SECONDARY EMISSION EFFECTS IN

RETARDING-FIELD OSCILLATORS

DISSERTATION

Presented in Partial I'ulfillment of the Requirements

for the Degree Doctor of Philosophy in the

Graduate School of the Ohio State University

By

Richard Arthur Neubauer^ B.S., M.S.

The Ohio State University

195U

Approved by:

< t -

Adviser ACKNOWLEDGEMENTS

The research described in this dissertation was conducted under contract between the Air Materiel Command,

Wright-Patterson Air Force Base and The Ohio State

University Research Foundation. The author wishes to express his appreciation to Professor E. M. Boone for his valuable criticism and

suggestions in the capacity of adviser and project super­ visor. The author would also like to thank Professor

G. E* Mueller and Mr. M. 0. Thurston for many helpful suggestions concerning the theory. Appreciation is expressed for the help given by the other members of the

Electron Tube Laboratory. Finally the author would like to express his gratitude to his wife, Norma, for without her help, this graduate work would not have been undertaken.

ii

A 48129 TABLE OP CONTENTS Pag©

Introduction ...... 1 Equations of Motion for Primary and Secondary Electrons 5

Ballistics of Primary and Secondary Electrons...... 11 Energy Terms and Conversion Efficiency ...... 50

Performance Curves, Theoretical...... 81 Experimental Results Using iSealed-Off Tubes...... 95 Experimental Results Using Demountable Tubes ...... Ill

Quantitative Check on the Theory ...... 129

Conclusions...... 132 R e f e r e n c e s ...... 156

ill LIST OF SYMBOLS a]_, a.g Entrance phase angles for primary electrons for which/3 is equal to regardless of K.

d Gap spacing, e Charge of an electron,

f Frequency, m Mass of an electron n Number of primary electrons Injected Into the gap

per cycle. v^ Instantaneous voltage drop from cathode to repeller.

x Displacement of primary electron. xmax dc displacement of primary electron when K is aero. x Velocity of primary electron.

x 0 Initial velocity of primary electron.

xa Displacement of secondary electron. xs Velocity of secondary electron. Ea Average voltage rise from cathode to nose.

Ep Average voltage rise from cathode to repeller. G.£ Reflected load conductance at the gap. G sh Shunt conductance of the cavity. Ia Average anode current. Io Average.beam current. K Vm/vx N Number of primary electrons which have arrived at

the repeller at arrival angle ' . iv N Total number of primary electrons which strike

the repeller per cycle. Pc Average value of rf power lost in the cavity. Po Average value of rf power delivered to the load.

Rsh Shunt resistance of the cavity. V]_ Average gap voltage drop from nose to repeller.

Va Average gun voltage drop from nose to cathode.

Vm Maximum value of the sinusoidal rf gap voltage.

Vr Average voltage drop from cathode to repeller. oC Entrance phase angle for primary electron.

*=

**C Arrival angle of primary electron at the repeller.

/ Angle at which repeller bombardment begins. Angle at which repeller bombardment stops.

Transit angle of primary electron, nose-to-nose.

/?o DC transit angle of primary electron.

@ s Transit angle of secondary electron, repeller-to-nose. y^os DC transit angle of secondary electron. y ^l/Va, gap spacing factor.

cf Average secondary electron yield from repeller tip.

Kl Electronic conversion efficiency.

© u)t Limiting angles between which the repeller is above cathode potential. v © D Delay angle of production of secondary electron.

© h Transit angle of primary electron, nose-to-repeller. Primary transit angle, nose-to-repeller, when «<.

is ^ 2 or 2 * A * Wavelength at resonance.

^p Dimensionless velocity of primary electron.

Dimensionless impact velocity of primary electron at the repeller. . , Dimensionless exit velocity of primary electron p exit 0 0 at the nose. s exit Dimensionless exit velocity of secondary electron at the nose.

O5 Dimensionless velocity of secondary electron. Dimensionless displacement of primary electron. Dimensionless displacement of secondary electron.

<0 tirf -r if

vi Secondary Emission Effects in

Retarding-FIeld Oscillators

Introduction

The retarding-field oscillator, shown in Figure 1, is one member of a family of electron devices used for the generation of microwaves. Some other members of this family are the klystron, the magnetron, and the travelling- wave tube* While the construction of the retarding-field oscillator somewhat resembles that of the reflex klystron, there are important physical and electronic differences between the two. Among these differences are the following:

a. The reflector electrode in a reflex klystron is located in an rf field-free region, whereas the repeller in a retarding-field oscillator Is'part of the rf circuit.

b. The electrons in a reflex klystron remain In the gap for a length of time which is only a small fraction of the period of the rf voltage, but the electrons In a retarding-field oscillator remain in the working gap for a length of time greater than the period of the rf voltage.

The retarding-field oscillator is easily tuned over a wide range of frequencies. A two-to-one tuning range is common, and In special cases the range can be considerably greater. The tube is simple in design and therefore ' / / s'y/y/'/'i

Model of a C&pacitively Tuned* Demountables 2- U cm Retarding-field Oscillator

Figure 1 3 promises to be relatively easy to produce in large

quantities. Its power output is good; in the 2.5~to-5-om wavelength region it ranges from about one watt for the planar gap geometry to several watts for the capacitive

geometry. Because of its excellent tuning range and power out­ put, the retarding-field oscillator is a good source of microwave energy for measurement purposes. It could also

be used as a local oscillator in microwave receivers. High power output under pulsed operation has not been investi­ gated because there are commercial tubes available for this

purpose. Rather, the retarding-field oscillator is best

adapted to filling the need for a low-voltage, easily tuned microwave energy source which can cover a wide range of frequencies.

The basic design for the oscillator studied in this paper was introduced In 1947 by Dr. Oskar Heil^- who was then associated with the Electron Tube Laboratory of the Ohio

State University. The original work of developing the

oscillator was largely done by J. J. Ebers^- under the supervision of Dr. Hell. The first models operated in the

5-toiO-cm wavelength range. They used the half-size Hell electron gun and loop output coupling.

Scaling techniques have since been applied and the oscillator has now been successfully operated in the 7-to-14- mm wavelength region. There is evidence that the tube can b© scaled further if the techniques of fabrication can be refined. Loop output coupling is no longer used, having been replaced by the repeller output coupling and waveguide system shown in Figure 1. The experimental work covered by this paper was performed in the 2.5-to-5-cm wavelength region.

Reference to Figure 1 shows that the oscillator consists of an electron gun, a cavity resonator, and a repeller electrode. High velocity primary electrons enter the resonator through an orifice in the nose of the gun assembly. In the working gap between repeller and nose, the electrons reverse direction and return to the nose where they are collected. When conditions are correct, an rf gap voltage will develop, being supported by the resonator with energy obtained from the electron beam. Tuning Is accomplished by moving the repeller, and the frequency of oscillation increases with gap spacing. The cavity and repeller form a coaxial line by means o-f which rf energy may be extracted from the resonator. In normal operation, the injected electrons remain in the working gap for a length of time longer than the period of the rf voltage. Their trajectories are therefore complicated functions of time and entrance phase angle.

Some electrons extract energy from the rf field and strike the repeller. Here they give rise to secondary electrons which are accelerated through the gap to the nose. The number of secondary electrons produced depends, among other

thingsj upon the shape and surface of the repeller, and

upon the energy and number of primary electrons striking it. Both positive and negative repeller currents have been

observed. At the low-frequency end of its vd.de timing range, the oscillator is particularly sensitive to the production of secondary electrons.

The purpose of this investigation is to determine

theoretically and experimentally some of the effects of secondary emission on the operation of planar retarding-

field oscillators. The theory is generalized in dimension­

less form and covers not only the range where oscillations are self-sustaining, but also the range where the cavity is driven as in hot admittance measurements or amplifier

applications.

Equations of Motion for Primary and Secondary Electrons

The analysis of the retarding-field oscillator is

made with the assumption of planar geometry, uniform electric field intensity (function of time only), and

complete coupling to the beam. Figure 2 illustrates the voltages present in the working gap. The force per electron is

V1 ■+■ vm 3in (e+oC) z , . — ------e newtons/electron (1) d where e is + 1.601 x 10~^® coulomb/electron, © = ci>t, and FL&ss© of to® Hepollos*

BsgEroeoatetdLoa of to© Voltages® PpsoQiat. in to© tJarkisis G©p. Figaro 2 is the entrance phase angle of the primary electron.

Newton1s law of motion gives the acceleration as g — — — 2. P V n + V sin (©+oC )*"] meters/second^, (2) ^ 2 m«sl L- -J

where m = 9.107 x 10” kilogram/electron. Integration of the acceleration yields the velocity

x = - _g j^V-^t - Xg cos (©*<

When t — 0, x = xQ, the initial velocity of the Injected

electrons. Therefore

^1 — x0 - ®Zn? cos cC. (4) mu)d

If K = Vm/V^, the velocity can be put into the form

x = x0 - eVl { 0 -K ["cos (©+«c)-cosd I -s)

Let j30 be the dc transit angle. Then, with Vm =■ 0,

- i o = i o - rrnM P 0 } * ° r (6)

eVl _ 2 Xo • * 7>

The value used for is 7.7253 radians as found by. M. 0.

Thurston.^ The dimensionless velocity for primary electrons is obtained as

^ P = i=l-5{©-K [cos (©+*)- o o s k V, . (8) *o f o I J J

Integration of the velocity of the primary electrons gives

the displacement as When t = O , x -- O , and

c2 = - . (10, m d

The displacement can be put into the form

x _ ___ ^o9 „ eVi /0^ _ k Psin (©+<)- 0 cosot -sin<|\(ll) mdU^d 1 2o -v meters, or

cDx _ eVi f 02 _ -* ■£ = ® ------X --- - Kjjsin (e+<<-)_ © cosoC - sin<]| . (12) ° xQm^d (2 ~ )

The dimensionless form used for the displacement of primary electrons is

¥ p = ^ = 0 " ^ | ~ - K [sin (e+cc)_ © cos«C - sin<]|. (13)

Similarly the velocity of secondary electrons released at the repeller is

Xs ” " Sd £Vlt ” IS cos (e+^ 0 + C3 . (14) co In Equation 14, o£s specifies the entrance phase angles for the secondary electrons. It will be shown later that eCs Is restricted to certain values which are determined in part by the entrance phase angles of those primary electrons which give rise to the secondary electrons. When t = 0, x s = 0 (negligible initial velocity is assumed), and C3 — - f^m C03 ^ a (15 ) mu)d

The velocity of secondary electrons can be put Into the form 9

x Q =. - — Y.1. I © - K j^cos ( ©* <*c ) - c o a cd 1 The dimensionless velocity for secondary electrons is therefore

v) s - x s _ _ fL_ /© - K P cos ) - cos** l} . (17) io Pol J This is the same as the second term of Equation 8.

The maximum displacement of primary electrons in the absence of rf fields occurs at 0= an

Xraax dc - x° Po - eV^ /302 xn B n 2^ -fsr ’ (18)

The dimensions gap spacing factor, Jf , is defined as the ratio of the gap spacing, d, to the maximum penetration into the gap, x max dc, of the primary electrons in the absence of an rf gap voltage. The gap spacing d can now be expressed as

d = K xmax dc = v xo / -i n \ o 4 ^ • (19)

Integration of the velocity yields the displacement of secondary electrons

x s * - - K sin (©+«*)+ Kt C03(Cg] +C4 . (20)

When t - 0, x s = d s y xo fe and 4u) C = E sl-^o y. - 2xQ k sin oC . (21) 4 4w> p oo s

Therefore x s ‘ {•§" ” K Csln (Q+c|)- 0 cos«*s -sin

(23)

Xt will be shown later in Figure 5 that the dimensionless gap spacing factor, if, is also equal to the ratio of the dc gap voltage, to the gun voltage, Va. The second term of Equation 23 is the same as the second term of Equation 13.

The dimensionless forms of the equations of motion were first used by M. 0. Thurston^ In his analysis of the retarding-field oscillator. The large-signal theory of the planar retarding-field oscillator which is presented here depends upon knowing where each electron is at every instant of time while it is in the working gap. Since the equations of motion are transcendental, the analysis is carried out by graphical means. The aid of the IBM Computation Unit at Wright-

Patterson Air Force Base, Dayton, Ohio, was enlisted to perform the bulk of the calculations. Equations 8, 13,

17, and 23 were evaluated at entrance angle increments of 0.2 radian. The parameter K was assigned the values

0.1, 0.2, 0.3, 0.4, and 0.5. A wide range of gap spacings was included. The results were printed in tabular form as indicated below: 11

© P Oi i> ' ® ji FOft if-10

5v AO/C fs re* s'- /SL J£ eaft *'t-3 ?5 FOB s’. I H J* pow / 5 An estimated 1300 man-hours are represented by these calculations. The floating decimal system was used, and the last five columns were rounded off In the fifth decimal place. This provided more than sufficient accuracy for the analysis. Prior attempts to calculate the electron trajectories by means of the more rapid analogue computers both at the Ohio State University and at Wright Field had to be abandoned because sufficient accuracy was not obtainable.

