining kinetic energy of the beam.

The best r-f structures available rarely a^e capable

of converting more than 40 per cent of the beam power to r-f

power. The remainder is generally dissipated as heat.

It Is possible to reconvert some of tbis remaining

kinetic beam power into electric power again in a manner suit-

able for use at the electron gun. This is accomplished by

slowing electrons down with a retarding d-c electric field

produced by a segmented collector, the several segments

being at a negative potential with respect to the drift tube.

Sufficient power can be reused so as to reduce significantly

the net power input.

- 1 -

ssaaJ

(I. INTRODUCTION)

This report is devoted to the problem of designing,

building, and testing a collector which will reconvert some

of the beam power and increase the net tube efficiency (de-

fined >w the ratio of the r-f power- output to the net d-c

power input).

A collector for a 2-Mw pulsed klystron amplifier was r

built and tested. The beam had a perveance of 2 x 10"

amp/v^' and 10 kw of maximum average power. The special

collector resulted in a recovery of 24 per cent of the beam

kinetic energy. The r-f efficiency of the tube without the

special collector was 21 per cent. The special collector

thus provided an improvement in over-all efficiency to

21/(100 - 24) m 28 per cent.

On the basis of the measurements taken, it is esti-

mated *"hat an easily constructed collector should recover

30 per cent of the beam power. A properly designed klystron

should have an initial r-f efficiency of $0 to 40 per cent.

The addition of such a collector would increase the net ef-

ficiency to 4j5 to 57 per cent.

The addition of such a collector would thus result in

a reduction in power-supply requirements corresponding to de-

livering 30 per cent less current than would otherwise be

required. This is an obvious saving in power-supply compo-

nents and in the cost of electric power over the life of the

tube. These savings must be balanced against the added cost

of the collector and the more explicated operation. In

high-power tubes, the addition of such a device would appear

to be indicated. - 2 -

. •

II. STUDY OP R-F STRUCTURE

To design a collector one should study the character-

istics of the beam entering the collector, i.e., the beam

leaving the output gap.

Very complicated things happen to the electrons prior

to their arrival at the output gap. They interact with focus-

lng electrode fields, image charges, gap fields, magnetic

fields, gas ions, etc. But nothing disrupts the beam so

violently as do the output-gap fields.

For maximum output gap efficiency, the gap voltage

is about equal to the d-c beam voltage. In a gap-coupled

klystron (as opposed to a grid-coupled klystron) the electric

field at the gap has a significant radial component. These

fields are a function of both radial and longitudinal

position.

f t

•

The interaction between gap fields and electrons has

been studied by Ziteili. In the small-signal theory, the

electrons which are not accelerated in a longitudinal direc-

tion are accelerated radially, and vice versa. The magnitude

of these accelerations is (in the case of a d-c beam entering

the gap) such as to keep the current density constant. A

bunch, then, is not so much a crowding together of electrons

L. T. Ziteili, "Space charge effects in gridless klystrons," Microwave Laboratory Report No. 1^9* Contract N6onr 25123, Stanford University, October, 1951.

- 3 -

.

- . "

1 (II. STUDY OP R-F STRUCTURE)

but rather an increase in the current bpcause of a larger

beam. The maximum slope of the beam edge is -jrak'a. It can

be seen from Fig. 2.2 that the largest pulses of current

leaving the output gap are displaced by about 90° on either

side of the bunch center, at just the time the largest radial

accelerations exist.

For typical tubes k'a and a are about unity, so that

the maximum slope of the beam edge is approximately +0.25-

It is possible to make a graphical construction from

which electrons can be simply traced through a gridded gap.

If one were to follow a single electron through a gap and

plot the distance traveled against time, he would find the

path curved. However, by a suitable transformation of vari-

ables the electron path can be made a straight line and the

boimdarles, the input and output grid, be curved.. This tech-

nique is described by Garbuny and is developed in the

Appendix.

If space-charge forces are neglected and it is assumed

that the klystron gaps are formed by parallel planes, It is

possible to trace a number of electrons, say 30, through a

klystron and find tneir exit times and velocities. The effi-

ciency of such a klystron can be calculated from a summation

of their exit energies.

One can extend the technique to a gap-coupled tube by

assuming that the existing field can be replaced by a constant

field of finite length.

