Applied Electronics Laboratory Stanford University Stanford, California A HIGH-POWER S-BAND BACKWARD-WAVE OSCILLATOR by J. L. Putz and W. R. Luebke Technical Report No. 182-1 February 24, 1956 Prepared under Signal Corps Contract DA36-039-SC-63189 and under Office of Naval Research Contract N6onr 25132 (NR 373 362) Jointly supported by the U. S. Army Signal Corps, The U. S. Air Force, and the U. S. Navy (Office of Naval Research, Bureau of Ships, and Bureau of Aeronautics)

SUMMARY The tubes described in this report are S-band backwardwave oscillators of the folded-line type with a nominal power output of 100 watts cwo These oscillators were developed under Stanford Electronics Research Laboratory Projects 182 and 185. Both continuously pumped and sealed-off versions are described but experimental results are given for only the demountable tubes. These tubes operated over the frequency range 205 - 3~5 kMC9 with a power output of about 75 watts at the low-frequency ends and 100 - 150 watts at the highfrequency end. The efficiency varied between 6 and 12 per cent, The experimental results agree very well with theory0 Detailed design information for the folded-line type of BWO is presented in an Appendix, mostly in the form of charts. - iii

TABLE OF C ONTENTS Page Part lo —Tube type S-182 I Introduction...,... *, * * * 1 IIo S-182 specifications........ o. o 1 III. S-182 operating characteristics....... 5 A. Matches and insertion loss a..... o W O 5 B. Tuning curves,....... o *. 7 Co Power output and efficiency..... o 10 D. Starting currents,......... 14 E. Spurious outputs. o......... 14 IVi Conclusionso O,..,..0... o o o 16 Part 20 —Tube type S-185 I, Introduction * * *, *.. 17 II. Sub-assemblies..., o o. o o, 17 A, Block and end bells'. o o o o o...... 17 B R-f lines and seals,... a W.. 4 20 C, Electron gun.... 0 * * *...t 24 D. Collector assembly..... 0 a *.... 27 III. Tube assembly,.....,.. *.... 34 IV. Processing.. l........", o o o Appendix A: Design of folded-line backward-wave oscillators. l. 0 e o. 37 List of references o., o.. 57 - i.v -

LIST OF ILLUSTRATIONS Figure Page 1, Folded-line structure o 80 o.... o p. 1 2, 100-watt S-band tube type S-182-A o *.. 13 3. Cross-sectional view of tube S-182-A. o o o o 4 4. Gun-end VSWR of S-182-A with the collector end terminated in a 50-ohm load o.. o.... 6 5. Gun-end VSWR of S-182-H2 with the collector end terminated in a 50-ohm load.,... o.... 6 6. Insertion loss of S-182-A and S-182-H2 with internal "pads" in place,.... ~...... 7 7o Tuning curves for tube S-182-A...... a... 8 8. Comparison of measured and theoretical phase velocities for the folded-line structure of S-182. 9 9. Power output of S-182-A for various beam currents. 11 10,. Power output of S-182-H2 for various beam currentso 11 11i Efficiency of tube S-182-A o.......a 12 12. Efficiency of tube S-182-H2 l..... o... 12 13. Oscilloscope tracing of the power output of S-182-H2 as a function of beam voltage, for several beam currents.0. o o * 0 0 o... 13 14, Starting current for tube S-182-A l. l..... 15 15, Starting current for tube S-182-H22.. l.. 15 16. Assembly drawing of tube S-1850. o a. o. 18 17. 100-watt S-band tube type S-185.... *. 19 18, Gun end bell,...0,... o 0 *. 21 19. Collector end bello o..... 0.. o o - 0 22 20. Construction of high-conductivity coaxial r-f seal, 23 21. R-f line center conductors.. a.. o. o 25 22. Gun-end match of tube S-185 o o.. o.... 26 23. Insertion loss of tube S-185, o,..o..,... 26 24, Electron gun for tube S-185 0 o *. 28 25o Collector parts drawings o, a...,o. 29 26, Assembly of collector 0 o, > n * * * 30 27. Construction of coaxial collector seal,o. 32 28. Complete collector subassembly........., 33 A-1. The folded-line structure showing the notation used for dimensions, 0 0 o *.. l a. a 0 37 A-2. Universal tuning curves for a folded-line BWO. o. 50 A-3, Relationship between dimensions and low-frequency cut-off for a folded-line structure., * o o o 51 A-4o The factor M for use in Eq. A-11...... 52 A-5. Space-charge parameter cq/co. a o 0 53 A-6. Starting length, efficiency, and operating voltage as a function of the space-charge parameter Wq/wC, for zero circuit loss. a o 0 o'.... 54 A-7. Reduction factor for efficiency.. *.0. * 55 A-8. Chart for computing starting currents.. a.. 56

LIST OF SYMBOLS Defining equation Symbol Definition or figure a hole radius Fig. A-I b velocity parameter (A-16) C gain parameter (A-6) (A-ll) Cl first approximation to C (A-21) c velocity of light = 3 x 108 meters/s D structure dimension F1 plasma frequency factor (A-15) F2 function relating starting CN and Fig. A-6 space-charge parameter h structure dimension Fig. A-1 I0 d-c beam current (amperes) I strt d-c beam current for startoscillation (amperes) In(x) modified Bessel function of the first kind, order n, argument x K tube constant (A-20) i interaction gap length Fig. A-1 L structure period Fig. A-1 M impedance reduction factor (A-7) Nstart number of start-oscillation beam (A-17) wavelengths P total r-f power transmitted on the circuit Q space-charge parameter (A-19) r beam radius R1 component of impedance reduction (A-8) factor due to variation of field across the beam - vi -

LIST OF SYMBOLS (Cont'd) Symbol Definition Defining equation or figure R plasma frequency reduction factor u0 d-c beam velocity V peak r-f voltage across the gaps V0 d-c beam voltage V_1 circuit" voltage corresponding to vl (A-2) v-l phase velocity of the first "backward" (A-l) mode on the circuit W structure dimension Fig, A-1 Z characteristic impedance of the line (A-5) (ohms) V-1 /lo D phase constant of the circuit (A-1) Be phase constant of the beam (A-10) ey radial propagation constant (A-9) efficiency Fig, A-6 "unadjusted" efficiency Fig. A-6 X0 free-space wavelength p dummy variable X) operating frequency (radians/sec) Uq reduced plasma frequency (radians/sec) (A-15) - vii -

PART l. —TUBE TYPE S-182 I. INTRODUCTION The tubes described in this part of the report are S-band backward-wave oscillators of the folded-line type with a nominal power output of 100 watts cw0 These oscillators were developed under Stanford Electronics Research Laboratory Project 182, and are designated generally as S-182, with additional letters and numerals indicating various modifications0 S-182 is a continuously pumped, demountable tube designed to permit easy modification of the structure and gun. Several versions of this tube were tried, two of which are described in this report. II. S-182 SPECIFICATIONS The basic structure of tube type S-182 is a folded-strip transmission line with an axial hole for the beam. Figure 1 shows the form of the structure and the notation used for dimensions. D D -WFIG. l. —Folded-line structure. The requirements for this tube were (1) a power output of 100 watts cw, (2) a tuning range from 2500 to 3500 MC, and (3) a beam voltage of about 3000 volts at the center frequency.