Ballistics of Primary and Secondary Electrons

Transit angles for primary electrons are determined by the graphical solution of Equation 13 in which the dimensionless displacement factor, , is set equal to zero when 0 is equal to /3 .

(24) ( 12 0 = f ( , & ). (25)

This equation defines /$ implicitly as a function of . Equation 24 can be rewritten as

Let have the particular value of a when /3 is equal to /3Q . 12

Then O » J|£ £ sin a ) - /3Q 003 3 “ sin 3 3 *

For all values of K,

0 = sin (/% + a ) - P 0 cos a - sin a . (28)

The result is

tan a _ sin/% - /% _ 6.7336 _ 7,79A7 (29) 1- c o s /^q ~ 0.8717 - 5 and a = a^ = 1.70 , or (30)

a = ag s a-^+TT - 4.84 radians. (31)

The primary transit angles are plotted as unsymmetrical curves in Figure 3 where it can be seen that the curves for all values of K intersect when < is either a-^ or q.% , and the intersections occur where /3 is equal to will be shov/n later that primary electrons injected into the gap with entrance angles of a^_ and ag return to the nose with velocities which depend upon K, even though their transit angles are independent of K. From Equation 24,

f(* ,/3 ) = o ; aj? _ Sf/J* a * T i / z p > (32) where, according to Equation 8,

= ^ p exit =r ~ ~ |/3 - K [cos (/*+oC) - cos«/|J, (33) and

^f/c)< - % [ coa (fi+<) - cos ■+ /3 sin^J . (34) fio Since is never zero in the range of K considered here, dP/dcC vanishes when <^f,^oc vanishes. /S Transit Anglo 9 Bediaas ®C Entrance AnglSp Radians Entrance AnglSp ®C Primary Transit. Anglo Ctar^os Transit. Anglo Primary 3 U 3 2 iue 3 Figure - E

13 14

From Equation 33, “ 3^ j^cos (£+et) - cos*J = \)p e x i t - 1 -*- — . >®0 /^o B y substitution of this expression into Equation 34 and setting Equation 34 equal to zero with ftQ equal to 7 . 7 2 5 3 , one obtains

0 = 0 . 2 5 8 9 ft (1+ K sin* ) + ( 0 p ex±t - 1 }. (35)

For any K, the solution of this equation using values of

<<. and ft which satisfy Equation 24 will yield the values of

K _®£when /3 is maximum when is minimum 0.1 3.292 0 . 1 0 5 0.2 3.316 0 . 0 8 1 0.3 3.329 0 . 0 6 3 0.4 3.344 0.041 0.5 3.356 0 . 0 2 3 The scale to which Figure 3 is drawn makes it appear as though the transit angle curves reach their maximum and their minimum values together.

Dimensionless exit velocities for primary electrons returning to the nose can now be calculated from Equation 8 by setting Q equal to the transit angle ft . Because the energy of a returning electron is proportional to the square of its exit velocity, curves of ( 0 p 0 X it; )2 as functions of entrance angle «=C are presented in Figure 4. These curves are very unsymmetrical in form. They are sensitive to small errors which may exist in the values of ft used in the calculations. They show how the exit velocities 15

Region of Gap

1.0

0.1

Region of Gap Driving

ax g l.TjP

&C I^tpanoo Anglo, Radians

Essit t e r g f Cu p t o o for PriEapy Electron© Pignr© 4 16

depend upon K when «£ is a^ or ag, even though these electrons have identical transit angles.

When (*p exit}^ greater than unity,- the electron has extracted energy from the rf field and has loaded the gap. When (Op exit}^ -*-s ^ess than unity, the electron has lost energy to the rf field and is said to have driven the gap. Figure 4 shows that the range on entrance angles over which primary electrons load the gap decreases as K increases.

This indicates that the efficiency of the oscillator should increase. Ebers^ has shown that as K increases beyond 0.7, the shoulder of the curve, indicated by A in Figure 4, will develop into a second distinct maximum, and the loading angle will increase, thereby reducing the efficiency.

Not all primary electrons return to the nose. Some strike the repeller where they are elastically or inelasti- cally reflected or where they are collected after releasing true secondary electrons. To determine the limits on cC over which primary electrons will strike 'the repeller, data giving the maximum excursion, ,?p max , of the primary electrons into the gap for each value of «< were extracted from the WADC calculations. The results are plotted in Figure 6.

Since the repeller is normally operated at a potential negative with respect to cathode, only values of ^ p max corresponding to values of ■=. greater than unity are Va 1 7 included. When^is increased, tlie value of \ ^ must be increased in order to maintain the proper dc transit angle. Figure 5 illustrates tliis point.

Consequently, when K is fixed and ^ is increased, the rf voltage will increase. The value for if equal to unity corresponds to a gap spacing equal to the maximum pene­ tration of electrons into the gap in the absence of rf fields. At that point, such electrons have no kinetic energy, and the potential distribution curve crosses the axis of zero potential. For values of / less than unity, the repeller must have an average potential positive with respect to cathode. And for values of ^ greater than unity, the repeller must operate below cathode potential. This study is confined to the usual mode of operation of retarding- field oscillators, although it might be possible to obtain strong oscillations with a positive repeller. This latter type of oscillator has been called the dynatron. Figure 6 shows that when is equal- to unity, the range on entrance angles over which injected primary elec­ trons will strike the repeller is approximately TT radians for values of K between 0.1 and 0.5. In other words, about half of the Injected electrons will extract energy from the rf field, strike the repeller, and release secondary electrons. It Is graphical proof of the importance of secondary emission phenomena in retarding-field oscillators.

As the gap spacing factor, 2f , is increased, fewer 18

Plasm of Plamio of tbo tho loa© Eopollor for Various Valuss of Y

Eeprssoutatlou of fch® ¥olt&@®@ Prosoat in th© Workissg Gap

Figur© 5

20 injected electrons will strike the repeller, and the number which do strike depends more and more upon the value of K.

Finally, when ^ exceeds 1.35, none of the injected electrons will reach the repeller, because in these calculations, rf fields yielding values of it exceeding 0.5 are considered unlikely.

The transit angles, required by the primary elec­ trons to reach the repeller have been obtained with the aid of the WADC calculations. The angle of arrival of a primary electron at the repeller is designated by the symboleC’ and is shown in Figure 7 to be equal to the entrance angle, °C , plus the transit angle, In Figure 7 and in Figure 8, the sinusoidal waves represent the instantaneous values of the ac component of the gap voltage drop in the direction from nose to repeller. Values of oC* are important because they determine the entrance angles for secondary electrons.

The transit angles, ® jj, reveal a very important fact about the production of secondary electrons. Among the primary electrons which strike the repeller, let one be injected into the gap at time t^ as shown in Figure 8.

This electron will strike the repeller at time tg. A second primary electron, injected at time t2, will overtake and pass the first electron and will arrive at the repeller at time tg. Still a third electron, injected at time tg, will arrive at the repeller simultaneously with the first. And finally, an electron injected at t4 will arrive belatedly 21

• 6 h Transit Angle tc> th© Espalier

Angle of the Arrival of the Primary Electron at the Repeller

Mathod for Botorsaining the Entrance Angles of Secondary Electrons

Figure 7 22

EF Cosipos^ssiffe of Gap 7olt®p Drop

p . ■fc, ■fej

Raproaontatlosi of th® Entranco Angles for Priaas^- Bleotroas and tholr Corresponding Ahgla® of Arrival at tho Eopall©r.

Figure 8 2 5

at time ty. This ability of primary electrons to overtake

one another results in intense bombardment of the repeller surface. To determine the rate of arrival of primary electrons

at the repeller, a double-valued curve of the number of electrons which have arrived as a function of the arrival

angle e>C 1 is plotted as curve A shown in Figure 9* The method of obtaining curve A is given in Figure 10. The

single-valued curve (B) is obtained from curve A. Between

and oC 2 3 points on curve B are found by plotting the perpendicular chord of curve A. This process yields that unique curve (B) whose derivative for each value of 1

is the sum of the magnitudes of the corresponding deriva­ tives of each of the two arcs comprising curve A. An alternative method of finding curve B may be based on the principle of the conservation of electric charge. On the y * ' interval <>Cg to , curves A and B are coincident, because curve A is not double-valued there. The slope of curve B determines the rate of arrival of primary electrons at the repeller. Bombardment begins y s abruptly at an^ ceases at Figure 9 suggests that the initial bombardment will be severe. To investigate the ✓ slope of curve B at the point ^the information contained in curve A is presented in a different manner. In Figure 10, curves of and as functions of entrance angle are shown for the particular operating condition where K is 0.5 5h c3 O i!

* «sC Arrival Anglo

Cuttob Shoving the &thod for DBt«ndniog th@ Rato of Arrival of* Frlsary Blsctrons at fcfa© Rap© Has*®

Flgrar© 9 25

•(3*U1» 7.79) Mult of & „ vs. ©c mm approaches 1.35

s 0 al<(s 2. 6 8 h radians «c- 5 . 8 5 0 radians

V

sc ©

IS WELL- N. BEHAVED

2.3 3.3

and Y Is 1.1. Although a large value for K has been chosen, the resulting curves are typical of those obtained over the entire range of rf fields and gap spacings

considered in these calculations. The bowl-like appearance

of the curve Is a consequence of the phenomenon dis­

cussed earlier in connection with Figure 8. When the curves

for and are added vertically, a curve of oC' as a

function of <=<1 is obtained, from which for any given entrance angle, , one may determine the corresponding

angle, 1 , at which the electron will reach the repeller. The curve of 1 has a minimum which must lie to the left

of the minimum point on the curve; Its exact location is

determined by the condition that

d ® H — - - -1, (36) d <<

because the ©C curve has a constant slope of plus one. The physical nature of the electron tube Insures the continuity

of and its first derivative. In the-vicinity of ©c equal to 2.6, a finite power series expansion is used to determine the equation for in terms of «<.

© H ” C0 + G1 (‘< -2.6) + C2 « -2. 6)2 -b C 3 (<* -2.6)3 . (37)

The constants Gji may be determined from the conditions listed below; oC ® H 2.6 3.255 2.8 3.059 3.0 2.915 3.2 2.810 27 The result is 3 = 3.255- 1.1307 ( << -2. 6) + 0. 8099 ( < -2. 6)2-0. 2604 «- 2 . 6), and (38)

£2? = -1.1307 +2(0.8099) (

The equation

d < = -1 (40) has two roots; the only one with physical significance occurs at equal to 2.684 radians. The corresponding value for is 3.166. The coordinates of the minimum point of the «*C » curve of Figure 10 are;

2.684 »-«ac+o * 2.684 -+• 3.166 = 5.850. (41)

Curve A of Figure 9 may be obtained from < ’ of Figure,

10 by rearranging the axes of Figure 10, because the number of electrons which have arrived at the repeller is directly proportional to << . Since «< > of Figure 10 has a minimum point at ( 2.684, 5.850) where its derivative is continuous and equal to zero, curve A of Figure 9 has a corresponding point indicated by«£^ where its derivative is infinite.

Consequently, curve Bis perpendicular at where the bombardment of the repeller commences with an infinite

electron current that exists for an infinitesimal length of

time. The bombarding current decreases very rapidly to a value on the order of 0.5 IQ. In Figure 11, steep-fronted waves are presented to illustrate typical repeller current BepsHss1Ctsreat to To Bl©ct?oa@CO 10 Q Obtain C s m n t in t n m s C Obtain Multiply Ordlnato© by by Ordlnato© Multiply Bo®bardIs^| entrant Pole©© entrant Bo®bardIs^| Figrn*®11 a 5 . o a s To Infinity) To I r-i q to 8.0

28 29

waveforms. A wide range of gap spacing3 is included.

As the value of Y is increased, the curve of in Figure 10 remains bowl-shaped; both its diameter and depth

decrease uniformly. When Y has the value 1.35, the only

electrons which reach the repeller are those injected when od is equal to 3.41, and these electrons just graze the

repeller surface. When this occurs, the bowl degenerates to a single point whose coordinates in Figure 10 are (3.41,

7.79). During the shrinking process, there will always be one point on the bowl where the derivative is equal to

minus one. Therefore the curve of ®c' in Figure 10 will always possess a point at which its derivative is continuous

and equal to zero; this insures the existence of the infinite bombarding currents.