MVi. Garbuny, "Graphical representation of particle trajectories in a moving reference system," d. Appl. Phys., 21: 1054 (1950).

- 4 -

t - . . .«;. >;*.» •-. ••-*

*

>

(He STUDY OF R-F STRUCTURE)

It Is Interesting to see what the minimum electron

exit velocity is for different gap spacings and a = 1. This

value of a is very close to that necessary for maximum effi-

ciency for all gap spacings. The minimum value of gap transit

angle is generally in the vicinity of 1 radian. In gap-

coupled tubes, the equivalent gap along the axis of the beam

may be 5 radians. Minimum electron velocities found by trac-

ing electrons are shown in Fig. 2.1. The output-gap effi-

ciencies shown are perhaps Incidental to this discussion.

They are derived from Fig. 12, Chapter I, of Feenberg's

report.

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Gap spacing D (radians)

PIG. 2,1—Exit velocity and output-gap efficiency vs gap spacing for a gridded klystron.

E. Feenberg, "Notes on velocity modulation," Sperry Gyroscope Co. Report No. 5321-1043, September, 19-45 •

- 5 -

<A.t.-,fc,J -

(II. STUDY OF R-F STRUCTURE)

One might expect that for maximum efficiency the mini-

mum exit velocity would be zero. Fig. 2.1 indicates that the

minimum velocity is by no means small. In a gap-coupled kly-

stron with 1 radian between gap faces, the minimum velocity

into the collector is one third of the beam velocity.

The results of trajectory studies on thirty electrons

in a grldded-gap klystron whose output-gap transit angle was

2TT/5 = 2.1 radians are shown in Table 1 and Fig. 2.2. These

computations do not include space-charge or radial accelera-

tion effects. The average current is measured by the number

of electrons per unit time creeping the exit plane. For ex-

ample, during the one-half cycle centered on the antibunch,

5 electrons cross the exit plane where in the d-c case, 15

would cross. The average current is therefore 5/15 = 0-552

times the d-c current.

The r-f power output is calculated by a summation of

the energy of the thirty individual electrons and comparing

it with the d-c energy.

L

Table 1.--Electron beam leaving output gap.

Average current per half cycle

Estimated average voltage

(Beam perveance per half cycle)

Percentage of d-c

(d-c perveance) beam power

•w- cycle centered on bunch

1.67 I0 0-^9 VQ 4.87 0.41

•T* cycle centered on antibunch

0.55 I0 1.44 v0 0.195 0.24

R-f power output 0.35

Total i

0.98

- 6 -

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(II, STUDY OP R-F STRUCTURE)

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(II. STUDY OF R-P STRUCTURE)

The beam perveance averaged over one half-cycle cen-

tered on the bunch Is many times larger than the d~c perveance.

Likewise, the beam perveance averaged over the one half-cycle

centered at the antibunch is many times smaller. It is signi-

ficant to determine over what distance the beam maintains the

character represented by the half-cycle data, that is, before

the electrons become mixed. If tw<-> electrons of potential

0.49 V~ and 1.44 V^, respectively, leave the output gap one

Hnlf-cycle apart, and the d-c potential V0 is 80 kv, they will

pass each other 1.7 in. from the gap. Assuming the initial

beam diameter is 0.500 in., Lhe une half-cycle cf electrons

centered on the bunch considered as a d-c beam will almost

quadruple its diameter in that 1.7 in., whereas the antibunch

half-cycle will remain essentially unchanged (see Pig. 2.3)•

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III. GENERAL DISCUSSION OF COLLECTING DEVICES

The object of the collector is to retrieve as much

power as possible from the beam without disturbing the condi-

tions in the r-f section of the tube.

To convert the kinetic energy of the electron to elec-

tric energy one must slow down the electrons with an electric

field. To bring an electron of velocity u to a standstill,

it must be acted upon by an electric field E, such that when

the electron has traversed the distance.^, the following re-

lationship applies:

E«d

0

mu2 = e \ E»ds

'•••ij,^

•-

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- •

If the electron alights on an electrode just as it is

stopped, this implies the potential difference V between the

point at which the electron enters the field E and the point

at which it alights is n

V = - i E-ds oj

so that •1= _eV

If the potential differince between the beam and the drift

tube is neglected, the potential difference V is equal to

that between the drift tube structure and the collector

electrode.