Using the design procedure given in Appendix A, the following dimensions for the tube structure were arrived at: L = 0o140 in, i = 0o080 in, h = o.600 in, W = 0~400 in, D = O0600 in. a = 0o063 in. Length = 6~ in. (active) Cathode diameter =.090 in, This version of the tube is designated S-182-Ao Figure 2 is a photograph of the tube, and Fig0 3 is a cross-sectional view showing some of the mechanical details0 All parts of the tube body are made from OFHC copper except the r-f line bead seals, which consist of Teflon, and the collector seal which utilizes ceramic. The gun is mounted inside the vacuum manifold, giving a large pump-out cross-section0 All joints are soft-soldered, or sealed with wax, Water-cooling is provided for the collector and on the tube body to protect the wax seals, A later version of this tube, designated S-182-H2, is identical with S-182-A except for the beam hole size, the tube length, and some minor modifications of the collector and the r-f matches0 For S-182-H2: a = 0o0938 in, Length = 5o5 in0 (active) Cathode diameter =.150 in. All other dimensions are the same as those given for type S-182-A

~'~'~.............. ~ z.......~........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........... ii~ i [~[11[ i ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1.......... ii~~~~iii!11:i;~iiii~~~~~~~~~~~~~~~~i~~~il~~- X:;!~i!; ii!!iiii~iii~iiiiFIG.i ~ 2!;;0- at S- a d tu e t p S 1 2

IIIo S-182 OPERATING CHARACTERISTICS A. MATCHES AND INSERTION LOSS The problem of matching from a 50-ohm coaxial line to the folded-line structure was solved by attaching the center conductor of the coaxial line to one of the "teeth" of the interdigital structure and providing a short-circuit a quarter of a wavelength beyond the junction. (See Fig. 3.) This type of match is very similar to that used for ridge-guide to coaxial lines. In addition, the center conductor of the coaxial line was tapered over a length of about two inches in an attempt to provide a gradual transition from the 50-ohm impedance of the coaxial line to the somewhat higher impedance of the structure. For satisfactory operation, the r-f match at the collector end of the tube should be as good as possible. If reflected energy from the load is re-reflected at the collector end, the resulting degenerative or regenerative feed-back will cause the output to vary rapidly with frequency. In order to improve the match at the collector ends some internal loss was added in the form of a carbon film on ceramic plates, placed next to the folded line for approximately the last two inches. The ceramic plates were cut at an angle to produce a gradual transition to the lossy region. The position of these "pads" can be seen in Fig. 3. Two plates were used in tube S-182-A, one on each side of the line, The surface resistivity of the carbon film was about 300 ohms per square0 In tube S-182-H2, only one plate was used, with a resistivity of about 500 ohms per square. Figures 4, 5, and 6 show the measured matches and insertion loss for both S-182-A and S-182-H2. Without the "pads", the insertion loss was less than 1 dbe - 5 _.

2.2 2.0 12 O_ 4.<C 2.4 2.6 2.8 3.0 3.2 3~ 4 3 f - kMC FIG. 4. —Gun-end VSWR of S-182-A with the collector end terminated in a 50-ohm loads 2.2 2. 0 1.8 1 o0, _,.......*.... —-. — 12 6 1., 2,~4 2.6 2~8 3~0 3.2 3~.4 f - kMC FIGo 5. —Gun-end VSWR of S-182-H2 with the collector end terminated in a 50-ohm load, - 6 -

16 14 Z 12 10 r-~ 8 6 4 _ _ -182-H2 2,4 2.,6 2o8 3~ 0 3~ 2 3.4 34 Frequency - kMC FIG. 6, —Insertion loss of S-182-A and S-182-H2 with internal "pads" in place. B. TUNING CURVES Figure 7 shows the tuning curves for tube S-182-A. The effect of beam current on frequency ("frequency pushing") is readily apparent. A comparison of the calculated and extrapolated zero-current curves shows that the simple picture of a wave following around the folded-line structure is somewhat in error. A better comparison between the theoretical and actual (extrapolated) propagation velocity is given by Fig. 8. For 7 -

1 I i ~I e- / oH X /, I v / ~ — Extrapolated >.. zezeroro current 1 X 0 _ _ _ _ -_ _- zero current 2)4 2~6 2o8 3.0 3o2 304 3~6 f - kMC FIG. 7. —Tuning curves for tube S-182-A, Note the large "frequency pushing" effect. - 8 -

a- Measured 0.2 heoretical v p c 0.1 2.4 2.6 2.8 3~ 0 3.2 3.4 Frequency - kMC FIG. 8o —Comparison of measured and theoretical phase velocities for the folded-line structure of S-182o this figure, the "fundamental" phase velocity of the wave is defined by: v Period length 2w c Free-space wavelength e where c is the velocity of light, and e is the phase shift per period neglecting the 180~-shift introduced by the fold in the line. If the wave followed the folded line exactly, the "geometric" ratio of the phase velocity to the velocity of light would be vp/c = L/(L + h). Figure 8 indicates that the actual phase velocity is greater than the "geometric" value by about 5 to 15 per cent, The tuning curves for tube S-182-H2 were essentially the same as those for S-182-A, except for a narrow "hole" at -9

2975 MCo This discontinuity was traced to a resonance in the pumping manifold~ The enlarged beam hole was apparently responsible for the coupling between the manifold and the structure. Presumably, such a coupled resonance could be eliminated by proper design. Co POWER OUTPUT AND EFFICIENCY The power output and efficiency of tubes S-182-A and S-182-H2 are shown in Figs. 9 to 12,inclusiveo The theoretical efficiency curves shown are based on the theory developed 1 by Ro W. Growl The results of this theory which apply to the folded-line type of tube are presented in Appendix Ao The agreement between the theoretical and measured efficiencies is very good, considering the fact that the effective size of the beam is not accurately known. Figure 13 shows an oscilloscope tracing of the power output of S-182-H2 as indicated by a crystal detector, while sweeping the beam voltage at 60 cps over the entire tuning range~ The response of the crystal detector was flat within ~ 05 db over the frequency range of interest. The rapid changes of power output with frequency near the high-voltage end of the range can be correlated with mismatches in the tube0 (See Fig, 5.) In other respects, the power output appears to be fairly smooth, The beam current is not exactly constant for the curves shown since the current depends to a small extent on the voltage, but the total current variation from one end of the range to the other is less than 10 per cent0 As seen from the curves, the efficiency of S-182-A is higher than that of S-182-H2, This higher efficiency is the result of the greater beam current density used in S-182-A (7a/cm2. as compared to 265a/cm2 used in S-182-H2)o In order Superscript numerals refer to the List of References that appears at the end of the report~ 10 -