These conclusions extended to Figure 11 indicate that

as Y is increased by withdrawing the repeller, the steep

front of the repeller current wave moves to the right with

unchanging amplitude. The pulse width decreases, and

finally, when Y has the value 1.35, the instantaneous

repeller current consists of only a limiting pulse infinitely high and infinitessimally narrow located at oC ' equal to

7.790 as shown by the dotted line in Figure 11. For any value of Y greater' than 1.35, the pulse vanishes completely. Similar conclusions may be drawn for cases where K is less than 0.5.

The average values of bombarding currents ma.y be 30 obtained by integration of the waves of Figure 11. A dc ammeter in the external repeller circuit will read the average value of the net repeller current. This net current consists of the bombarding current minus the current due to secondary electrons leaving the repeller. For all values of K less than unity, a secondary electron immediately upon being released will experience a force accelerating it towards the nose. If K should exceed unity, it might be possible for a secondary electron to be released at an instant when the repeller is above anode potential. In such a case, the electron could not leave the repeller surface unless it had sufficient emission energy to over­ come the potential barrier. As mentioned earlier, only values of K equal to or less than 0.5 are considered here; consequently all secondary electrons will leave the repeller and be collected at the nose.

The number of secondary electrons produced by each primary electron depends upon the energy of the primary electron. If J Is the average yield, a family of curves illustrating the decrease in average repeller current with increase in yield may be drawn as shown in Figure 12. When the curves lie above the horizontal axis, more electrons will arrive at the repeller than leave it. When cf is unity, the externally measured repeller current will be zero. For values of

y B Iq

31 32 nature can presumably be obtained from an oscillator by

adjusting the load so as to maintain a constant value of K

while cf is being varied; but this would be a difficult experimental task.

The dc retarding field extracts from each primary electron that strikes the repeller an amount of energy, equal to that with which it was originally injected into the

working gap. Each of these electrons in turn extracts from

the rf field an amount of energy measured by the square of its velocity of impact at the repeller plus an amount determined by the instantaneous level of the repeller below

cathode or reference potential. The energy of impact is

partially converted into heat at the repeller and partially

distributed among the secondary electrons which may be

released. These losses are all factors in the computation of efficiency.

Curves of the squares of the dimensionless impact

velocities at the repeller are presented *in Figure 13. As y” is increased, the dc transit angle is kept constant by

increasing IVll • . When K is constant, an increase in|Vi|

requires an increase in y m . For example, when )f changes

from 1.0 to 1.2 and |Vi| changes from 1000 to 1200, Vm must change from 500 to'600 to keep K constant at 0.5. The

change in jv^l is 200 volts while the change in V1TJ is 100 volts. The result is that as Y is increased, fewer elec­ trons will strike the repeller, and those which do strike P. M C Dinansionlsss Impact Velocity^ 9 .2 o 1 3 Impact Energy Curves Tor Primary Electrons Primary Tor Curves Energy Impact 2 o C Extranc© Angle Extranc© C o iue 13 Figure 3 9 Radians h

33 34 it will have lower impact velocities. These facts are illustrated in Figure 13. For values of K greater than unity, an increase in Y will produce the opposite effect; the actual change in Vm will be greater than the change in

\H- This might result in more electrons striking the repeller with higher impact velocities as Y is increased; but the mechanism is so complicated that the only way to verify this supposition is to perform lengthy calculations resulting in curves of th.e type shown in Figure 13.

In Figure 14, the squares of the dimensi onless impact velocities are plotted as functions of ©C', the angle of arrival of primary electrons at the repeller. When Figures 11 and 14 are superposed, some interesting facts become evident. For instance, when Y is 1.1, it can be seen with, the aid of Figure 15 that the leading edge of the repeller current waveform Is composed of primary electrons arriving with energies in the range 0.1 to 0.25. The figure 0.25 indicates an electron has one-fourth of its initial energy. The body of the pulse Is composed of some low energy elec­ trons and many with rather high energy. Those electrons associated with the trailing edge have very low energy. The terras high and low are relative only, and in normal operation of the oscillator any primary electron with an energy figure exceeding 0.03 could be expected to release secondary elec­ trons. Hence the low-energy electrons mentioned above are good sources of secondary emission. y) p£ BHwasioiil®®© Insist ¥

10

8 'fc, -

.3 6 CM.

t> ©2 h

•—i ea a • 1 2

Trailing I dg© Opl CUA o O r> 5 6 8

Impact Eacrgy Curv© and Bcafejardisig Car?*©nt Pulse

Figur© 15 37 The secondary emission properties of pure metals have

been studied by many and reported upon by Bruining.4 While

the results are in general agreement, still no two investi­ gators have obtained exactly the same data. The reason is

that the yield depends strongly upon surface conditions,

and no two samples are identical. The approximate secondary emission properties for a pure copper repeller are presented

in Figure 16, where a gun voltage of 800 volts dc is

assumed. Data for the curve were adapted from material published by Bruining.4 The minor maxima and minima found by some to exist when slow primary electrons are used have

been suppressed because they are not germane to this problem.

For convenience, the yield, J , is considered the

independent variable in Figure 16, and the corresponding

energy of impact, i)2p i , of the primary electron is treated as the dependent variable; such usage is not customary.

There is also reproduced in Figure 16 the-curve of 02pi

as a function of 1 for the case where K is 0.5 and Y is 1.1. To supply additional needed information, a curve of

the number of primary electrons which have arrived at the

repeller as a function of the arrival angle, », is given. Thus for any 3mall 'increment, A the energy of impact of

the primary electrons, the secondary emission yield, and the number of primary electrons involved may all be determined from Figure 16. From these data, the expected 38

K » OoS y s 1 . 1

vo©<<

2.0 .14 Edarjr Ele ©terns t o . sC'

1.5 o3

CUfSt

1.0 .2

0-5 *1

0 0

Cu t t o s for th@ Bstoraia&tion of &QG©mI©£y ISaiBsloia Resulting freza High Prlmr^ Eloateons.

Flgor© 16 39 number of secondary electrons may be obtained. The delay time of production of secondary electrons is not fully 5 understood, but recent estimates give an upper bound of

less than 10 -14 second. In the 2.5 centimeter wavelength

region, the corresponding delay angle would be on the order

of 7.5 x 1 0 “4 radian. Such a small phase shift would not be noticeable in Figure 16. The results are plotted as a

curve giving the number of secondary electrons produced as

a function of the arrival angle of primary electrons. It can be seen that secondary emission effects begin at the

instant bombardment starts and that they will continue

until the bombardment ceases, even though the trailing

edge of the bombarding pulse contains very low-energy primary electrons. These low-energy electrons can be

elastically reflected, thus enhancing the yield.

The two curves of Figure 16 showing the number of primary and the number of secondary electrons involved have been reproduced in Figure 17. Each is similar in shape to curve A of Figure 9. By a process already described, each can be converted to a single-valued curve. By taking the difference between such curves, the net number of electrons remaining at the repeller can be obtained. The result is shown in Figure 17.' The slope of the net curve determines the net repeller current. By subtracting the net current from the bombarding current, the secondary emission current can be obtained. For comparison, curves of all three Curves for the Determination of the Hot Humber of Electrons of Humber Hot the of Determination the for Curves Hnbar of Primary Electrons Ehich Have Eaached tim Espalier It f e t e of Secondary Electrons ihich Hay© Bean fblcased. Multiply by 3U/^o 2.5 6 o 6 5

= ti n 0V " “ : 800V 0.5 l.i iue 17 Figure C 8 9 8 7 i y r iim r P ^ Secondary Hat 40 41

currents are assembled in Figure 18. Here it is seen that

the secondary emission current pulse closely resembles the

bombarding pulse except near the tail where the primary electrons have energies which result in low secondary emission yields. The current waves differ principally on

the range between the seventh and the eighth radian where

but ten per cent of all secondary electrons are involved.

Figure 18 suggests that the secondary current pulse be

assumed proportional to the bombarding pulse. This is

almost equivalent to the assumption that all primary elec­

trons produce the same yield regardless of their respective impact velocities. The average value of J computed for Figure 18 is 0 . 7 7 9 .

Special'equipment is used in the experimental deter­ mination of the secondary emission properties of copper as

given in Figure 16. In the operation of an oscillator, the

repeller is in line-of-sight with the hot cathode of the electron gun. Cathode material will be evaporated onto

the repeller surface, and a change in the emission proper­

ties of the repeller can be expected. The geometry of the oscillator Is not adapted to secondary emission yield

measurements, so in general the exact properties of the repeller cannot be determined. This fact and the results

of Figure 18 make it desirable to base the calculations on an average value for cf . 42

ID

Multiply Ora&nmtoe fesr Iq to ObtaSp toparao

A w i p tf e Oo7?9 i

Prinax y Bossbardaaz t Current

Soeoadary 1 aisaloa S ^ ^ 5 a 8aa,cl®t Cm

Campari©®® of Primary Seeossda^j, and Wat Currant Pdesi

Flgur® 18 It has been demonstrated In Figure 13 that as Y is increased, fewer primary electrons will strike the repeller, and those which do will possess lower energies. Such a

situation is pictured in Figure 19. The yield curve was

obtained from the lower portion of the yield curve of

Figure 16. Even though the maximum energy figure for

primary electrons is only 0.0223, there will still be

copious secondary emission. The secondary current pulse

can be obtained as before, and it will closely resemble

that of Figure 18, except It will have a much shorter time

base. The pulses of bombarding current, secondary emission

current, and net current are superposed for comparison In

Figure 20.' The similarities existing among the three waves

are even more striking than for those of Figure 18. The average value of tS for Figure 20 is 0 . 1 9 1 as compared to 0 . 7 7 9 for Figure 18. Later calculations will show that

Figure 18 corresponds to a condition of driven oscillation, and Figure 20 to a condition where oscillations are self- sustaining.

To determine the effects of the secondary electrons upon the operation of the oscillator, the transit angles required by these electrons to travel from the repeller to the nose must first be calculated by setting © equal to 3 and g s equal to zero in Equation 23. The results for the particular value of equal to 1*1 are presented In Figure 21«. The dc transit angles for secondary electrons are } } p^Steoaloal©®@ falosity2 <,03. »GI| ,02 & I « 10 7*0 0 Slootrono. mission Eooulfcingmission Chun?®© of Secondary for th® Dotomlnatloa . eT O02 O T e 0.1 «' 7l5 <«£' io© 19 Figor© Bombarding (hnT8i!& Bombarding From, Law Emrgy Prlmsy Emrgy 0.3 K r s 0.5 1*335 =

44 45

ID

1. Primary ISlootroQ Current 2. 1st w ® i 3« Secondary *» « j

K is 0©$ If© 1*33$ Va 2 8G0 V

Average «T « 0*191

7.0 Ccaparleon of Priiaayy,, Secondary* ami lot Current Pulm & Figaro 20 /3q Secondary Electron Transit Angle5 Radians h 2 3 1 0 5 cCQ ScnayEeto nrn©Age Radians Angle, Bntranc© Electron Secondary Secondary Transit Angle Curves Angle Transit Secondary _g « 1 iue 21 Figure

46 o o o o 47 obtained by the further substitution of K equal to zero in

Equation 23. The result is

A , a = I s f f . (4S)

For Figure 21 where Y Is 1«1, the value of fios is 4 . 0 6 radians. When Y h as t*10 particular value of unity, the dc transit angle for a secondary electron is exactly half the dc transit angle for a corresponding primary electron. By a method similar to that applied to the primary transit angles of Figure 3, it can be shown that the curves of Figure 21 intersect each other at ft3 equal to when c>C3 is either 1 . 8 9 radians or 5 . 0 3 radians, irrespective of the value of K. It will be shown in Figure 22 that these electrons have exit velocities which depend upon K, even though their transit angles are independent of K.

With the transit angles known, the dimensionless exit velocities ( 3 for secondary electrons can be com­ puted by substituting ft3 for Q in Equation 18. The kinetic energy possessed by each secondary electron upon collection at the nose is proportional to the square of its 2 exit velocity. Therefore, typical curves of Qxit as functions of entrance angles, «CS, are presented in Figure 22. The rf field strength factor K is the parameter, and the gap spacing factor Y was selected as 1.1 so that the curves of Figure 22 will correspond with the transit angle curves of Figure 21. The scale of Figure 22 makes ( O s m t ) 2 1.1 jH^g.% a^sfs Q©3ls © ® ® s t f©s» e SQ8©£3slasy e m Cas^os

K, even though these electrons have transit angles which are independent of K. The curve for K equal to 0.1 is missing from Figure 22 because when K Is 0.1, no primary electrons will strike the repeller when the gap spacing factor exceeds 1 . 0 6 6 . The average gap voltage, V-j_, is directly proportional to Y as shown previously in Figure 5. In the absence of an rf field, an electron released at the repeller will arrive at the nose with a kinetic energy proportional to

Y . Therefore when the curves of Figure 22 lie above the value 1.1, the secondary electrons have extracted energy from the rf field, and they have arrived at the nose with more energy than they could have obtained from the dc supply. S u c h electrons are said to have loaded the working gap. Conversely, when the curves of Figure 22 lie below the value 1.1, the electrons have given up energy to the rf field and have arrived at the nose with less energy than they obtained from the dc supply. These electrons are said to have driven the gap. Figure 22 shows that the angle of gap loading increases as K increases. Of course, secondary electrons do not enter the gap uniformly, but are produced In pulses as already demonstrated. The pulse width depends upon K and Y . It remains to be seen whether the actual 50 secondary electron pulses will have the effect of loading or driving the gap. This matter is discussed in detail later.