- 10 -

~)

(III. GENERAL DISCUSSION OP COLLECTING DEVICES)

This implies that in order to bring all the electrons

to a standstill, one needs electrodes at potentials corres- »

ponding to every different electron velocity. Actually, one

13 limited to a few electrodes. Their potentials must be se-

lected so as to optimize the electric power collected.

If we have a number of electrodes at voltages V,,Vp,

v., , . . . in order of decreasing potential, all the electrons

going faster than ui = >/2ev"i/m should go to the first elec-

trode. All those electrons whose velocities lie in the range

ui =\£?eVi/m to uS: =J2eV2/m should go to the second electrode,

etc.

t r r

It Is obvious that the collector should have not only

a means of slowing down the electrons, but also of directing

them to the proper electrode.

If one knows the distribution of current in small in-

crements of velocity, vs velocity, then one can calculate how

much power It is possible to collect with any electrode or set

of electrodes. Prom the data of Pig. 2.2, it is easy to de-

rive a curve, Fig. 3.1, of captured collector power vs collec-

tor voltage for the hypothetical klystron discussed on page 6.

A large number of distributions were studied to deter-

mine the sensitivity of the power collected to the shape of

the distribution curve. Typical values are 25 to 40 per cent

of the beam power recaptured for a one-electrode collector,

35 to 50 per cent for two, and 45 to 65 per cent for three.

The triangular distribution shown in Pig. 3.2 closely ap-

proaches the results for the hypothetical klystron. A single

collector can recapture 28 per cent of the beam power and a

- 11 -

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r (III. GENERAL DISCUSSION np COLLECTING DEVICES^

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GENERAL DISCUSSION OF COLLECTING DEVICES)

Electron velocity

PIG. 3«2--Electron current per Increment of electron velocity vs electron velocity.

three-electrode collector can recapture 49 per cent. This

corresponds to net tube efficiencies of 46 per cent and 65

per cent for a klystron whose r-f efficit-r^v is J53 per cent.

It was with the goal of 65 per cent in mind that work

was initiated on a three-electrode collector.

In the design of a collector, a number of precautions

should be observed. Any device which will reflect electrons

back into the r-f section must be ruled out* The necessity

of this is two-fold. Electrons delivered at random to the

output gap would generally reduce the power delivered to the

circuit. More serious is the Influence of stray electrons

entering the input gap where the r-f power level of a typical

three-cavity tube is lower by a factor of several thousand.

If only electric fields are present, any electron which is

• - 13 -

1

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(III. GENERAL DISCUSSION OF COLLECTING DEVICES)

"brought to a standstill before reaching a collector electrode

will be reflected ba^K along its original path.

- 14 -

.

t ;»s iTMCTSMcygiW1'" iwnjwwiifi nii*f iiinnihiwiinmii»M"namw

.

IV. COLLECTING AND VELOCITY-SORTING DEVICES >

Two important functions must be performed in the col-

lector. The high-velocity electrons must be sorted from the

low-velocity electrons in such a, manner that they will go to

the proper electrode. Obviously, a high-velocity electron

that strikes a low-voltage electrode does not give up as much

energy as it would If it reached a high-voltage electrode.

Second, the electrodes must be capable of capturing and hold-

ing the electrons which should properly go to it.

A. VELOCITY SORTING >

A number of velocity-sorting devices immediately come

to mind. A transverse magnetic field or electrostatic deflec-

tion plates similar to those used on cathode-ray tubes will

deflect low-velocity electrons more than high-velocity ones.

It is possible to think of many axisymmetric electrostatic

deflection schemes which will cause the electrons to "fountain"

outward,

All these devices run into one difficulty. The space-

charge forces of the high-perveance beams typically used In

klystrons have a greater effect on the electron paths than do

any external forces.

The obvious answer to this difficulty is to U3e the

space-charge forces to velocity-sort the beam.

A beam of mixed velocities even In a region free from

all forces except space-charge forces will sort itself in such

- 15 -

t •

n

r (IV. COLLECTING AI.'D VELOCITY-SORTING DEVICES)

a manner that the slow electrons will be on the outside of

the beam and the core will be composed of fast electrons.

The sorting is not perfect since even slow electrons right

on the axis are subjected to no radial force, but one would

expect the over-all sorting to be reasonably good.