-P IM 1 lefr euencsI 300 m Multiple frequencies 0 100 observed in this region cies5 50 ~ 10 2.4 2.6 2.8 3.0 3.2 3.4 3.6 f - kMC FIG. 9. —Power output of S-182-A for various beam currents. An axial magnetic field of 1800 gauss was needed for high beam currents. Mulitiple -P frequencies 0 2 50..,i, Is ~\~~ ~_____...... 2~,4 2.6 2.8 3.0 3~2 3.4 3.6 FIG. l0o —Power output of S-182-H2 for various beam currents. Focus field = 1250 gauss. - 11 -

C 2)i4 206 2a8 3C4300 ma re quency - k...C FIGO 1Io —Efficiency of tube S-182-Ao [ Theoretical I^ = 300 ma __ C)0 *rH 2,,4 2,6 2.8 3.0 352 3.4 3.6 Frequency - kMC FIG I2l, —Efficiency of tube S-182-H20 12 - 4-' D _~~ — I- 300 ma 12

100 I ~ 300 ma-/ Power output 200 (watts 2 3 4 5 6 Beam voltage - kv FIG. 13o —Oscilloscope tracing of the power output of tube S-182-H2 as a function of beam voltage, for several beam currents. Compare with Fig. 10. - 13 -

to obtain good tube life at the higher current density, a convergent-flow gun might have to be used; this is one possible disadvantage of this type of operation. (In the experimental tubes, life was not important, so confined-flow guns were used.) Do STARTING CURRENTS Figures 14 and 15 show the start-oscillation current as a function of frequency for S-182-A and S-182-H2, respectively, Again, the agreement with theory is fairly good, considering that the active lengths of the tubes are not accurately known owing to the presence of the internal attenuators~ Eo SPURIOUS OUTPUTS As shown by Figo 9, multiple frequencies were observed at the low-frequency end of the tuning range in tube S-182-Ao Under the worst conditions, as many as ten extra frequencies were observed in the output0 These frequencies were spaced at about 50 MC-intervals on either side of the normal operating frequency. The strengths of these extra outputs increased rapidly with increasing beam current, the strongest reaching an output level perhaps 5 - 10 db below the main output, in some cases. One explanation for these multiple outputs is that higherorder solutions of the equations describing the startoscillation conditions are possible if the value of CN is large enough. (See Reference 2~) These solutions indicate that, for a given beam voltage, the frequency of a higher-order oscillation would be slightly lower than the normal operating frequency0 Since a backward-wave oscillator is not "saturated" in the usual sense, it also appears possible that the tube could oscillate on two frequencies at the same time. The presence of more than two frequencies in the output has been explained by Johnson3 as being the result of intermodulation effects in the beamo - 14 -

30 Measured 20 C6 1 I` Theoretical 10 2.4 2,6 2.8 3.0 3.2 3.4 3.6 Frequency - kMC FIG., 14 —Starting current for tube S-182-Ao 60 20. 0Cd~ ~Measured 2~4 2.6 2.8 3~0 3.2 3.4 3~ 6 Frequency - kMC FIG, 1i5 —Starting current for tube S-182-H2, - 15 -

As was expected9 multiple frequencies did not appear in tube S-182-H29 except at the very highest perveances. The shorter length (5-1/2 in6 as compared to 6-1/2 in, for S-182-A) made the starting current for the spurious oscillations higher than the normal operating current of 300 mat IV CONCLUSIONS It appears that the performance of the folded-line type of BWO can be satisfactorily predicted from the usual theory of BWO operation, both as to tuning range and efficiency. In addition, the essentially all-metal construction of this type of tube provides good heat transfer away from the interaction circuit, thus minimizing the problem of heat dissipation in a high-power tube. The circuit is relatively large, and scaling according to wavelength should be possible, with the power output varying as h\ for constant beam current density. - 16 -

PART 2o —TUBE TYPE S-185 Io INTRODUCTION This part of the report will be chiefly concerned with a description of some of the techniques used in the construction of tube S-185, the designation given to the sealed-off version of the S-182 demountable tube described previously. A photograph of the tube is shown in Fig. 17, and Fig. 16 is an assembly drawing which shows most of the mechanical details of the tube, The general specifications of tube S-182 were used except that the length of the interaction structure was shortened to approximately 6 inches to eliminate some spurious frequencies at the low end of the tuning range, The hole for the beam was 0o120 in, Mechanical design changes were limited to those made necessary by the more rigorous processing schedule of sealed-off tubes, In general, these changes involved the substitution of high-temperature brazing alloys for soft solder, and the use of glass instead of Teflon for insulated vacuum seals, II. SUB-ASSEMBLIES A. BLOCKS AND END BELLS The construction of the blocks was straightforward except for the problem of producing the longs straight hole for the beam. In the demountable tube, as in similar tubes previously built here, the hole was made by first milling semi-circular grooves in two blocks of OFHC copper. The blocks were then silver-plated, clamped together around an oxidized stainless steel mandrel and brazed together in a hydrogen furnace. After removing the mandrel, the r-f structure could be milled out. - 17 -

a AI-~L 80kTS USELD IN AS,~N- l- TILS TLE L~ O 4- LEADS, TUNG~STEN (2.040 DIA tKOVAR~.I~~~;TE 1AICOSL /57 - BRAZING ALLOY —-ll~U-~j /~i/DDN T/S( GU/N AfO(,IITIIV CYLINDER VACUUM TU,8lLA7'0, —--- G UN-E~ND PI A rE A FIG, 16. —A S5EMBL) RWN OF TU5EE S - 185. CNECORSPPR 0 15Y ~ ~ S J NG-~ \ (PUAFT7- POAD T17Y

: 0 An J ~~~~~~~~~~~~~eisrr:~e.:;: ~::I::I':.::.~l:~::~i::: i::: A::E:.:::: z FIG. 17o —100-watt S-band tube type S-185o