Energy Terms and Conversion Efficiency

The conversion efficiency, 1^ , is a figure of merit which predicts the ability of an oscillator to convert dc energy into rf energy. If the cavity and the circuit which couples the load to the cavity were perfectly lossless, the conversion efficiency would equal the conventional effi- ciency. But an oscillator which is tuned for maximum power output will have losses within its cavity and output circuit which are comparable in magnitude to the actual rf power delivered to the load. Consequently, the conventional or overall efficiency will be on the order of one-half of the conversion efficiency. Oscillator coupling and circuit theory alone encompass a wide field in which much work is now being done, and this field will not -be treated here. For purposes of studying the electronics of the oscillator, the conversion efficiency is ideal. It is defined as follows: (total energy per cycle input)-(total energy PI _ per cycle lost)______100 (43) * total energy per cycle input

100 (44)

The symbol A represents the total energy per cycle Imparted to the primary and secondary electron beams by the dc power 51 supplies which drive the oscillator. It is divided into two parts as follows: Energy Term No. 1, the energy per cycle input to the primary electrons by the accelerating gun voltage, Va. Energy Term No. 2, the energy per cycle input to the secondary electrons by the secondary beam accelerating voltage, V^. The symbol B represents that portion of the total energy per cycle input which is not converted into rf energy; it is computed as the sum of four separate energy terms defined as follows: Energy Term No. 3, the energy per cycle lost by pri­ mary electrons striking the nose.

Energy Term No. 4, the energy per cycle extracted from the rf field by those primary electrons which are captured by the repeller.

Energy Term No. 5, the energy per cycle lost by secondary electrons striking the nose.

Energy Term No. 6, the energy per cycle extracted by the component Va of the beam decelerating voltage from those primary electrons which strike the repeller.

These energy terms will be considered individually and discussed in detail in the sections that follow. Since the analysis is made on a per-cycle basis, the term energy as used here will always mean energy per cycle. 52

Energy Terra No. 1.

The symbol IQ represents the dc beam current in

amperes Injected through the orifice In the nose by the

electron gun. The value of IQ may be obtained from the externally measured cathode current If the transmission

efficiency of the gun is known. This transmission effi­ ciency Is a function of the gun voltage Va, and in the normal operating range of the gun, it may be as high as

90 per cent. For low gun voltages, on the order of 400

volts, the transmission efficiency may be only half as good. Therefore the value of IQ to be used in the calcu­

lations may be considerably lower than the value of the

experimentally determined cathode current.

The symbol n represents the number of electrons per cycle injected into the working gap by the electron gun.

n = = 2TT electrons per cycle. (45) ef toe The energy possessed by each injected primary electron Is 2 Energy/electron «. § mxQ , (46)

where xQ Is the initial velocity of the electron as it

enters the gap. The total energy per cycle is given by 2 .2 Energy Term No. 1= mnx0 = 7t m °x° joules per cycle. (47) 2 c°e The expression m I0 x0 /^© will be common to all the

energy terms; it expresses the dependence of the energy

terms upon the quality of the electron gun, the value of gun voltage used, and the resonant properties of the cavity. 53 Energy Term No. 1 enters Equation 44 as a constant equal

to 7T , because the expression T °x°*2 is common to all of uD © the other terms in Equation 44 and therefore cancels out. Energy Term No. 1 is not a function of the repeller spacing

factor Y nor of the rf field strength parameter K. The statement regarding the spacing factor if implies that

changes which would normally occur in the resonant proper­ ties of a capacitively tuned cavity as a result of changing

the gap spacing can be compensated for independently by properly retuning the cavity inductively.

Energy Term No. 2.

Figure 5 shows the dependency of V-, upon Va and )f . . 2 V-^ = V - mxQ if /Ze. (48)

In the absence of rf fields, K is zero, and the exit velocity for a secondary electron is obtained from *2 / , N xs exit dc 2 0 ^l/m J (4 9) or

*s exit dc = ill2 f k ko* = * o (5°)

Let N be the total number of primary electrons which strike the repeller per cycle, and let J be the average secondary electron yield. Then the energy per cycle possessed by the group of secondary electrons when it strikes the nose Is

Energy Term No. 2-^-mN J / , (51) where N Is a function of I 0/a>e which can be obtained from curves similar to the one presented in Figure 16. For a given value of K, the number N of primary electrons striking

the repeller will decrease as the gap spacing factor Y is

increased. Figure 6 shows that when Y is unity, the angle

over which the repeller will intercept primary electrons

is approximately '7T* radians and does not change rapidly with

K. Therefore the values for Energy Term No. 2 computed for different values of It should all be about equal when Y is

unity. Figure 6 also shows that as ^ is increased, the

angle over which the repeller will intercept primary elec­ trons will decrease, and the rate of decrease will be much more rapid for the smaller values of K than for the larger

values of K. Consequently Energy Term No. 2 initially

should drop more rapidly for the smaller values of K. When

Y is made sufficiently large, no primary electrons will

be able to reach the repeller, no secondary electrons will

be produced, and Energy Terra No. 2 should vanish. These

facts are demonstrated in Figure 23 in which Energy Term

No. 2 is plotted as a function of Y , with K as parameter.

It must be remembered that this term gives only the energy imparted to the secondary electrons by the dc supply voltage.

It is evaluated in the absence of rf fields. It remains to be seen whether the group of secondary electrons will arrive at the nose with more or less than this amount of energy when K is not zero.

Although Energy Term No. 2 appears explicitly only in part A of the equation for , it will later be shown that ?

Itergy Tara Ea. 2 * KoltlpSy W 1*6 1.0 1 . 1 ©rargy T o m Ho. 2 vOc Gap Spaclisg Gap vOc 2 Ho. m o T ©rargy

Y

1.2 im® 23 Figm*® 1.3 s s / 1*0 55 56 it appears implicitly in part B, and therefore it has an overall effect only on the denominator of H . It will also be shown later that Energy Term No. 2 is small when the oscillator is working well. For this reason, and because it cannot be determined by external measurements on the oscillator, Energy Term No. 2 is usually disregarded in computing the conventional efficiency. However, in a general study of the electronic properties of an oscillator, this term should not be ignored. Energy Term No. 3. Among the primary electrons which are Injected into the working gap there are those which strike the repeller and are captured and those which do not strike the repeller, but which return to the nose where they are collected.

Energy Term No. 3 deals with the latter group. The kinetic energy possessed by a returning primary electron is converted into heat when it strikes the nose. The total energy per cycle lost as heat is obtained by summing over the entire number of primary electrons Involved. The work can be reduced greatly if the calculations are based on entrance angles rather than exit angles. This arises from the fact that the rate of injection of the electrons Is constant, whereas their rates of return are complicated functions of K, oC , and Y . The exit velocities for primary electrons can all be computed from Equation 8 by using the known values for primary transit angles, f t . 57

Then

Energy Term No. o Q (52) « < aO •<='*<4 where exit ls a function of x 0 and °C ; and A n, the incremental number of injected primary electrons is given by A n = AoC (53) e

The angles <=C, and *<. g, defining the range over which primary electrons will strike the repeller, may be determined from Figure 6. For any value of K or , Figure 6 shows that the interception range is centered approximately on the value of ©C equal to 3.4 radians. When either K is increased or V is decreased, or both, the range, ©Cg - will increase. In Figure 4, the center of the range is seen to correspond to a point where returning electrons would load the gap, but not heavily. The net effect is that almost as many electrons would have returned to the nose and driven the gap as would have returned to the nose after loading the gap--if they had not been captured by the repeller. In other words, plate sorting effects are not confined to the elimination of only those primary electrons which would have loaded the gap anyway.

For any given value of K, the greater the value of ^ , the fewer will be the number of electrons captured by the repeller, and the greater will be the total energy per 58 cycle contained in the returning primary beam. When Y becomes so large that no primary electrons are captured by the repeller, Energy Term No. 3 will have reached its maximum value, and further increases in Y will not affect it. These conclusions are borne out by the curves of

Figure 24. Because the interception angle when Y is unity does not change rapidly with K, the curves of Figure

24 will begin with values not greatly different from each other. The spread will be greater than in the corresponding case of Figure 23, because now the exit velocities are functions of K. As Y increases, the rate at which the interception angle decreases is most rapid for the smaller values of K. Therefore the curves for the smaller values of K should initially rise in Figure 24 more rapidly than the curves for the larger values of K. Energy Term No. 4.

The dc retarding field extracts from each primary electron which strikes the repeller an amount of energy equal to that with which it was originally injected into the working gap. This loss is considered later under

Energy Term No. 6. When Y exceeds unity, the repeller operates at some average voltage, VR , below cathode or reference potential as shown in Figure 5. Therefore a primary electron which strikes the repeller will have to overcome this additional potential barrier. The energy required to do this will be designated by the symbol W-j_. fiwrgy Tara Ho*3 . Multiply by © 1.5 1.0 Itosrgy Spacing IbrsaOap vs. 3 loo lu® 24 Flgur® K aa Parses®ter aa 59 60 The total instantaneous repeller potential with respect to the nose is a function of time given by

VR - Va + VR ■*" Vm sin ^ * <54 > During the first half-cycle, the rf voltage drives the repeller more negative, thus increasing the potential barrier which must be overcome by primary electrons that strike the repeller. On the second half-cycle, the rf voltage reduces the potential barrier. Consequently there will be an additional energy factor to correct for the instantaneous repeller potential, and this factor is called

Wg. The total energy required to overcome the potential barrier must be extracted from the energy stored in the resonant cavity. The factor Wg might be a negative correc­ tion on Wx, as would be the case if all of the electrons were to strike the repeller during the second half-cycle of the rf voltage. The kinetic energy of impact must also have been obtained from the energy stored in the cavity, and this energy is designated by the symbol W3. Energy Term No. 4 is defined as the following algebraic sum:

Energy Term No. 4 = + W 2 + W3 . (55)

It represents the grand total of energy per cycle extracted from the rf field by the group of primary electrons which strikes the repeller.

Whenever the rf voltage drives the repeller above cathode potential, bombardment is invited; and whenever the rf voltage drives the repeller below cathode potential, 61 bombardment Is discouraged. Whether or not electrons will actually strike the repeller depends in a very complicated way upon previous history* For Instance, when the repeller rises above cathode potential, there may be no primary

electrons available in positions favorable to and with

energies sufficient for reaching the repeller. By the time the electrons can alter their positions and acquire suf­

ficient energy, the repeller may have already dropped below cathode potential again, thereby discouraging bombardment. These electron inertia effects are evident in Figure 25.

The left-hand family of curves gives the angle over which

the repeller remains above cathode potential. The limiting angles, © , are found as follows;

vx - va jr (56)

vm - KVp * i w a Y (57)

Va tf + KVa ]f sin © = Va (58)

(59)

The right-hand family of curves in Figure 25 gives the angle over which bombardment of the repeller takes place. For instance, when Y Is 1.325, the repeller remains above cathode potential for an angle designated as A in Figure 25, while bombardment of the repeller occurs over the angle marked B. The bombardment actually occurs while the repeller Is experiencing Its most negative potentials; that is, bombardment occurs when the repeller Is least 62

J n 1.32$

I ^3^

Curves Showing th@ Angles Over Which ths> Espalier io Abow© Cathode Potential and fcfa© Angles & m r Which BBsbarctasnb of the Espalier Takes Plae®. Figaro 25 63 receptive. But if Y is close to unity* bombardment will begin a short time before the repeller drops below cathode potential. Remembering that the initial bombardment is very severe, one can see that the correction factor VJq can be negative for this case. The steps in obtaining and

W q follow.