Be COLLECTING

The problem of collector design resolves itself into

one of selecting a suitable arrangement of electrodes. To

be compatible with the space-charge sorting, the collector

device should obviously be axisymmetric

A variety of collector electrode shapes are sketched

in Pig. 4.1. All of them take advantage of the space-charge

velocity sorting which causes the electrons to move to the

outside of the beam.

Fig. 4.1(a) Is Included to indicate one difficulty

that can be encountered. There is a similarity between the

electrons entering the retarding field of the collector and

a ball thrown into the air in the gravitational field. The

•

1

.

ball must be thrown vertically to reach the highest distance.

Likewise, the electron must move in the direction of the elec-

tric field lines in order to move to the highest potential

possible. In Fig. 4.l(a} the electrons are always acted on

by a radial force outward, so that electrons which have suf-

ficient kinetic energy t:> reach the collector actually slide

off to the side and fall back to ground (the body of the tube).

The collector shown In Fig. 4.1(c) seemed to offer

the greatest possibility of success. Slow electrons entering

the lower chamber are most likely to hit the top surface

!

•

r (IV. COLLECTING AMD VELOCITY-SORTING DEVICES)

I -,

/ TTT~ \ / i \ v

\ y (a)

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(b)

^

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PIG. Jl. 1—Collector electrode shapes (force on electrons indicated by dotted lines)

17

• *,— 1

(IV. COLLECTING AND VELOCITY-SORTING DEVICES)

where the field is such as to reflect the secondary electrons

back into the surface. This feature is inherent In all cham-

bers except that at the highest voltage. The fast electrons

presumably : o straight through into the end chamber.

The radial field oscillates so as to accelerate elec-

trons first outward and then inward. The longitudinal field

along the axis is essentially constant. The fields within

the chambers are relatively low. For the most part, the elec-

tric flux lines from the lower half of any chamber are direct-

ed to the upper half of the next chamber below. This should

reduce the possibility of electrons returning to the drift

tube.

The large sizes of the chambers adapt themselves to

cooling.

Unfortunately, the space-charge forces are so large

as to eliminate the possibility of determining electron tra-

jectories from a Laplace solution of the fields in the col-

lector region, so that any collector design will rely on

educated guesses.

- 18 -

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•

.

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n

V. DESCRIPTION OF COLLECTOR *

A. KLYSTRON

A part of the project was the design and construction \

of a high-power pulse klystron. The klystron parameters were

chosen in such a fashion that the tube would be useful for

such applications as driving linear electron accelerators.

The outgrowth of this design are the Type 272 klystrons built

at Stanford University. The original design had anticipated

2 Mw r-f output, 40 per cent efficiency, cathode perveance

2.0 x 10" amp/v^' , 25 kw of average beam power, and 10 p.sec

pulse length.

The design was such that either two- or three-cavity

tubes could be built, the simple addition of one cavity and

a drift tube being the only difference. An assembly drawing

of the three-cavity tube is shown in Fig. 5.1 •

Since electrons reflected from the collector to the

input cavity might cause some difficulties, the special col-

lector design was made on a two-cavity version.

The klystron was tested without any special collector

to ascertain the operating performance of the tube.

The efficiency was lower than anticipated, being only

30 per cent at 2 Mw. A survey of test data and design calcu-

lations indicated that the beam diameter was possibly too

small.

- 19 -

t' " —

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r (V. DESCRIPTION OF COLLECTOR)

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(V, DESCRIPTION OF COLLECTOR)

The pertinent data for the collector de3lgn are that

the output gap spacing is 1.0 radians (0.355 In.) at 90 kv,

tP.e drift tube radius is 1.1 radians (O.781 in.), and the

peak output gap voltage is equal to the d-c beam voltage.

B. COLLECTOR

drift tube. The length of the chambers was chosen such as

take place and to give the electrons time to move radially

into the chambers.

An equipotential plot for the fields in the chambers

is shown in Pig. 5*2. Because of the shape of the chambers, 1

there are radial fields in addition to the longitudinal

fields. The maximum radial field is about one=half the maxi-

mum longitudinal field which was of the order of 30 kv/in.