The blocks for this tube were made in essentially the same manner, except that gold-plating was used, chiefly because it was thus possible to assemble the rest of the tube by using the silver-plating technique. In addition, since the mandrels had always been difficult to remove, only two short sections of ceramic rod were used at the ends of the blocks to align the section during the brazing operation. These end plugs were cuit off during subsequent machining operations. The plating thickness of the gold was 0.0005 in., and the furnace temperature was raised until the brazing material flowed at about 9500Cr It was convenient to preassemble the end bells for the tube. These subassemblies, shown in Figs. 18 and 19, consisted of an end plate and a mounting cylinder for the collector end of the tube, and an end plate, mounting cylinder, and the vacuum tubulation, for the gun end of the tube. The brazing of these parts was carried out in a straightforward manner in a hydrogen atmosphere using copper-gold alloy (Cu-62.5, Au-37X5). Be R-F LINES AND SEALS The vacuum seals for the r-f lines were designed so as to introduce as little discontinuity as possible when placed in a standard 3/8-ins coaxial line using standard type-N fittings. The glass dielectric was made as thin as possible (less than 0ol wavelength), and the size of the center conductor was chosen to produce a constant-impedance lineo Since the power level to be transmitted at the gun end of the tube was relatively high (approaching 100 w), it was necessary to have a bead assembly with very low losso Such beads were constructed following a procedure described by Turnbull,9 The Kovar parts were first copper-plated to produce high conductivity, and then given a flash coating of chromium which was oxidized, leaving a surface suitable for the glass-sealing operation. The steps in the process are enumerated in Fig, 20. - 20 -

Braze with copper-gold FIG. 18. —Gun end be ll

Copper-gold braze FIGo 190 —Collector end bello

.o100".025H - T Z//////////,'//,Z"g -KOVAR SLEEVE 0_ Ln L O,- 0.060" KOVAR --.600 -- 1. Polish rod and inside of sleeve. 2. Clean and degrease. O. Fire in wet H2 at 1000~C for 20 minutes. 44 Copper-plate all surfaces, 0.001 in, thick. 5o Fire in H2 to check plating at 900~C for 15 minuteso 6. Chromium-plate only areas to be glassed, 0,00005-0,0001 in. thick, 7, Fire in dry H2 (-50~C dewpoint) at 9500C for 10 minuteso 8. Fire in wet H2 to oxidize the chromium at 9000~C for 10 minutes. 9. Glass center rod with sufficient glass (7052) to make the entire beado 10, Assemble the two parts in a glass lathe, using shaped graphite mandrels, one to hold the sleeve and rod in the correct position, the second to apply pressure to the glass to make a flat bead, The resulting bead should be clear and free from bubbles, and the oxide color should be dark green. The quality of the bead can be checked by firing it in hydrogen at the temperature that will be used in a subsequent brazing operation, A good bead will be unchanged after this treatment, but any small bubbles present that escaped visual detection will become noticeable through their growth in size, sometimes to the point of producing a hole through the bead~ FIGo 20, —Construction of high-conductivity coaxial r-f seal, - 23 -

Tests made on seals constructed according to this procedure indicated that they would carry 100-150 w cw, at 3,000 MC without noticeable heating. The two parts comprising each of the r-f line center conductors were brazed together using Nioro foil brazing alloy with a hydrogen-oxygen torch supplying the heat. A simple brass jig was used to hold the two parts in the proper position during the operation. After brazing, a 00050-ino hole was drilled into each line at the corner, as shown in Fig. 21. The quartz rods that were fitted into these holes during final assembly were necessary to hold the center conductors while the coaxial seals were being placed on the r-f line. Although satisfactory matches were obtained in the demountable tube by simply tapering the r-f lines in size and impedance between the structure and standard 3/8-ino lines, the combination of the glass dielectric in the seals and the quartz support rods in the S-185 tube degraded the matches considerably, and it was necessary to modify the center conductors. Because the two lines were of different lengths, different matching techniques were used, as indicated in Fig. 21. The resulting gun-end VSWR with the internal termination is shown in Fig. 22. The insertion loss of the tube is shown in Figo 23, and since the loss of the structure itself is less than 1 db, the loss is that of the coated ceramic plates used as the internal termination, as described in connection with the demountable tubeo C0 ELECTRON GUN The electron gun used in the S-185 tube was a standard laboratory item having an L-cathode 0.090 in. in diameter. The guns were originally designed to mount in 1-1/4 inch (Au:17,5, Ni:8245) Proprietary alloy of the Western Gold and Platinum Works, San Francisco0 - 24 -

No, 55 drill 3/32" deep Brazed with Nioro foil Gun end No. 55 drill 3/32" deep Brazed with Nioro foil Collector end FIGo 21 —R-f line center conductors0

2.4 2~6 2~8 300 3~2 3.4 3,6 Frequency - kMC FIG, 220 —Gun-end match of tube S-1850 60 co 40 i- 20 - t C I 2,4 2;6 2,8 3150 3,2 3.4 3. 6 Frequency - kMC FIGo 23. —Insertion loss of tube S-185. - 26 -

precision-bore glass using a three point suspension system made up of two ceramic "dumb bells" and a spring. Since the S-185 tube is of all-metal construction it was necessary to modify the mounting arrangement to permit use of larger insulators between the gun and its mounting cylinder, and to insulate the spring. The mounting arrangement used is shown in the assembly drawing of tube, Fig. 16. A drawing of the gun is shown in Fig. 24. Although the maximum current density requirements for this tube were very high (approximately 6 a/cm2), tests made with a diode using one of these guns indicated that a life of about 100 hours could be obtained. Do COLLECTOR ASSEMBLY Although the collector used in the S-182 tube performed satisfactorily, its construction required that water be supplied to it at a relatively high pressure to produce sufficient flow. A new water jacket was designed that reduced the input pressure requirement and was, in addition, easier to construct. Collector drawings are shown in Fig. 25. Assembly of the collector involved a step-brazing procedure which is outlined in Fig. 26o In order to reduce the overall tube length to a minimum, and because the voltage insulation requirements were moderate (approximately 200 v) a coaxial Kovar-glass seal was developed for use at the collector. The seal assembly, as finally used, is compact and rugged; since the techniques used in its construction were new to this laboratory, they will be described here. The powdered glass used for this seal is prepared in the following way: 1o Corning 7052 glass was ground to pass through a 20-mesh and collect on a 30-mesh sieve. 2. The powdered glass was boiled in dilute hydrochloric acid to remove iron contamination. (The only ball mill - 27 -

' FIG. 2IElcr gun.......be S 1,'~~~~~\i CO~~~~~~~/''T' ~ ~ ~, FIG. 2~o —Electron gun for tube S-185.