VR " va ( * -1) (60) Vra = K Va * (61)

vR - Va ( V -1) H- K Va Y sin «c' . (62) The energy lost by each electron in overcoming the potential barrier vR is

vRe=*eVa { (* -1)+ K* sin* } joul©s/electron. (63)

But eVa is the initial energy with which the primary electron was originally injected into the gap. i * 2 eVn - 3 mxc . (64) The energy loss per electron is given by . 2 21 vv”’"0mx { ( ^ -1) ■+ K X sin «£ ] • (65) Let A N be the number of electrons which arrive at the repeller on the incremental arrival angle Then the

/ energy loss on the interval i 3

■|r mXp | ( y -1) + K X sin ^' } A n , (66 ) where A n is a function of *, and A N has the dimensions

IQ/ «>e. The total energy lost per cycle is W and is equal to

w= S i ( 6 7 ) 64 m l . i j W u3 e. { (6 8 ) W = Wx + Wg . (69)

The term W]_ is actually computed by multiplying Energy

Term No. 6 by ( Y -1). The term Wg is obtained by using A N and from Figure 16 and performing the summation.

It will be observed that Wx must vanish as Y ap­ proaches unity, because Vp approaches zero. For large values of ^ , Wx will also vanish because N approaches

zero. As mentioned before, the angle of interception will decrease as Y Is increased, and the rate of decrease will be lower for the larger values of K. Therefore it is concluded that for a given Y , the larger the value of K, the larger will be the corresponding value of W^_. These facts are all illustrated in F’igure 26, where Wx is plotted against Y , with K as parameter.

Term Wg is computed from the equation

la; „ m (70) 2 ~ ” Reasons have already been discussed why Wg can be either positive or negative, depending upon the particular values of K and Y . Restating in different words, when bombard- ment begins in the second half-cycle, sin «C 1 will be negative and A N will be large. As the bombardment con­ tinues, sin eC 1 will turn positive, and A N will decrease very rapidly. Therefore, when Y is small and K is large, the summation can result in a negative quantity. The terra K as Parsaatsr

0„1(

1 . 1 Y 1 . 2 1 Energy T @ m vs. Gap Spacing

Flgur© 26 6 6

Wg must vanish for large values of K, because then there will be no primary electrons reaching the repeller. The function Wg Is plotted against Y in Figure 27. As in the case of the final rapid drop towards zero is caused by the equally rapid decrease in the number of bombarding electrons.

The energy of impact possessed by the group of primary electrons which strikes the repeller is designated by the symbol W3, where 0<=‘

1, because the rate of Injection of electrons is constant, but their rates of arrival at the repeller are complicated functions of , Y , and K. For a given value of K, an

Increase in X will cause a decrease in the number of primary electrons reaching the repeller, and at the same time it will cause a decrease in their velocities of Impact.

Consequently, for each value of K, the value of W 3 will be greatest for Y equal to unity, and when Y is Increased,

W3 will rapidly decrease as shown in Figure 28. For large values of Y , W3 will vanish because no primary electrons will strike the repeller.

Energy Term No. 4 is computed as the algebraic sum of W-j_, Wgs and W3* It represents the total energy per 67

0.1

EsosfgSr T&im Ig vae Gap Spaolng Figrar® 27 6 8

0.1

1 . 0 1.1 1.2 1.3

Eoargy Tom vs. Gap Spacing

Pigur© 28 69

cycle extracted from the cavity by those primary electrons which strike the repeller. Because the initial rates of rise of and Wg are greater than the initial rate of decrease of W 3 , Energy Term No. 4 will rise to a peak value. Then, because all three components decrease rapidly,

Energy Term No. 4 will drop sharply to zero as shown in Figure 29.

Energy Term No. 5.

The energy per cycle converted into heat by secondary electrons striking the nose is designated as Energy Term No. 5. It is computed as follows;

Energy Term No. 5 = T i m S 02S exit AN (72) where A N, a function of XQ/«>e, is the number of primary electrons which strike the repeller on the increment £k«*C< .

The exit velocities for secondary electrons are calculated by substituting /®a for ^ in Equation 17. Because most of the secondary electrons have initial energies corresponding to only a few volts, and because of the usually large values for the gap voltage the effects of the initial velocities have been disregarded in these calculations.

To illustrate this point, an initial energy of 100 volts was assumed for the secondary electrons, and curves of velocity were run on the computer. This initial energy is about five times the average value which might be expected. The resultant curves were so nearly identical to those £rrpo©dg dco °oa •ou &©rgy Tern Mo, 1*. Multiply by Multiply 1*. Mo, Tern &©rgy VJ\ O 71

obtained under the assumption of negligible initial energy,

that the difference could not be read with certainty.

The values of J represent average yields, because

the exact yield properties of a given repeller cannot be

determined while the repeller is working in an oscillator. To determine the effects of time delay, a uniform delay angle, ^ £>, was assumed for all secondary electrons

irrespective of the energies of the corresponding primary

electrons. For each value of Energy Term Wo. 5 was computed. The results for equal to aero are plotted

against if in Figure 30, where K is the parameter. In

Figures 31 to 34 inclusive, the results are plotted against

€3 p with Y as parameter. Figure 30 shows that the energy possessed by the group of secondary electrons will decrease rapidly as Y increases, because the number of electrons involved will decrease so rapidly as to more than offset the gradual increase in V-^ •

Figures 31 to 34 illustrate some Important points. For equal to zero and for any value of K, secondary electrons will load the gap when Y la small and drive the gap when Y Is large. This can be seen by observing the positions of the vertical intercepts relative to the short horizontal lines which separate the regions of gap loading from the regions of gap driving. When the intercept lies above the short marker, the group of secondary electrons BtePjy Tqjh So« 5# E^^Iu&tsd with j ® 1«0« liultiply by ■lyiu^ro

2 § vn GJ O

vn

-a w 73

©merges with more energy than it would have had if it had

been released at the repeller in the absence of an rf field.

Thus the group is said to have loaded the gap. In each case pictured, the initial slope of the curve Is negative.

ThQi’Qfore, as the delay angle increases from zero towards

one radian, the degree of gap loading will decrease, making

conditions more favorable for oscillations. As the delay

angle is Increased further, the energy curves reach their

minimum points where the group of secondary electrons is

returned to the nose with' optimum phase for driving the gap. Further increase in the delay angle will cause the

group of electrons once more to load the gap. For a given

value of K, the optimum delay angle is smaller for the

larger values of Y . This latter tendency is fortunate,

because It will be shown that when the repeller Is under

bombardment the oscillator works best when Y is large. 5 Recent estimates on time delay give an upper bound of less

than 10"^ second. This corresponds to a negligibly small value of © £ In the frequency range considered here. For example, even In the six millimeter range, the delay angle would be on the order of 3.1 x 10"3 radian. Such a small angle cannot be read in Figures 31 to 34. Xt is interesting to note that the passing years have seen a continuous

decrease in the values estimated for the time delay of production of secondary electrons.

The energy per cycle Imparted to the secondary 2 Bnorgy Tern Bo. 5> Evaluated/- at 1.0. Multiply by

o

H r

4 ©

f vn \j J i

01 H? er I S' 2 Energy fara ioo 5S Evaluated at / s l„a Multiply by

fO o in

H

Os 2.G

!§ 0.5 £a>

& I 0

3 D Dolay Anglo, Radians

Energy Term No. 5 vs. Delay Angle

Figure 33 77

j 2.5

0 I J? 2 . 0 * 0*4C.

I

3 1.5 it

ts

I1 1,0 e> 1 . £5 «% xr\ i .5 oe Fbr K - 0.5 & J 0 . 0 2 h 6 &D Da lay Angle* Radiane

Energy Tern No. 5 ve. Delay Anglo

Figaro 34 78 electrons by the gap voltage has been computed as

Energy Term No. 2 Tor the case where K Is zero. A large

portion of Energy Term No. 5 is the result of the energy imparted to the secondary electrons by the average component

of the gap voltage. Therefore, Energy Term No. 2 appears

implicitly in Energy Term No. 5. In other words, Energy

Term No. 2 is automatically cancelled out of the numerator

of the equation for conversion efficiency; the energy has

appeared first as part of the input to the system under Energy Term No. 2, and later as part of the losses under

Energy Term No. 5. The only effect it has on the'results of the calculations arises because of its presence in the

denominator of H , where it lowers somewhat the conversion

efficiency. Since the effect is small, this energy is

usually neglected in the determination of the conventional efficiency of an oscillator. It should be noted that the

principal reason for the introduction of Energy Term No. 2 into these calculations, aside from the "increase in accuracy which results, is to permit the present definition

of Energy Term No. 5, which is now in its most easily evaluated form.

Energy Term No. 6 .

The energy per cycle extracted by the dc retarding field from those primary electrons which strike the repeller Is divided into two parts corresponding to the components

Vr and Va of the gap voltage V]_. The former was calculated 79

under the symbol the latter is now computed as Energy

Term No. 6 . The easiest method is to determine the initial energy of injection possessed by the group of primary electrons in question. Let N be the total number of primary

electrons which strike the repeller each cycle. Then

Energy Term No. 6 - | m x^ N . (73)

This factor is plotted against Y in Figure 35. The curves

originate close together where Y is unity because the number of primary electrons, N, does not vary rapidly with

K. For large values of Y , Energy Term No. 6 vanishes

because no primary electrons strike the repeller, and N is

zero. As Y is increased, the rate of decrease of N is more rapid for the smaller values of K. Therefore the curves

for the smaller values of K in Figure 35 will initially drop more rapidly than the curves for the larger values of K.

The foregoing six energy factors are the only ones

involved in the electronic conversion efficiency. Electrons in transit between nose and repeller wild induce currents

in the electrodes. These currents will cause additional

losses which are part of the circuit problem; but these losses will not be computed here.

The total energy per cycle input to the system is designated as A, where

A - Energy Term No. 1 -+• Energy Term No. 2. (74) The total energy per cycle not converted into rf form is designated by B, where 80

©

& I 1.0 1 . 2 1.3

Ej&argy f e m lo. 6 ?i* Gap Spacing

Figure 35 81 B = Energy Term Wo. 3 4* Energy Term W o . 4 (75)

+ Energy Term Wo, 5 + Energy Term Wo, 6 . Curves of A (input) and B (loss) are plotted against Y in Figure 36 for the case ’where is unity. Xt can be seen that for each value of K, the losses exceed the input

except where Y is so large that bombardment of the repeller either does not occur or is very light. For each value of K, then, there is a wide range of gap spacings for which

self-sustained oscillations are impossible.

Performance Curves, Theoretical

The efficiencies computed on the basis of Figure 36 are plotted in Figure 37. For each value of K, the efficiency is independent of X until X is reduced to the point where bombardment of the repeller begins. Any further reduction in Y causes the efficiency to drop rapidly to zero. Continued reduction of Y causes Y\ to become negative. This behavior is principally-due to the sharp rise in Energy Terms 4, 5, and 6 the moment bombardment begins.

The portions of Figure 37 where H. is positive have been expanded in Figures 38 to 41 inclusive to illustrate the effects of changing the secondary emission yield. It can be seen in this group of figures that an increase In

ef will always cause the efficiency to rise. The losses 82

5.0 Q 3

* * §

t>

Si a il 3 .5 & ©s

1 3.C

& I SHQ8 l.o 1.1 r i-2 1.U

E^srg7 injrat w d lo@o ©liaraeterio tie©

Flgisr® 36 83

1 2

Comroroion efficiency Too gap spacing Figur© 3 7 84

have combined in such a way as to make self-sustained

oscillations impossible except over the range where those

secondary electrons which may be produced will drive the gap. It will be noticed in Figure 38 that the efficiency

for J equal to zero increases as Y Is increased. The maximum efficiency occurs where bombardment ceases. For

a given value of t , as ef is Increased the efficiency

Increases to a maximum at cS equal to infinity. When <$ is infinite, the efficiency rises to a maximum with Increasing Y , and then as Y increases further, the efficiency falls to the value of 1.6 per cent at Y equal to 1.135. Such behavior Is to be expected, since the number of primary electrons striking the repeller will decrease as the gap spacing is increased, and the efficiency will become Independent of the yield, J .

Since oscillations are self-sustained only where bombardment velocities are low, average 'values of <$ considerably less than unity are to be expected, except for large values of gun voltage, Va. Under conditions of low secondary yield, the curves of H vs / similar to those of Figure 37 will drop even more rapidly to zero. An Idea of the rapid drop may be obtained by watching the decrease in the vertical intercepts in Figures 38 to 41 as Y is reduced. The result corresponds to a very special case, since 3 will in general never be zero so long as any 85

n %

For K s 0.2, © - 0 -2

Conversion efficiency vs. secondary emission yield

Figaro 38 8 6

bombardment takes place® Many interesting effects are predicted by the curves

of Figure 37. For Instance, assume Y is held constant at 1.2. The load can be adjusted so as to provide low

efficiencies at low values of K or higher efficiencies at

higher values of K. providing bombardment of the repeller is prevented by keeping IC below the approximate value of

0.29. The maximum power output will be obtained when the

load is adjusted to give K the value of 0.29 because

maximum K and maximum Y\ occur together. Xf K is allowed

to exceed 0.29, the repeller will experience bombardment, and the lower efficiencies will now correspond to the

higher values of K, and vice versa. This is the reverse

of the preceding case. Unless cf can be made greater than

unity, values of K greater that about 0.31 will not permit self-sustaining oscillations because becomes negative.