- 21 -

-

1

n

to give an opportunity for the velocity-sorting action to

In the previous section it vras indicated that a col-

lecting device composed of a series of chambers offered some

promise of success. It was this sort of device that was

assembled and tested. Since the beam spreads so rapidly fol-

lowing the output gap, the collector was designed in such a

manner that a longitudinal magnetic field could be applied

to constrain the beam and also to reduce the possibility of

returning electrons. >

The velocity-sorting action is due mostly to the

space-charge forces. The electrons are caught in the cham-

Ibers if they move far enough radially.

The geometry of the chambers was chosen to reduce

the possibility of electrons returning to the drift tube.

The holes in the chambers were four times the area of the

(V. DESCRIPTION OF COLLECTOR)

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r (V. DESCRIPTION OP COLLECTOR)

The chamber fields are of the same order of magnitude as the

space charge fields. The radial f:'eld of a i-In. diameter,

80-kv, perveance 2.0 x 10"i amp/v-^d beam Is 11.4 kv/in. at

the beam edge.

In the retarding field region the beam will spread

faster than In a region free of external fields. However,

some idea of the spreading can be gained by studying the

field-free spreading curves, a few of which are shown in

Fig. 2.3.

An estimate of a suitable collector design was made

which took Into account the fact that the magnetic field

would constrain the beam somewhat, and the necessity for

utilizing existing materials as much as possible. An assem-

bly drawing of the collector is shown in Pig, 5«3»

The klystron i3 mounted with its cathode end down in

a tank of oil. The collector magnet coil form doubled as a

necond tank of oil to protect the collector ceraiuic seals

which Insulated the collector chambers from one another.

A single loop of Tygon plastic tubing between each

chamber provided it with cooling water. The collector was

capable of dissipating some 1C kw of average power.

I a

23 -

•

TTIMOTI

(V. DESCRIPTION OF COLLECTOR)

m-f-p~ •

- 24

• _J

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VI. EXPERIMENTAL DATA

A 2-Mw klystron was disassembled and rebuilt including

the special collector described in the previous section. Due

to failure of a glass vacuum window during processing of the

tube, the cathode became temperature limited at voltages

greater than J50 kv. This upset the beam focusing so that

without r-f drive, the maximum beam transmission was 86 per

cent. The gain and sufficiency are low enough that some frac-

tion, say, 15 P--r cent, of the beam might be assumed to be

lost before the beam reaches the output gap. Since one might

presume the beam is off center, the collector operation should

not be as good as is possible.

Previous data Indicated the tube operated properly

into a matched load. With the temperature-limited cathode,

the tube output is a maximum with a load resistance 1.9 times

a matched load.

A. MEASURING TECHNIQUE

The object of the tests is to measure the increase in

tube efficiency achieved by the collector. The r-f output,

d-c beam input, and collector-chamber average powers are suf-

ficient data for a calculation of the efficiencies. This

avoids the measurement of pulse length. The average power is,

of course, the product of voltage and average current.

The r-f power output was measured with a thermistor-

operated in a d-c bridge circuit.

- 25 -

(VI. EXPERIMENTAL DATA)

The Dulser circuit is shown in Fig. 6.1. Three sepa-

rate devices gave a check on the beam voltage; (l) the volt-

age rise on the 52-u-f condenserj (2) the peak reading voltmeter;

and (3) the condenser voltage divider. The collector voltage

can be calculated from the transformer turns ratio and checked

with the condenser voltage divider.

The average currents into the collector and body of

the tube are known. However, if the tube is not matched to

the pulse line, this measured current may be greater than the

average current due to the initial pulse, because the pulse

line retains some charge after the initial pulse. If ';he tube

impedance is 50 per cent more than a matched impedance, the

average current reading will be 25 per e_jnt too high. This

mismatch is indicated by a stepped beam-pulse shape in which

the second step is 20 per cent of the initial pulse amplitude.

The result of feeding power from the collector to the

pulse transformer does not lower the required pulser supply

voltage, but rather increases the effective tube impedance.

In any event, on a line type pulser, the beam voltage is a

function of the r-f operation of the tube.

The r-f drive pulse width was made longer than the

klystron beam pulse so that the tube would be operating under

substantially the same conditions throughout the pulse.

E. EXPERIMENTAL RESULTS

Pigs. 6.2 through 6.4 show the klystron operation

with all the collector electrodes grounded. The low effi-

ciency of the existing tube compared to the previous data in-

dicates the difficulty encountered with the beam focusing.