Part 1 1 required Part 2 1 required I-EI Part 3 2 r equired Part 2 Part 4 1 required Part 4 1 re quired FIG. 25o —Collector parts drawings. - 29 -

Part 4 ~~~Parts 3! Part 1- Part 2 Nicoro strips Nicoro ring Step 4) Nioro ring A (Step 4) B A Nicoro ring Section A-A tep 2 (Step 4) Section B-B Assembly Procedure 1i. Assemble Parts 1, 2, and 3. The free ends of the vanes, Parts 35 may be held during brazing with wire. 2, Braze in H2 using Nicoro alloy. 3. Shape outer edges of vanes so jacket, Part 4, can be placed in position, 4. Braze in H2 using Nicoro alloy. 5. Counterbore 1/4" holes for water lines. 6o Insert water lines (each about 1" of 1/4" copper tubing). 7o Braze with Nioro alloy. Proprietary alloy of Western Gold and Platinum Works, San Francisco. (Au:359 Ni:300, Bal.Cu)e FIGo 260 —Assembly of collector, - 30 -

available for the grinding was constructed of iron. The use of a porcelain ball mill would eliminate the contamination that results ) 3. The glass was washed thoroughly with distilled water with a final rinse in acetone. 4, The powdered glass was dried in hot air. After this preparation, the powdered glass apparently could be stored for some time in a covered container. Just prior to use, the glass was treated according to the following schedule: 1o The glass was washed in dilute hydrofluoric acid (50 per cent by volume) 2. The glass was washed in distilled water with a final rinse in acetone. 3. The glass was dried in hot air. 4, The glass was transferred immediately to the jig assembly. After machining and polishing, the Kovar sleeves were cleaned, degreased, and fired in wet hydrogen at 10000C for 20 minutes, following normal procedures, The sleeves were then oxidized at 8000C for 20 minutes in air, In the experiments conducted here the oxidation was accomplished by using a gas-oxygen flame with the work rotating in a lathe. Since the quality of the finished seal is a function of the amount of oxide on the sleeve, more consistent results could be achieved by oxidizing the sleeves in a temperature-controlled oven as described by PaskO 1 After the oxidation, the sleeves were transferred immediately to a graphite jig, as shown in Fig, 27. In order to produce a bead of sufficient thickness in this configuration, it was found necessary to completely fill the space between the sleeves with powdered glass. The whole assembly was heated in a nitrogen atmosphere at 975~C for ten minutes. The furnace was cooled at a rate of about 200C per minute, held at 450~C for ten minutes, and then allowed to cool to room temperatures - 31 -

Kovar sleeves Powdered glass or Graphite jig FIG. 27o —Construction of coaxial collector sealo The glass in the resulting seal was clear, and the Kovarglass interface had the normal gray color. The oxide was removed from the Kovar by electrolyzing the assembly in 20percent hydrochloric acid, after which a flash plating of copper was applied to the sleeves. The brazing of the seal to the collector and to the collector mounting flange was accomplished with the aid of a simple cylindrical graphite jig which served to support the three pieces in the proper position, without force, other than its own weight, being applied to the glass~ This precaution was necessary to prevent deformation in the glass since the brazing temperature was near the softening point of the glass. The brazing alloy used was silver-copper eutectic, and the assembly was heated for approximately five minutes, or until the alloy flowed, in a hydrogen atmosphere at 8000~Co The furnace was again cooled slowly to prevent strain formation in the glass0 The completed collector assembly is shown in Figo 280 - 32 -

Silver-copper eutectic ///~~~~~-1777771/1/ \ i 77 ZZ=\ _V \ 77777~i - FIG. 28. —Complete collector subassembly.

IIIo TUBE ASSEMBLY Construction of the tube was simplified by the use of step-brazing processes which made possible the elimination of several complicated jigs that would have been necessary if all the tube parts had been assembled in one operation. After the subassemblies described in the previous section were completed, the mating surfaces of the blocks, side plates, end bells, and r-f lines were silver-plated to a thickness of 0~0003 ino The parts were then assembled and bolted together, using stainless steel bolts. The ends of the center conductors of the r-f lines were held on their axes by simple cylindrical ceramic jigsa The whole assembly was heated in a hydrogen furnace at a temperature of about 8000~C until the brazing alloy flowed. The brazing alloy in this operation is silver-copper eutectic~ a thin interface layer of which is formed during the plating process, After this assembly was leak-checked, the r-f beads were mounted at the ends of the r-f lines. A ring of 0.020 ino TAW (tantalum-tungsten alloy) was placed at the end of the slotted center conductor to insure good contact between it and the center conductor of the bead assembly. The brazing alloy used was Incosil 15 formed into a ring and placed adjacent to the joint in the outer conductor0 A graphite jig was used to maintain alignment of the conductor of the bead during the brazing operation, since the flow point of the alloy is near the softening point of the glass, The tube was heated in hydrogen at about 7000~C until the brazing alloy flowed. Cooling was done at a slow rate to prevent the formation of strains in the glass sealso The ceramic loading plates, coated with "Aquadag" to a resistivity of about 300 ohms per square, were then installed,. Proprietary alloy of the Western Gold and Platinum Works, San Francisco g(Cu:24; In:15; Bal:Ag) 34 -

and the r-f matches were checked. After determining that the matches and insertion loss characteristics were satisfactory, the collector was installedo The graphite jigs were again used on the r-f seals, and another such jig was used at the collector to take some of the weight of the collector off of the glass seal. Incosil 15 formed into a ring was again used as a brazing filler metal, and the tube was heated to about 700 C in hydrogen, If it were not necessary to check the matches and insertion loss, the collector and r-f seals could be installed in one operation. The final seal on the tube was made at the gun end. After the gun and stem assembly was in position, the tube was mounted vertically in a hydrogen bell jar. A ring heater inside the copper cup holding the stem was used to heat the joint to the flow point of Incosil 15 alloy, which was placed as a ring adjacent to the joint, The gun-end r-f line and the glass in the stem assembly were protected by heat-shields during this operation. IV PROCESSING Except in a few details, the processing of the 185 tube was carried out in the same manner as for any other tube. Since the tube is constructed almost entirely of copper, it was desirable to prevent, or at least retard, heavy oxidation of the tube during bake-out, Therefore, the tube was wrapped with aluminum foil, and a forming-gas line was introduced into this package. During bake-out an atmosphere of forming gas (5 per cent hydrogen, 95 per cent nitrogen) was maintained around the tube. A flow rate of about 10 cubic feet per hour was used. This procedure resulted in negligible oxidation of the tube surfaces. The tube was baked for about eight hours at 400~C. The tube was connected to the glass manifold of the pumping station by means of a Kovar-glass seal, with a spare getter

placed in the glass part of the tubulation. After activation of the cathode, which followed normal procedure for L-cathodes, the tube was operated with a magnetic field in order to clean up the collector and parts of the r-f structure by electron bombardment s The tube was sealed off in the glass part of the vacuum tubulation for several reasons. First, this procedure avoided the necessity for replacing the copper tubulation in case gun difficulties developed in the first few hours of operation~ Also the getter which was placed inside the glass part of the tubulation gave a rough qualitative indication of vacuum conditions inside the tube. Finally, although a pinch off would be made in the copper tubulation if the tube performed satisfactorily. an operation of this kind with the tube connected to a glass manifold would be somewhat hazardous, - 36 -