For every value of Y , there Is a maximum value of K for which oscillations are possible, and this value of K

increases with Y ■

The curves of Figure 37 show that maximum power

output will usually be obtained when the load Is adjusted

so that bombardment of the repeller Is just prevented. In

special cases where the average secondary yield is higher than unity and K is as low as 0.2, maximum power output can be expected where the repeller current is maximum in the reverse direction. However, this condition would be 87

-2 For K s 0*3* s 0

Conversion efficiency vs* secondary omission yield

Fignr© 39 8 8

s 1 o278 or mor®

-2 For K - OoU, ©£> = 0

Convoroiora ©fficios^y f s « secondary calcsIon yield Figur© 40 89

10

a 1«35 hr Eoro

r\ 2

For K 3 0«,5p 0 o s 0

Conversion efficiency vs* secondary ©mission yield

Figure 41 90 difficult to achieve experimentally.

When K is 0.3 or larger, bombardment of the repeller will produce useful results only when J is 5 or more. Such large secondary yields are not expected from a pure copper repeller. But as previously mentioned, some unusual effects might result if barium oxide were evaporated onto the repeller surface from the hot cathode. The evaporation of metallic barium onto the repeller would probably result in low yields. Both forward and reverse repeller currents should be obtainable by adjusting the load for high values of K.

Vi/hen bombardment of the repeller occurs, but the impact

velocities of the primary electrons are low, $ will be

low, and small forward repeller currents will be detectable.

When K is raised so that the impact velocities increase to

the point where S becomes greater than unity, small reverse repeller currents will be detectable. In all cases, the measured repeller currents will be the net currents, and the values will range from a few milli-

amperes at most down to barely measureable currents on the order of several microamperes. The curves of Figure 37 Imply that large efficiencies can be obtained for large values of . However, the refocusing properties of the planar geometry are not good.

The result as Y is increased will be spreading of the electron beam. Returning electrons will strike the sloping 91 sides instead of being properly refocused to the flat surface of the nose. The planar geometry assumption will be less valid, multiple transit angles will result for electrons with common entrance angles, and the efficiency will drop sharply. It Is possible that the oscillator will fail to work at all when Y is large.

On the other hand, when Y is small, capacitive loading effects will reduce the shunt resistance of the cavity. This fact and the poor efficiencies predicted by the curves of Figure 37 mean that oscillations may not be possible when Y is close to unity, even when all the external load Is removed.

In Figure 42, the conversion efficiency Is given by curve (2) for the case where bombardment of the repeller Is ignored. All of the primary electrons are assumed to return to the nose without giving rise to secondary elec­ trons. The efficiency obtained in this manner is independ­ ent of the gap spacing. For comparison,- the results of the calculations made by J. J. Ebers^ are given as curve (1) in Figure 42. The difference between the two curves is probably accounted for by the fact that Ebers used a value of equal to 7.60 radians whereas the value of A used in these calculations Is 7.7253 radians.

The general conclusions that may be drawn from the results of these calculations are summarized as follows:

1. Maximum power output will normally be obtained CoHrorsion efficiency neglecting eecen&aiy emiosion effects % n 10 of planar geometry neglecting secondary emission secondary effects. neglecting geometry planar of Theoretical conversion efficiency characteristics efficiency conversion Theoretical 2 Acrigt Esubausr to According (2) (1) According to to According (1) iue 42 Figure Eboro K C2) ( 1 )

92

93 when the load is adjusted so as to just prevent repeller bombardment. 2. Operation with large values of Y will be more

efficient than operation with small values of Y , providing the electrons can be properly refocused onto the nose. 3. For each value of Y there is a maximum value of K for which oscillations are possible, and the value of K increases with Y . 4« For unusual cases where very high secondary yields are obtainable, bombardment of the repeller can be advanta­ geous. But such secondary emission effects are likely to be highly unstable and therefore not generally desirable. 5. Both forward and reverse repeller currents can be obtained by adjusting the load for various high values of K. The adjustment is made at the sacrifice of efficiency and power output, unless very large values of yield are obtained.

6. Measured repeller currents will be relatively small, ranging from a few milliamperes down to several microamperes. When unusually large repeller currents are measured, leakage currents or field emission are to be suspected.

7. The conventional or overall efficiency will be much lower than the conversion efficiency because of the losses within the cavity and the waveguide. 94

The preceding analysis of the retarding-field oscillator Is based on some restrictive assumptions, among which are those of planar gap geometry, negligible space charge effects, uniform yield and delay time of production of secondary electrons regardless of the energies of the primary electrons, and negligible initial velocities for the secondary electrons. These assumptions are necessary to make a solution possible with the facilities available.

The results of the analysis are to be interpreted in the light of these assumptions. In addition, one of the most important parameters of the oscillator, Its rf gap voltage, cannot be determined by direct measurement. Therefore an exact quantitative check on the theory cannot be made using experimental data.

The experimental program provides a qualitative rather than a quantitative check on the theory. By varying the repeller voltage over the repeller mode, the effects of a changing rf gap voltage on the secondary emission yield are observed. The effects of the secondary electrons on the power output are determined by changing the secondary emission yield of the repeller tip. Corrolation of the experimental results with the theory leads to a conclusion regarding the time delay of production of secondary elec­ trons. Finally, a quantitative check on the theory is attempted using a calculated value of rf gap voltage. 95

Experimental Re suits Using Sealed-off Tubes

Chronologically the experimental work on secondary emission effects was begun prior to the theoretical work, because the opportunity to utilize the computor at Wright Field did not present itself until later. It would have been helpful if the theoretical results had been available to guide the work. In planning the experimental procedure, the following points were listed as being desirable. 1. The secondary emission yield, S , of the repeller should be variable while the oscillator Is operating. 2. The method of varying J should of Itself have a minimum effect on the operation.

3. A baked-out, sealed-off tube should be used.

4. Planar geometry should be used to afford a check on the theory.

5. Repeller coupling to the load should be used. A solution including these five points was proposed as shown in Figure 43. It consisted of a fixed-frequency, planar retarding-field oscillator in which the coupling to the cavity was made through a glass seal which located and supported the repeller. The standard half-size Hell gun 6 was used, and the planar geometry was obtained from J. Cookb tube. The oscillator was designed to operate in the five- centimeter range. In order to change the secondary emission coefficient, the repeller tip was lightly coated EJopallor Esabop Cefmoctioa

' | Rspallor Shaft Glass Saal l^vogalxt©

\ \ \ W V ' V 1 - Cavity Birfco&sioa t Coasi&X M m \\. \ .\ \.._\

Ralf-sico Goa AssGsabXy

Skirt

Cathods-ho&bor CoiHIQCt lofts

Tip-off

Tubs m>, 3 Figaro 43 97 with cathode coating material, barium-strontium-carbonato,

and the repeller was equipped with a heater coil so that

the temperature of the repeller could be varied. While the

7—11 t literature is not agreed as to whether J increases or decreases with temperature, it is generally conceded that

it does one or the other, and it was believed that any

change either way would be sufficient for the problem. The repeller was made by brazing a length of kovar

tubing into a copper rod which had been drilled and reamed

to receive the kovar. Then the copper was turned down until it formed a shell ten mils thick around the kovar. At the same time the repeller tip was formed. The kovar

tubing gave the repeller excellent rigidity and made

possible the required glass to metal seal. A three-quarter

wavelength repeller was chosen so as to locate the repeller

heating coil as far as possible from the glass seal.

The next step was to seal the repeller shaft into a

short length of half-inch diameter kovar- tubing. This

seal was made with glass while the shaft and cylinder were held in position by means of a stainless steel jig. After

annealing the seal, the jig was removed, and the kovar parts

were deoxidized by heating in kovar cleaning solution. The wide spacing between the shaft and cylinder made the

cleaning operation possible. No attempt was made to silver plate the parts. The next step was to braze the repeller into the 98 cavity. The kovar cylinder was slipped over the cavity extension which reduced the coaxial line spacing to the required ten mils. A thin, split-sleeve jig of stainless steel was inserted to correctly center the repeller shaft in the cavity extension. A second jig was slipped into the cavity itself to properly locate the repeller tip. The braze was made in a hydrogen atmosphere using rf energy to heat the parts. During the brazing operation, the cavity was held upside down with the glass seal under water to protect it. After the braze, the jigs were removed, the joint was leak-tested, and the repeller position was measured on the tool-maker’s microscope; the repeller v/as found to be less than one-half mil off center.

The next step was to simultaneously braze the nozzle and skirt to the cavity. Once again the glass seal was kept under water for protection. After passing the second leak test, a special tool was used to spray cathode material through the orifice of the nozzle onto the surface of the repeller. A coating one to two mils thick was obtained.

Then the standard half-size gun and the getter were mounted, the tubulation was applied, and the tube was sealed on the bake-out station.

Bake-out lasted approximately three hours at 500 degrees Centigrade. After cooling to room temperature, the gun v/as activated. The repeller v/as outgassed and the repeller coating v/as reduced and activated by electron 99 bombardment. Then tbe getter was flashed, and the tube was sealed off. Next, the repeller heater was inserted into the repeller shaft; the shaft was roughed out on a forepump and sealed off. The entire assembly procedure proved to be very difficult, and several failures were recorded before the tube was successfully completed.

Five fundamental tests were made on Tube No. 3 to determine its performance. Because of the usually large dc potential difference between nose and repeller, the small gap spacing, and the uneven repeller coating, field emission from the repeller is to be expected. The first test,

Figure 44, shows that field emission may not be neglected when the potential difference exceeds 1200 volts. However, below 1200 volts, the repeller current due to field emission is less than 2 microamperes and may be neglected.

An observed fact is that field emission currents are entirely independent of repeller temperature throughout the region of operation. The data discussed below were obtained under conditions such that field emission was negligible. The object of the second test was to determine whether the secondary emission coefficient of the repeller could actually be varied. Figure 45 shows that the repeller current changed from 1 ma (net electrons striking the repeller, S < 1.0) to - 0.6 ma (net electrons leaving Espalier Currents /a & IX? 2 1 10 Rapall©r~noEa potential^ volts do volts potential^ Rapall©r~noEa Field BaieeioQ jfroa Rapallsx* BaieeioQ Field Uoo a©H. 3 Ho. Tab© la© 44 Flgar© loo

1200 0 0 1 Espalier Current, Hi DC -0.5 0.5 0 . 1 hnei h , d l e H the in Change Variation in Repeller Current '©1thIndicated Current Repeller in Variation lift Electron© Leaving Repfller Leaving liftElectron© w t Electrons Striking; Rape11©r Electrons t w iue 45 figure u®N. 3 No. Tub® S 1.0 cTci.O

. 90 V Incident Electrons. Incident V 90 . Fcner,Watte

1 0 1 1 0 2

the repeller, S > 1-0) when the repeller was heated with about 6 watts of power. For this te3t, 90 volt incident

electrons were used. It is to be expected that different curves would be obtained for different incident energies.

No data are available concerning the actual repeller tip temperatures involved, but considering power input, thermal

losses, and the proximity of a glass to metal seal, it is

apparent that the repeller v/as below temperatures at which thermionic emission would be evident. The object of the third test v/as to determine how the frequency changed with repeller temperature. Figure 46 shows that the frequency changed from 6.12 KMCPS to 6.04 KMCPS v/hen the repeller was heated with about 6 watts of power. This represents 1.31/£ change in frequency, and the change is believed to be principally the result of the

expansion of the repeller and the corresponding increase in gap capacitance. Such a large change means that the bolometer power measuring elements must- be kept tuned as

the repeller changes temperature.

The object of the fourth test v/as to determine how the loaded Q, of the circuit changed when the repeller was heated. The results are tabulated below for eight measure­ ments. Cold Repeller Hot Repeller 334 328 323 330 317 298 328 301 repeller and the corresponding increase in gap capacitance. gap in increase corresponding the and repeller

Frequency change of Tuba Ho. 3 caused by expansion of the of expansion by caused 3 Ho. Tuba of change Frequency %v@E8t©r Reading 1.235 1.225 1.215 1.205 1.185 0 Re pa H e r Heater Passer, Watts Re Heater r pa e H 6.12 KMCPS 6.12 2 iue 46 Figure U 6 103

104

The hot tests were performed with the repeller heated with 7. 35 watts. The data are all within the experimental error inherent in the Q, measuring system and show no measureable change in Q as the repeller was heated. The coupling was very close to critical for the tube and did not vary. The loaded Q, is low, probably due to the glass and kovar in the output circuit. The object of the last test v/as to determine how the power output changed with repeller temperature. Figure 47 shows that the power output decreased rapidly with increased repeller temperature. Data were taken at approximately 3- to 4-minute intervals, so perhaps the repeller had not reached equilibrium temperatures. In as much as S appears to have increased with repeller temperature, it might be concluded that secondary emission loading of the gap occurred. However, since the gap spacing did change, there is the possibility that the decrease in power output was not due to increased secondary yield, but rather to other effects. This problem cannot be resolved by further measurements on the tube, and it points out the principal disadvantage to this experimental approach. It was thought

that sufficient information might be obtained by building and testing other sealed-off tubes using different spacings and geometrys.