- 26 -

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- 30 -

The collector efficiency curves are taken at 80-kv

beam voltage which corresponds to 42.1 amp and a perveance

of 1.86 x 10 amp/v5'2. The Figs. 6.5-6.7 «- 'e taken with

the three chambers at the same potential, a one-electrode

collector.

The longitudinal magnetic field did not improve the

collecting efficiency in any but the case shown in Fig. 6.10.

Hence the field is zero for all except as noted there.

A symptom of trouble is noted in the curve for no r-f,

Fig. 6.5. The beam transmission is 65 to 85 per cent. The

loss of 15 per cent of the beam with a grounded collector is

<• a result of the poor focusing. Another 20-percent loss at

high collector voltages indicates that either electrons are »

not reaching the chambers or that secondary electrons art.

falling back from the chambers to the tube body.

The high output gap voltage curve corresponds to the

klystron output cavity loaded for optimum power output. The

low output gap curve is for a matched load in the output

waveguide.

The product of current transmission in per cent of

beam current and collector voltage in per cent of beam volt-

age is the power captured by the collector in per cen'G of

beam power. This we define as collector efficiency. ;.

Figs. 6.6 and 6.7 are derived from Fig. 6.5. Fig. 6.6

' should be compared with Fig. 5.1 to ascertain whether this

I

collecting device is capturing as much power as is available

In the "beam. The r-f efficiency of the klystron at thin volt-

age is only 19 per cent, while the theoretical data were for

- 31 -

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w

F (VI. EXPERIMENTAL DATA)

an r-f efficiency of 7>J> per cent. The measured peak colIsc=

tor efficiency is 21 per cent. The theoretical efficiency-

is 29 per cent. There is a wide divergence from theory in

the shape of the curve, the theoretical curve "being much

higher on the low voltage end. The space-charge forces may

cause an interchange of energy between electrons but perhaps

a better explanation is that the low-vol';age electrons are

spreading so fast following the output gap that they never

reach even the first collector chamber.

Figs. 6.8 through 6.10 indicate the gain in efficiency

obtained by using a two-electrode collector rather than a

single-electrode collector. The gain in efficiency was dis-

appointingly small: the highest efficiency was 2k- per cent,

a gain of I per cent over- a single-electrode collector. The

change in efficiency for a triple-electrode collector was

undetectable. The theory bad indicated collector efficiencies

of ^9 per cent for a perfect triple-electrode collector.

Two things might account for this: one is the beam

spreading of the low-velocity electrons, and the other is

the collector may be too long so that even the high voltage

electrons are spread too much. The magnetic field which had

been counted on for such an eventuality may cause the elec-

tron beam to converge too much at just the wrong time so that

the electrons fall back through the holes In the chambers and

are lost.

Secondary electrons which had been a matter of great

concern may be no problem at voltages in the vicinity of 8C kv.

•

*

- 33 -

W 1

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1 i

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Data available'1 indicate a falling off of secondaries at high

incident voltages. If they had been a problem in this design,

the two-electrode collector should work considerably better

than the slngle-eiectrode type.

1 K. R. Soangenberg. Vacuum Tubes. McGraw-Hill Book Co.,

New York, 1948.

- 39 -

r

VII. POSSIBLE IMPROVEMENTS

I

It is quite likely that it will be impossible in any-

simple design ever to extract the energy of the low-velocity

electrons due to their rapid spreading following the output

gap.

If one were satisfied with a single-electrode collec-

tor., it seems likely that 30 per cent of the beam power could

be extracted. The most obvious step to improve the design

would be to reduce the spacing between the chamber and the

output gap. Pour possible single-electrode collectors are

shown in Pig. 7.1. Pigs. 7.1(c) and 7.1(d) assume the glass

or ceramic path is long enough to withstand the pulse voltage

in air.

Provision must be made in all cases to cool the col-

lecting chamber^ to provide a high-voltage lead, and to she

shield the collector with lead.

A typical ceraric cylinder 2 in. long has a pulse

breakdown voltage of 270 kv in oil. A 1-in. seal should give

a good margin of safety for 100~kv tubes.

It should be possible to make a 5- to 10-kw collector

similar to Fig. 7.1(a), 5 In. In diameter and whose length

from the output gap is only 6.5 in-

On a typical klystron whose r-f efficiency Is J>0 per

cent, the addition of such a collector would raise the over-

all efficiency to 4> per cent. Likewise a 40-percent effi-

cient tube might be raised to 50 per cent.