APPENDIX A: DESIGN OF FOLDED-LINE BACKWARD-WAVE OSCILLATORS The basic structure considered in this analysis can be thought of as either an "interdigital" structure or a foldedstrip transmission line. Since the latter concept has some advantages with regard to visualization of the interaction process, the "folded-line" designation is preferred. Figure A-1 shows the basic form of the structure and the notation used for dimensions. the notation used for dimensions of Ii' wave h D -I'I- W a FIG, A-l,, —The folded-line structure showing the notation used for dimensions. In the following analysis, certain simplifying assumptions are made as follows: (1) The operating frequency is far enough - 57 -

from any cut-off value so that the presence of side walls and periodic discontinuities owing to the bends has negligible effect on both the impedance of the structure and the velocity of the wave~ The analysis is still valid for other cases, provided the proper values of impedance and velocity are used in the equations. (2) The value of the electric field at the edge of the hole is the same as that which would obtain with no hole (or a gridded hole)o In cases where this assumption is obviously in error, a suitable adjustment can be made in the impedance, and the analysis carried out as before. If the diameter of the hole is not greater than one-third the smallest dimension of a "tooth'l faceP the above-stated condition probably holds very wello (3) The value of the gain parameter C is small (less than 0ol)o This limitation is probably not too important since it is difficult to produce large values of C in microwave tubes which use space-harmonic structures. It should be noted at the outset that the design of a backward-wave oscillator cannot be carried out in a straightforward manner. but requires several trials to bring all of the factors involved into agreemento For example, for a given frequency and voltage range. the power output may be insufficient due to limitations of beam perveance or beam density, necessitating a change in the choice of beam voltage0 Again, since the efficiency of the tube is not known in advance, the beam current required to produce a certain power output may require a beam diameter which is incompatible with the size of the structure initially choseno In the design procedure presented here9 reasonable estimates (based on experience) of some of the unknown quantities are presented in order to shorten the trial-and-error process0 1. STRUCTURE DESIGNO The first step in the design is the choice of structure dimensions0 The relationship between structure dimensions and operating frequency and voltage can be obtained by noting that the beam velocity must be near the phase velocity of the first backward-wave space-harmonic of

the circuit. If it is assumed that the r-f wave follows around the folds of the line with the velocity of light (experience indicates that this assumption is reasonable except near cutoff frequencies), the phase constant D of the desired backwardwave mode is given by a) 2vx frequency v - velocity of first backward-wave mode 2w -- (1 + h/L) - 7/L (A-l) 0 where A is the free-space wavelength and the other quantities 0 are defined in Fig. A-i, (For detailed derivation of Eq. (A-1), see reference 4). A corresponding "circuit" voltage V 1 can be defined as the accelerating voltage of an electron traveling at the backward-wave phase velocity: -1 - - - = - -- (A-2) 256,000 c ho where c is the velocity of light. Substituting for B, 1012 2 -1.. (A-3) V - 2(1 + h/L) Equation (A-3) is plotted in Fig. A-2 for various values of h/L, For a given value of V_1 (which will be less than the actual operating voltage Vo by perhaps 2 - 20 per cent), the value of L/Ao can be read off directly and the dimension L determined, Since L/Co is proportional to frequency for a fixed L, the complete tuning curve of a given structure can also be found from Fig. A-2. Of course, the particular tuning curve 39 -

will depend on the choice of h/La and here some judgment is needed0 As shown by the curves of Fig. A-2, small values of h/L result in a minimum voltage range to cover a given frequency range. However, considerations of line size and proportions including the need for a suitable hole for the beam and a reasonable value of characteristic impedance, limit the practical values of h/L to something greater than 2. A fairly good starting value is h/L = 3, but several trials may be needed to determine the best value for the desired beam size and voltage and frequency range, An upper limit to the value of h/L is imposed by the highfrequency cut-off of the structureo Owing to reflections from the corners. a high-frequency cut-off will occur at a frequency somewhat lower than that for which the distance between corners is one-half wavelength. If, in additions the teeth are not perfectly spaced but have alternate wide and narrow gaps between them, a stop band may occur at half the above frequency0 This limits the sum of h and L to about a quarter wavelength, or L (1 + h/L) < 1/4 (A-4) This limit is indicated by the dashed line of Fig~ A-2. Having determined L and h, the remaining dimensions R, W, D, and the tube length must be chosen. in general, the gap length ~ is made as large as possible consistent with mechanical and heat conduction requirements of the teeth. The width W, together with ~, determines the characteristic impedance Z0 of the line for matching purposes: Z 377 (A-5) Zo 377 W + - In Eq. (A-5), the effective line width W + ~ is used instead of W to account for fringing fields at the edges of the teeth0 This approximation appears to be in good agreement - 4o -

with observed results, For best matching into 50-ohm coaxial lines, W should be about 6,5 ~, but higher values of Zo pan be used, If W is less than 3 ~, the folded-line approximations probably do not apply too well; The distance to the side wall D determines the lowfrequency cut-off of the structure, and should be chosen so that the lowest operating frequency is at least 50 per cent higher than this cut-off. The low-frequency cut-off is approximately that frequency for which the inductance per unit length of the side section resonates with the capacitance per unit length of the teeth, The plot shown in Fig. A-3 can be used to determine the dimension D for a given cut-off frequency.2 CALCULATION OF C., In order to determine the length of the structure and the power output, it is necessary to evaluate the gain parameter C. Using the analysis and notation of Pierce,5 C is given by the following expression: (for a complete derivation, see reference 4) V2 M2 I C3 = (A-6) 8Vo rL)2 P where V is the peak circuit voltage appearing across the interaction gaps at the edge of the hole for a given total transmitted power P, Vo and Io are d-c beam voltage and current, respectively, and the phase constant P is given by Eq. (A-1). The factor M in Eqo (A-6) is a "gap coefficient" which takes into account the reduction in effectivenss of the r-f field on account of both the transit time of the electrons across the gap and the fact that the r-f field is not uniform over the cross-section of the beam. sin -f N 2 I (A-7) - 41 -