The theoretical value of VjL required to give the transit angle A- 7.725 as used in the calculations is Repeller Current, HU 1X3 (Electrons Striking Tip) 40 1 S J- 20 1

0 1 Maximus Power. Maximus Power Output and Repallor Current Characteristics Current Repallor and Output Power for Tub© Ho. 3* The Load wa© Kept Tuned for Tuned Kept wa© Load The 3* Ho. Tub© for Fbrrar to Repeller Heater, Watte Heater, FbrrarRepeller to iue 47 Figure

105 obtained as follows : Ea = 980 v dc, gun voltage.

d = 0.038 in., approximate cold spacing including the repeller coating.

x Q = 5.93 x 10^ 'f980' = 1 8 6 x 10^ m/sec, initial velocity.

cD = 2 TT f = 38.4 x 10® rad/sec, cold angular frequency.

2 rr>c)tO Xo v i =

V y = 1050 v dc, theoretical.

Vy = 980+ 27 — 1007 v dc, experimental.

The value of Y would be lowered by heating and expanding the repeller. The theory has shown that the efficiency will be very low in this region and that it will decrease with

Y . The theory also shows that for low values of K, the secondary electrons can be expected to drive the gap. Consequently, it is possible that the secondary emission effects were overshadowed by the effects produced when the gap spacing was decreased. To further test the theory, two sealed-off tubes were built with coated repellers which could be refrigerated with liquid air. In both cases, bombardment with 90 volt elec­ trons showed an apparent decrease in J as the temperature was lowered, and under conditions of oscillation, the power output increased. These results are consistent with those 107 obtained, on Tube No. 3. Repeated applications of liquid air to the repellers eventually shrunk the metal away from the glass, letting both tubes down to air. A sealed-off tube with planar geometry and loop output coupling was built. This tube gave no evidence of a change in S as the repeller was heated, and under conditions of oscillation, the power output remained constant. This gave some support to the hypothesis that the behavior of

Tube No. 3 might be related to secondary emission loading of the gap. Still another tube with planar geometry, but with a gridded repeller, was built to make use of those primary electrons which would normally cause secondary emission. These electrons could penetrate the plane of the repeller and enter an rf field-free region behind the grid. There they were turned around and sent back through the grid with easily controlled delay time. It was found that electrons returned with the correct phase would increase the power output. The grid used had a geometrical capture factor of approximately 50%,, which v/as much too large. The optimum delay was not obtained because It was found to be so small that the electrons could not be turned back soon enough. This fact supports the theory that secondary electrons produced after short or negligible time delay will drive the gap.

A great deal of experimental work was done In 108 attempting to improve the quality of the sealed-off tubes. Various designs were used; some had repeller coupling to the load, others had loop coupling. In all, sixteen sealed- off tubes were built. Not all were capable of oscillating. Studies ware made on the Q, meter using demountable tubes

In which parts could be added one at a time. In every case,

trouble arose when the glass seal was Introduced. In the case of Tube No. 16, the glass seal v/as made without

oxidizing the kovar with the torch. Then it was ground by

hand until It was only about thirty mils thick. But still

the Q, meter registered excessive losses. The drawing for Tube No. 16 Is given in Figure 48. A kovar shell, made in two pieces, houses the cavity and

supports the repeller. All kovar parts were silver plated.

The capacitive type geometry v/as used. The method of assembly was much simpler than that of Tube No. 3. However, the poor thermal conductivity of the kovar prevented proper

cooling of the cavity. The performance.of this tube is

shown in Figure 49. For nondestructive testing, the repeller heater power was limited to about 0 . 7 5 v/att when the cavity was hot. The general results approximate those

of Tube No. 3. There is apparently a slight increase in J with increase in temperature, and this is accompanied

by a decrease in power output. The frequency change v/as

only 0.072% as compared with. 1.31$ for Tube No. 3; but a shorter repeller and lower repeller temperatures were used. 109 > 6) 4> ! & ft

Cafch»d©*-H©at©r Cocnsetiona 1 Ropaller curroafc, ma, dc o o H H ro « • »• vn O VA O BV H to U> (r O o O O

V O •g « H to ff S & •> s r (3o 0 r I"* H o *=- © ] n 1 * g «* H p o H PO

o 110 eQD 1 X 1

Experimental Results Using Demountable Tubes

The difficulties in obtaining strong oscillations in the sealed-off tubes and in interpreting the data which were obtained lead to the adoption of a different experimental procedure. The program was moved down to the 2. 5 cm wave­ length region where the fifth-size gun could be used. A tunable, demountable tube was built in which the planar geometry was obtained by scaling the previous geometry by a factor of one-half. The tuning head was capable of

centering the repeller for optimum performance as well as moving it axially to compensate for expansion of the repeller when heated. The glass seal in the output circuit v/as discarded, and a mica window was placed across the waveguide.

Details of the planar gap geometry are given in Figure 50. A standard fifth-size gun and nozzle assembly were used, except that the nose was flat instead of sharply pointed as in the case of the capacitive geometry. The gap spacing, d, is shown in Figure 50 to be the distance

between the flats on the nose and repeller. This distance

was obtained by centering the repeller and then lowering it until it shorted against the nose. The calibrated tuning head was then used to determine the nominal gap spacing

in mils. To recover a given gap spacing after disassembly and reassembly of the tube, the approximate setting v/as 0.0 $6

Standard 3/5 oiso gun assenbly ©sc©pt for flat instead of pointed nosofusod with standard cavity, drawing AA-X596-5 Sc 21 (Bsdssd)

Planar 0@©®©try Batails Dnonntabl© Tub© Figaro 50 113 obtained using the tuning head. The exact setting was obtained with the aid of the wavemeter. The accuracy of this method depends upon the centering of the repeller. When it was desired to make accurate comparisons, the repeller was not disturbed when the tube was disassembled.

Data were first recorded using a bright repeller. Then the tube v/as taken apart, the cavity and gun cleaned, and the cathode recoated. The repeller tip was coated with dag (or cathode material) without removing the repeller from its holder. Reassembly of the parts resulted in unchanged repeller centering.

The curves of Figure 51 illustrate the great increase in efficiency of the demountable tube over the sealed-off tubes. The explanation probably lies in the substitution of the mica window for the coaxial glass seal. Much larger rf gap voltages v/ere obtained with the demountable tube.

The power was measured with a water load which matched the guide very well, causing a maximum voltage standing-wave ratio of only 1.1 over the frequency range involved. The use of a slide-screw tuner would have resulted in greater power output. But the v/ater load had such a long time constant that tuning for optimum power output v/as very difficult. Therefore to insure reproducible loads, the tuner was omitted entirely. The values of K and the power obtained with the flat guide alone were very satisfactory for studying the effects of secondary emission. RF powsr output, milliwatts liiO 280 O Spacing indicated in ails froa repeller shorting position* shorting repeller froa in ails indicated Spacing O Eg Repeller Potential, wolts DC wolts Potential, Repeller Eg 12 Porar output characteristics of demountable tub© demountable of characteristics output Porar 100 16 iue 51 Figure 20

Bright repeller Bright to flat flat to FOtsor delivered Ia a 62*5 62*5 a Ia % Q % 800 guid®* V DC V m 2 DC u

114 115

Figure 51 shows that the maximum power was delivered to the load when the gap spacing v/as approximately 16 mils.

The decrease in efficiency and the corresponding decrease

in pov/er output for gap spacings less than 16 mils have

been predicted in the theory. The decrease in power output for gap spacings exceeding 16 mils is contrary to

the results of the theory. But as has already been mentioned, the refocusing properties of the planar geometry

are very poor v/hen the gap spacing is large. The electrons are collected on the sloping sides of the nose instead of

on the flat portion. Multiple transit times result for electrons with common entrance angles, and the assumption of planar geometry is no longer valid. That the returning

electrons strike the sloping sides of the nose is clearly

evident upon inspection of the nose after disassembly of

the tube. Rings of discoloration indicate the areas of

bombardment. When operated in the range where the planar geometry assumption is valid, the discoloration is confined to the flat portion of the nose.

Figures 52 to 56 inclusive demonstrate the changes

which occur in the average secondary yield with changes in

the velocities of the primary electrons which bombard the

repeller. These figures refer to a bright repeller, that

is, a pure copper repeller recently cleaned and deoxidized in the hydrogen furnace. In Figure 52, the power output was relatively low, indicating a relatively low value for K. BP pcrrar output os LUO 210 200 70 1 £ •§ a 0 of Power output pnd repeller current characteristics current repeller pnd output Power demountable tub® demountable Eg ropellor potential, volts dc volts potential, ropellor Eg Bright ropollor Bright la a 600 V DC V 600 a la ia B B ia d s 16 MILS 16 s d -50 l a m a l iue 52 Figure dc _ dc Berner -100

Current dc -150 116 200 117

U20

8 2 8 0 «sj -Ea o 650 V DC— ia - U6 m DC 1 . H«fc d ia 16 MILS Bright Ropollor ** S a f« t 5 o m o O u

1 H a a

in ...... mi— a — a n d 200 rapQllor* potential^ volts dc

-1

-2

Fbwsr output and repeller current charactoriEtico of dozaoun table tube

FIguro 53 560

2*20

280 - 700 V D C _ Ia s 51 MA DC d Ej 16 MILS Bright Reps1lor

12*0 Io

g| 1.0 —2< Repallor Potential9 vdlto dc

-2

- 6

Power output and repeller current characteristics of daxsountablo tuba Figure 54 119

8 ^ 0

560 10 Eq s 750 V DC__ B Ia s 58 Ml DC d s 16 MILS Bright Ropsllor

280 i © M a a -50 -loo Ropaller Potrantialj, volit©

-10

-151 Ptawar output ami repallor current characteristics of demountable tuba

Figure 55 1 2 0

700

$ 6 0

1*20 150

2 8 0 100 *o& «sj

11*0 ■eo © a & & & <1 Eg Rapa He r potential Its

Power* Output and Repaller Currant Characteriot-ica of Demountable Tuba. Figure 56 1 2 1

The Impact velocities of the primary electrons at the repeller were low, resulting in average secondary yields less than unity. The external repeller current, which is

/ the difference between the bombarding current and the

current due to secondary electrons leaving the repeller, has

an average value which is called positive because the net

electrons strike the repeller. In Figure 53, the first lobe of the current wave is

positive because of the reasons discussed In connection with Figure 52. As the center of the mode was approached, the value of K Increased, the number of electrons striking the repeller Increased, and their impact velocities increased.

The result was an increase in secondary yield to average

values exceeding unity, and a reversal of the externally measured repeller current. For still larger values of the

repeller voltage, the value of K decreased, fewer electrons

reached the repeller, and those which did had lower impact velocities. The result was a decrease in the average yield

and a return to positive repeller currents. The current

curve touches the horizontal axis at four points. At the

two interior points, the value of ef is known to be unity. At the two outside points, the value of

zero, because the number of primary electrons reaching the repeller, their impact velocities, and the resulting secondary yield all approached zero together. Figures 53,

54, and 55 show similar characteristics. 122

Vi/hen the gun voltage was only 600 volts, the repeller mode was only 80 volts wide as shown in Figure 52. When the gun voltage was increased to 800 volts, the wi dth of the repeller mode increased to more than 130 volts as shown by Figure 56. The beginning of the mode was charac­ terized by rather strong oscillations at low repeller voltages. The result shown in Figure 56 was a tendency for the secondary yield to exceed unity. The initial repeller currents were recorded as small, negative quanti­ ties. As the repeller voltage was increased, the value of

K increased, but the yield decreased, reversing the repeller current. The reason for this behavior was that the value of K did not increase rapidly enough to offset the increase in repeller potential and the associated rejection of the primary electrons by the repeller. This situation was reversed for repeller voltages exceeding

130 volts; the yield increased again, and the external repeller current turned negative. In all cases, the measured repeller currents were low, ranging from about

130 microamperes down to barely discernible currents smaller than one microampere. This fact agrees with the theory and suggests that the actual change in the secondary yield covered a range from zero to very slightly more than unity.