- 40 -

i 1 3 i

•

• • •

1

(VII. POSSIBLE IMPROVEMENTS)

Plastic tubing

Lead In

—Oil level

Water cooling

— Ceramic insulator

rru \ onoorJ hnrrr>

\ N— Lead \ shielding

Collector chamber

Drift tube

1

(b)

3

f?o

L ooooQCQaQaobL

">

(c)

-Lead shielding

Ceramic insulator

Glass insulator

FIG, 7,1—Single-electrode collectors i

41 -

•

•

VIII. CIRCUIT CONSIDERATIONS

A collector of the sort described when connected to

a transformer, Increases the effective impedance of the tube

without decreasing the required voltage. This impedance of

the tube is a function not only of the beam voltage but of

the r-f power and the magnetic focusing. On a line-type

pulser then, the beam voltage is in turn a function of the

effective tube impedance. In a fixed operation., the pulse

line would be matched to the effective tube impedance rather

than the d-c beam impedance.

In general, without r-f drive, the collector effi-

ciency is very high. It is possible for a perfect collector

to cause a doubling of the beam voltage when the r-f drive

is turned off. Care must be exercised to see that this will

not damage the tube or that suitable interlocks are Included

In the circuitry.

- 4i

•

IX. CONCLUSIONS

A collecting device was designed, built, and tested

which was capable of recapturing energy from the electron

bears following the output gap of a klystron and feeding this

energy into the pulse transformer such that the over-all

efficiency of the klystron was increased. A single-electrode

collector recaptured 25 per cent of the beam power. It was

expected that a double- cr triple-electrode collector would

improve on this but the tests did not indicate any improve-

ment. It is felt the difficulty Is due to the extremely rap-

id spreading of a beam following the output gap.

The test did indicate that 50 per cent recovery of

the bean, power should be easily realized by a single-elec-

trode collector. The optimum collector voltage (about 75 I

per cent of beam voltage) Is simply tapped from the pulse j

transformer with pulse tubes. J>0 per cert recovery implies ! i

a 50-percent reduction in power supply current, with obvious

savings in component costs and electric power costs over the

life of the tube. In high-power tubes it would indeed seem

practical to add 3uch a collector.

u i; i! H

I

<

- 45 -

i i

APPENDIX

The following indicates a construction for finding

the exit velocity and time of an electron in a gridded gap.

An electron injected into a region between two paral-

lel planes is subject to the acceleration

P -E- eV ^0° a - 5 = — - metsln mt - -ar sln •*

if the voltage between the plates is V sin cot.

Integration of the acceleration gives the velocity

U = UQ 1 + -Sje (COS COt. - COS 0)t)J

and a second integration gives the position of the particle*

Z = ryfc (sin tot,, - sin cot) + f 1 + JL cos cot.J (cot - cot.)

These equations satisfy the boundary conditions that

Z = C and u = uQ at cot = cot. .

I If ET2D (z + "2B sin a>t) ls rePlaced by Y> then

i Y = sin cot. + (a/pn + cos art. j (cot - cot.)

A plot of Y vs ait is recognized as a straight line of slope

( .-"-, -j- cos cot. ] passing through the point Y = sin cot., when

1

lV

cot = cot. .

It is noted that cos cot. is the slope of sin cot..

The construction line indicated in Pig. A.l is drawn as an

- 44 ~

,—.

_

-•. -v ,

r (APPENDTX)

i

R -

-2

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-construction line

PIG. A-I--Construction for determining electron exit potential and time of exit for electrons passing through gridded gaps,

- 45

t »

(APPENDIX)

aid to finding the slope of sin oot.. Rather than measuring

the slope over an increment of 1 radian, the construction

line ia drawn in such a manner that the slope is measured

over 7T radians ( •- 180°; . The ordinal distance is therefore

TT j-t j-i. 1 ZtpBS •--««=- —— a/2J> *

The distance hetween the entrance and exit planes in

1 terms of Y is J grrgw )P»

It is useful to copy the exit plane and its construc-

tion line on tracing paper and lay it over Pig. A.l so as

D easily to adjust the gap spacing,

i

- 46 -

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a method of improving the - dticvoltage on second electrode of a two-electrode collector 35 - v -...

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