where R1 is a reduction factor computed by averaging V2 over the beam cross-section. (See reference 6). r1 2 R1 2 I2ya) pdp 0 I2(r) - (r) (A-8) = 0 1 (A-8) I2(ya) where I~ and I1 are modified Bessel functions and y is given by =2 - (/c)2 (A-9) (For slow waves, y is approximately equal to Bo) The factor M can be expressed as a function of i, y, o the beam radius r, and the ratio of the beam radius to hole radius, a. If it is assumed that y - P, values of M can be obtained from Fig. A-4. Enter the chart of Fig. A-4 with values of V_1 as determined from Fig. A-2, project both ways to the proper values of r/o/ and ~/o0 given on the diagonal lines, project up to the curves and then toward the center to the reference lines, The value of M is read from the alignment chart at top center, The value of 8r, as given in the lefthand section, should be noted for use in later computations. Equation (A-6) may be put into a more useful form if it is assumed that V2/2P is the ordinary characteristic impedance of a strip transmission line as given by Eq. (A-5). This approximation should be very good for W > 3Io Then, if a beam propagation constant e is defined as w 2w 506 e = =- (A-10) Uo u Vo A0 - 42 -

where u0 is the d-c beam velocity, the expression for C can be put into the form: 3 2,47xlO-8Z M2(b/) 21 l) o = (A-11) (L/o0)2 All of the factors of Eqo (A-ll) can be found from Eqs0 (A-3), (A-5), (A-7), and the circuit dimensions (or the appropriate charts) except be/B. Since Pe/B seldom exceeds 115, except for very high power tubes, this factor can be considered to be unity initially, and a correction made later if desired, 3o SPACE-CHARGE EFFECTS. For most practical tubes, space-charge effects are important in determining the required tube length, the power output, and the shift in operating frequency with beam current (frequency pushing). The evaluation of space-charge effects presented here is based on the work of Harman7 and Grow,1 For purposes of this analysis, the space-charge parameter wq/c appears to be more natural than the usual QC of Pierce. The relationship between the two is given by 4QC qA (A-12) In Eq. (A-12), Uq is the reduced electron plasma radian frequency, X is the operating radian frequency, and C is the gain parameter given by EqO (A-11) In terms of the beam and circuit parameters, fq = 7~96xlO10(Io )1/2 R ((rr/a) 7,,,.96xl 430 W(A-13)

where R is a plasma frequency reduction factor depending on the beam and circuit parameters1,7 Equation (A-13) is not convenient for computation because of the dependence of the operating beam voltage (or uo) on LUq For large values of Uq/w, (large space-charge), the ratio of beam velocity to circuit velocity is approximately equal to 1 + q/Ao (see reference 7)o Using this relationship and Eq. (A-2), the relationship between q/t and the beam and circuit constants can be expressed as 1 + 3O03xlO F(rr/a) (A-14) --! + = 3o03Xi0 V31/2 F1 where R2 F1 = (A-15) (ar) The function Fl(pr,r/a) is plotted in Fig. A-5 together with an alignment chart for determining w q/w. The values of hr for use in Fig0 A-5 can be found from the left-hand side of Fig~ A-40 42 OPERATING VOLTAGE. The actual operating voltage corresponding to a circuit voltage V_ 1 can be obtained by using the value of the velocity parameter b, plotted in Fig. A2 260 V- ( =\ )2~ = (1 + bC)2 (A-16) V-1 e This relationship is also presented in the alignment charts of Figs A-60 Having obtained an estimate of Vo/V 1s the tuning curves can be recalculated, if necessary, and some adjustment made - 44 -

in the structure dimensions if a particular operating voltage is desired, If the value of wq/w as found from Fig. A-5 is greater than 0.05, the value of C should be corrected also, and the entire design rechecked for the new value of C. The operating voltage does not depend on circuit loss to any great extent 5. TUBE LENGTHo The necessary length of interaction structure can be estimated from the values of CNstart' plotted in Fig. A-60 The quantity Nstart is defined as the number of beam wavelengths necessary to start oscillation at the value of C being used. The start-oscillation length is related to Nstart by 2wN A Jfv N start _ o 0 start (A-17) Lengths (A-17) He 506 The right-hand side of Fig., A-6 is an alignment chart for finding the starting length in terms of free-space wavelength, from appropriate values of CNstart" C. and Voo Experience indicates that the actual active length of the tube should be from 185 to 2 times the starting length, low-power tubes being in general relatively longer than high-power tubes. If an internal termination is used at the collector end, additional length will be needed. For moderate circuit loss (up to 15 db or so), the indicated length should be multiplied by a factor 1 + (db loss)/45. 6o EFFICIENCY AND POWER OUTPUT., The best available estimate of backward-wave oscillator efficiency is that presented by Grow. The theoretical relationship between efficiency and the space-charge parameter w q/, as presented in Fig. A-6, seems to predict the power output of practical tubes quite accurately8 The "unadjusted." efficiency o0 can be found from Fig, A-6 by multiplying the plotted value of %o/C by C. This can be done with the aid of the alignment chart at the left-hand side of Fig, A-6o The actual tube efficiency r is - 45 -

found by multiplying To by a reduction factor depending on Pr, This reduction factor is plotted in Fig. A-7 and is also incorporated in the alignment chart of Fig. A-6* The power output is given by the product of efficiency and d-c beam power. For a fixed frequency, the power output varies approximately as the 3/2 power of beam current for large space-charge conditions ( q/c > 1,5C), or as the 4/3 power of beam current for small space-charge conditions. The presence of circuit losses will reduce the power output from the value above. For moderate circuit losses, the reduction in db will be approximately one-half the circuit loss in db. When designing a tube for a particular power output, limitations imposed by permissible cathode current density and maximum beam perveance should be kept in mind. 7, CALCULATION OF STARTING CURRENT. One of the parameters of a BWO0 which is of some interest, is the starting current, or the beam current at which oscillations just begin. For a structure of given dimensions, the starting current can be calculated from Eqso (A-11), (A-16), (A-17), and the values of CNstart given in Fig, A-60 This may be a tedious process, however, because of the dependence of both C and N on V, which in turn depends on C and b. For purposes of computing starting currents, it is convenient to redefine all quantities in terms of parameters which do not depend on beam current. A space-charge parameter Q can be calculated from circuit constants alone, as follows: = aQ = -) (A-18) Using Eqs. (A-ll), (A-13) and (A-15), 7-55xl03F1 Q 1 (A-l9) K -i - 46 -