The ease with which the yield could be made to approach and exceed unity was not predicted by the results 123 of the theory. Perhaps the secondary emission phenomena at the repeller are more accurately described by the term "enhanced field emission." This phrase has a connotation similar to that of the term "enhanced thermionic emission" n o coined by Johnson to explain the apparent increase in yield with the increase in temperature of an oxide-coated target. The usually large dc gap voltage may bias the repeller to the threshhold of field emission, and subsequent bombardment of the repeller surface by primary electrons may result in yields exceeding those measured in low field

stu dies. To determine whether the secondary electrons have the overall effect of loading or driving the gap, repeller tips having different secondary emission capabilities were used. First the repeller tip was coated with dag to lower the

secondary yield. The results are shown in Figures 57 to 59 inclusive. Here it can be seen that the measured currents were always positive although the values of power

output were in the same range as those obtained with the bright repeller. This fact demonstrates that the dag

actually lowered the yield of the repeller; average values

of J exceeding unity were prevented. The measured repeller currents were very much larger, being recorded in the milliampere range instead of in the microampere range as before. Comparison of Figure 58 with Figure 56 shows that the decrease in yield was accompanied by a decrease in RF Proer output 1 1*20 280 560 U 0 H M $ o §f & u characteriotico characteriotico Power output and r©pallor current r©pallor and output Power 2 2 JO 3.0 H © p a R ipa 57 Piipma f o p o - 5 dmutbe tube demountable -loo o Potential, volto do volto Potential, d = 13 MIIS 13 = d Dag-coated popoller Dag-coated DC V 800 = I_ I® = 62 M4 DC M4 62 = I®

150 124 125

E - 800 V DC l| s 63 DC 700 d - 16 MILS

560

U20 g a jf 280 <§ v-t *4 I H v*t + & a 11*0 <§

-50 — 100 -150 Ra poller Potential* volts de

Poser Output and RapoXlor Current Character! sties of Dwountabl® Tub®

F*%ur@ 58 126

700

560 E_ - 800 V DC __ l“ - 61,5 Mfl. DC d 3 19 MILS Dag«coat©d ropsllor

U20

280 2C 8 «Sf

a 11*0 10 o Current 3 & eg -100 -150 >200 Repo He r Fbtontisl* volt© dc

Power output and repsllor current characteristics of dsesountabl© tub®.

Figur© 59 127 yield was accompanied by a decrease in maximum power output. The load, geometry, frequency, alignment, and spacing 'were unchanged; the repeller mode was altered and the efficiency at the center of the mode was decreased. The results are in agreement with the theory which predicted that secondary electrons liberated with small or negligible time delay will drive the gap. An experiment was attempted in which the repeller was coated with cathode material to provide very large values of secondary yield. The oscillator was so unstable that no data could be obtained. It was hoped that repeller current curves could be obtained showing large negative currents for comparison with the positive curves obtained with the dag-coated repeller. Also, the power curves were expected to throw some light on the time delay of production of secondary electrons for the oxide-coated target. However, no data have thus far been obtained. The data presented in Figure 60 were obtained on the demountable station with the repeller 90 volts and the anode 200 volts above cathode potential. The curves show the variation in repeller currents for three, cases, a centered bright repeller, a centered oxide-coated repeller, and an oxide-coated repeller five mils off center. The results were unexpected and show what appears to be a dependence of secondary electron yield upon gap spacing. Since the energy with which the electrons struck the IR Repeller Current9 Mi DC with 90 er Primary Electrons* Primary er 90 with Indicated Changes in Secondary Ikission Yield with Yield Ikission Secondary in Changes Indicated Change in Oap Spacing when Repeller is Bombarded is Repeller when Spacing Oap in Change d d b Oxide-coated Rep©liar, Rep©liar, Centered Oxide-coated b Rep©Her, Bright a xd-otdRple, Contorod Repeller, Oxido-coatod e Gap E Demountable Tub® Demountable Planar GoosesRepallor Planar Cold try, -a s 200 r

SpSGill^n Mil® r 90V DC 90V r Figure 60 Figure

_=. _=. Er® 90 5 Milo off Cental off Milo

200 V DC V 200

126 129 repeller* was constant at 90 ev, it is difficult to explain the apparent change in yield- Comparison of Curve C, Figure 60, with the curve of Figure 4 5 indicates that perhaps the latter is a segment of the former. When d was 18 mils, Curve C had associated with it a yield of unity. Dividing by the scale factor of one-half gives a corresponding spacing of 36 mils for Figure 45. This is close to the spacing of 38 mils built into that tube. The correlation between the two curves is good and indicates that the apparent change in yield was not caused by temperature dependence but rather by the change in gap spacing resulting from the heating and expansion of the repeller.

Quantits tive Check on the Theory

The following calculations of the theoretical shunt resistance of the cavity and the effective load impedance at the gap were made by R. Ward^-^ for the demountable planar retarding-field oscillator shown in Figure 50. The symbols refer to Figure 61. A gap spacing of 16 mils was used.

R Sk, the shunt resistance of the cavity, 69,000 ohms.

G s h 5 i » the shunt conductance of the cavity, 14.5 rahos. R sh the theoretical wavelength at resonance, 2.77 cm.

^ Q, the experimental wavelength at resonance, 2.71 cm. 130

HL °L

Rsh is the shunt resistance of tho cavity.

is the effective load resistance at th© terminals of the gap.

Representation of th© gap in a planar retarding- field oscillator.

Figur© 61 131 , the reflected load conductance at the gap, deter­ mined from data obtained on the Q-meter, 2.26 — 32.8 yU mhos.

The following data are obtained from Figure 56.

PQ , the experimental rf power output, 840 mw.

V , the gun voltage, 800 v dc. I , the gun current, 62 ma dc. Si From Figure 61, pQ =. — Vm or>

J gp 1 ______vm -Q- - Q I Q 6 - 226 volts. L v 32.8 x 10

Therefore IC =. XEi _ 2 2 6 _ 0.232, and V-l " 978

y = 12, = = 1 .22 . 6 v 800 a The power lost in the cavity is given by

P c = PQ £®h = 840 372 m w . c Gl 2.26

The total power, P, is the sum of the power lost in the cavity, Pc , plus the power delivered to the load, PQ.

P = PC + PQ = 372 + 840 = 1212 mw. The transmission efficiency of the electron gun^ when the gun voltage, Va, is 800 v dc is approximately 92^. The conversion efficiency is given by

P,Q______100 = .AJLQQ s=. 2.66 %. H " o ,92 V I 0,92 x 800 x 0.062 9. Sl 132

Th© results of the calculations are summarized below.

K - 0.232 1.22 S = l.oo 2 .66% Referring to point x on Figure 37, when S= 1 .0 , K - 0.232, Y - 1 .22 , the theoretical conversion efficiency obtained from Figure 37 is 2.15^ as compared with the value of

2. 66^o computed above. The values of K and Y place the point x in Figure 37 in a position where repeller bombard­ ment does not occur. Curve (1) of Figure 62 gives the results of similar calculations made over the entire repeller mode. Curve (2) of Figure 62 gives the conversion efficiency obtained from Figure 37 at the corresponding values of K and Y • Over the entire repeller mode, the values of K and Y correspond to points on Figure 37 where repeller bombardment does not occur. The experimental data show that bombardment of the repeller did occur.

Conclusions

There is a thread of consistency running through the results obtained with the sealed off tubes. In every case, heating the repeller decreased the power output when ac­ companied by an apparent Increase in yield as measured under dc bombardment of the repeller. In every case, cooling the repeller with liquid air Increased the power output 133

(2)

-100 -i5o -250 Ejj repeller potential, volts do Curve (1) is th© conversion efficiency obtained as shcrmi in the sample calculation.

Curve (2) is th© conversion efficiency read from Fig. 37 at th© values of K and Y obtained as ohoun in the sample calculations. Quantitative check on the theory Figure 62 134

and caused an apparent decrease in yield. In the few cases where heating the repeller did not affect the yield, no

effect was found on the power output. Gridding the

repeller provided data indicating that secondary electrons

produced with small time delay will drive the gap. These

facts seem to indicate that the secondary electrons loaded the gap, and therefore the delay time when oxide-coated

repeller tips were used was not negligible. For the low values of K obtained In the sealed off tubes, the theory shows that secondary emission loading of the gap will occur

for delay angles near 3 radians. This is equivalent to _1 -i 5 a time delay of about 8 x 10 second. DIemer and Jonker have determined the upper limit on the delay time for

caesium oxide as less than 3 x 10 ^ second.

There is conflicting evidence, also. It has been

shown that changing the gap spacing appears to affect the

secondary yield. There is physical evidence to support

the theory that reducing the gap spacing will reduce the efficiency and the maximum power output. There is no way

to determine whether the behavior of the sealed off tubes

was the result of the apparent change In yield or the

result of the change in gap spacing. The question could

probably be answered by building and testing a tunable

sealed-off tube. In this way, the effects caused by the expansion of the repeller when heated could be overcome 135 by withdrawing the repeller, keeping the gap spacing and the frequency constant. The results of the data taken on the demountable station indicate that the time delay of production of

secondary electrons from pure copper is negligibly small

in the frequency range considered here. The secondary electrons appear to drive the gap. Recent estimates for - 1 4 the upper limit on time delay for pure metals give 10

second. This corresponds to a negligibly small delay angle and agrees with the theory and results found here.

The experimentally measured repeller currents are in

the range predicted by the theory. The ease with which the yield can be made to exceed unity by increasing the

bombarding velocities indicates that perhaps the dc field has an effect in increasing the yield. The yield may be effectively lowered by protecting

the repeller tip with carbon. A stable oscillator results. Any attempt to Increase the yield by coating the repeller with cathode material is likely to result in a very unstable oscillat or. REFERENCES

O. , and Ebers, J. J. , "A Nqv; Wide-Range, High-Frequency Oscillator" Proc. X. R. E., Vol. 38, No. 6 , pp. 645-650, June, 1950.

^Thurston, M. 0., "Theory of the Retarding-FIeld Oscillator" WADC Engineering Report, August, 1954, (In process). ^Ebers, J. J. , "Wide-Range Retarding-Field Oscillators1,’ a doctoral thesis presented to The Ohio State University, 1950.

4 Bruining, H. , Physi cs and Applications of Secondary Electron Emission. New York: McGraw-Hill Book Co., Inc., 1954, pp. 31 and 46. ^Diemer and Jonker, J. L. I-I. , "On the Time Delay of Secondary Emission," Philip s Re search Report s , No. 5, 1950, pp. 161-172. ^Cook, J., "A Retarding-Field Oscillator with both Inductive and Capacitive Tuning," a thesis presented to The Ohio State University, 1952. 7 Morgulis, N . , and Nagorsky, A., J. Tech. Phys. U.S.S.R. 5, 848, 1938. ®Pomerantz, M. A., "The Temperature Dependence of Secondary Electron Emission from Oxide Coated Cathodes," Phys. Rev., Vol. 70, No. 1 & 2, July 1946, 33-34.

^Johnson, J. B., "Secondary Electron Emission from Targets of Barium-Strontium Oxide," Phys. Rev., Vol. 73, No. 9, May, 1948, 1058-1073. -*-^Woods, J. and Wright, D. A., "Secondary Electron Emission from Barium Oxide," British Journal of Applied Physi cs, Vol. 3, No. 10, October, 1952, 323-326. ^--^-Woods, J. and Wright, D. A., "Changes in Secondary and Thermionic Emission from Barium Oxide During Electron Bombardment," Briti sh Journal of Appli ed Physics, Vol. 4, No. 2, February, 1953, 56-61. -^Johnson, J. B., "Enhanced Thermionic Emission," Phys. Rev., Vol. 66 , No. 11 & 12, Dec. 1944, 352L.

136 137 ■^Ward, R., and Swiger, J., "The Resonant Cavity and Power Coupling System of the Retarding-Field Oscillator," WA DC Engineering Report, August, 1954, (in progress).

14Peck, J. L . , "Modifications of the Heil Electron Gun," WADC Engineering Report, August, 1953, p. 12. 138

AUTOBIOGRAPHY

I, Richard Arthur Neubauer, was born in Buffalo,

New York, July 10, 1919. I received my secondary school education in the public schools of the city of Buffalo, New York, and of the township of Amherst, New York. My under graduate training was obtained at the University of

Alabama, Tuscaloosa, Alabama, from which I received the degree Bachelor of Science in 1943. Prom the Ohio State

University, I received the degree Master of Science in 1947. While in residence at the Ohio State University, I acted in the capacity of instructor in the Department of

Electrical Engineering from 1948 to 1954 while completing the requirements for the degree Doctor of Philosophy.