where F1 is found from Figs A-5, V_1 is given by Eq. (A-3), and 2o47xlO- z M2 K = (A-20) (L/o ) 2 It is also necessary to have a first approximation to C, given by C= KI~ (A-21) and a "circuit" N, or the number of wavelengths on the cold circuit: 506 length\ (A-22) From the known relationships between CN, Q/N, and a at start-oscillation 7 a new set of relationships between C1, Nc and Q can be derived (for the no-loss case) such that the starting current can be solved for explicitly. The plot of Fig.) A-8 shows Ci(start) as a function of Q with Nc as a parameter. The starting current is obtained from Cl(start) by use of Eq,. (A-21). For moderate circuit losses, the starting currents will be increased approximately by a factor ( loss in db)3 8, EXAMPLE. The following sample calculations taken from the design of Stanford Tube Type S-182-A are presented to illustrate the use of the design procedure. The requirements of this tube were: tuning range: 2500 to 3500 MC power outputs 100 w cw (I) Structure design. The structure design depends largely on the beam voltage, which in turn is determined by the probable efficiency and maximunLm obtainable beam perveance, - 47 -

or current density~ For Tube S-182-A, a beam voltage of about 3000 v at 3 kMC was desired because of available guns and power supplies. From Fig. A-2, the value of L/~o for this voltage and frequency is 0.035 for h/L = 4, or L = 0,138 ino, h = 06550 in. For simplicity, L was actually made 0.140 in. and h = 0.600 ino For mechanical reasons, the teeth were made 0.060 in. thick, leaving - = 0.080 in. For a line impedance of about 65 ohms, a width W = 0.385 in. was needed, the actual value used being W = 0,400 in. The transverse dimension D was made 0.600 in. corresponding to a low-frequency cutoff of 840 MC. (A smaller value of D could have been used4) The electron gun for this tube had a cathode diameter of 0.090 in,, so the hole diameter was made 0.125 in. (2) Calculation of C. From the dimensions given above, the following quantities can be computed: L/? = 0.0356 h/L = 4.3 / — = 0.0204 r/? = 0o0114 r/a = 0.72 Z = 63 ohms From Eqo (A-3) or Fig. A-29 V_1 = 3350 v. (The voltage tuning range is 2100 to 5650 v and the highest frequency is below the possible high-frequency cutoff indicated in Fig, A-2.) From Eqso (A-2)9 (A-7) and (A-8) or Fig. A-4, the following values are found: Pr 0o625 g = 11o M = o.835 Using these values, C1 (first approximation neglecting variation with beam voltage) is found to be 0.098 I1/3 At an estimated 10-percent efficiency, a beam current of 300 ma would be needed, making C1 = 0.0655. - 48 -

(3) Space-charge parameter., From Fig. A-5, wq/w is found to be 0 108 making q/oC - 165 (first approximation). (4) Operating voltage. From Fig. A-6, Vo/Vi 124 or V0 = 4150 v, This ratio of operating to circuit voltage is not negligible in computing C, so a second approximation gives 0o0655 C =1/3 0,o61 q 1j7 9"q-!77 WC _l 1,s24 = 4150 v (5) Tube length, From Fig. A-6, the starting value of N is 7.69 which for an operating voltage of 4150 v corresponds to a length of 0,965 wavelengths., This value makes the starting length 3.8 in,. or the minimum operating length 1 5 x 3.8 - 5 in7 n. (Actually, the minimum length should be computed at the high-frequency end of the range, since the tube is electrically shortest there., The actual tube was made approximately 6-1/2 in. long,) (6) Efficiency and power output, From Fig. A-6, the "unadjusted" efficiency -o is 0,107, which after applying the reduction factor of Fig,. A-7 gives an efficiency r of 9 75 per cent, The power output is then 121 w, based on the calculated operating voltage. (The actual operating voltage and corresponding power output will usually be somewhat smaller than calculated on account of the error in assuming that the wave propagates at the "geometric" velocity,) Assuming that the power output varies as Io3/2 a beam current of about 265 ma should give 100 w output. (7) Starting currents For a tube length of 6-1/2 in., -4 N - 143 I, K = 95x10 4 Q - 11.,5, Cl(start) is found to be 000255k giving a starting current of 17o5 ma4 - 211 -

10,000 8 110:6 2 1: 5/ 27 -- 15 -:-.:.:' ~ ~;'' I =: = - -: -- v. -. -.:;:.-;- -.-.:.-.- = 7.:.::. /:-If' //!!/ 07- T: i7. _..__7_ 1.5 3 -:.:-: —--- L7 —; -:' -.U 10 1 1..02 2.-5 3 4. 5 6 7 8 9- -. —v 5- - -- 50 - 6 =q = 4 -t/ /gv / -.. p.............. 0 X._... - - 1_tl ly-o FIG. A2. —Uiversa J~unng cures fo a foled-lie BWO tt — L —-t~~-I50 —

.07 005 k = low-frequency cut-off.02 D wavelength D.01'o1 *007.005 *001.002.01.02.03.05.07 0.1.2.3.5.8 kcLi FIG. A-3. —Relationship between dimensions and low-frequency wW(h+Q)2 cut-off for a folded-line structure.

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* ~ou3 oT. Tjja Joj JoXouj uoTqonpgH —'*-v'tig t f l i'I II ILI)I t [l~J':,ATLt< itXi,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O

.02 /c6 0,051 X G.03.02 ~o6.007Q08~~~~~Q FIG0 A 8-C-Hart for comp.uting starting currents start / where K is given by Eq. (A-20 Q' and Nc are given by Eqs. (A-19) and TA-22) respective1y0

REFERENCES 1. R. W. Grow and D. A. Watkins, "Backward-wave oscillator efficiency," Proc. IRE, vol. 43, July 1955, pp. 848-56. 2. H. Heffner, "Analysis of the backward-wave traveling-wave tube," Proc. IRE, vol. 42, June 1954, pp. 930-37. 3. H. R. Johnson, "Backward-wave oscillators," Proc. IRE, vol. 43, June 1955, pp. 684-97. 4. J. L. Putz, W. R. Luebke, W. A. Harman, and K. R. Spangenberg, "Operating characteristics of a folded-line travelingwave tube," TR-No. 15 (N6onr 25132), Stanford University (Electronics Research Laboratory), 10 July 1952. 5. J. R. Pierce, Traveling-Wave Tubes, Van Nostrand, New York, 1950. 6. M. H. Steward, "Traveling-wave tubes using slow-wave structures," TR-No. 16 (N6onr 25132), Stanford University (Electronics Research Laboratory), 31 July 1952. 7. W. A. Harman, "Backward-wave interaction in helix-type tubes," TR-No. 13 (Nonr 22510), Stanford University (Electronics Research Laboratory), 26 April 1954. 8. J. R. Pierce, Theory and Design of Electron Beams, Van Nostrand, New York, 1949, pp. 161-64. 9. J. C. Turnbull, "A high-conductivity glass-to-metal seal," RCA Review, vol. XIII, September 1952, pp. 291-299. 10. J. A. Pask, "New techniques in glass-to-metal sealing," Proc. IRE, vol. 36, February 1948, pp. 286-89. - 57 -

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