ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR A NEW SINGLE-CAVITY RESONATOR FOR A MULTIANODE MAGNETRON Technical Report No. 6 Electron Tube Laboratory Department of Electrical Engineering BY J. S. NEEDLE G. HOK Approved by: W. G. DOW Project M762 CONTRACT NO. W-36-039 sc-35561 SIGNAL CORPS, DEPARTMENT OF THE ARMY DEPARTMENT OF ARMY PROJECT NO.339-13-022 SIGNAL CORPS PROJECT N0.112B-O January 8, 1951

ABSTRACT This report presents theory and experimental results pertaining to the operation of a new singlecavity resonator magnetron designed for operation at a wave length of 14 centimeters. Power output of 165 watts C-W at 55 per cent efficiency has been attained from one of several tubes built at the University of Michigan Electron Tube Laboratory. The geometry of the structure employed in this magnetron results in an inherent unbalance of r-f potential differences between the cathode and the anode sets of opposite phase in the t mode of operation. Experimental results show that good electronic efficiency is possible even though an appreciable r-f voltage unbalance (more than 25 to 1) exists. However, the maximum-current boundary for the tubes built so far is not as large as it should be with the available emission. The single-cavity resonator employed in this tube is capable of wide-range tunability, as well as parallel operation of several anode structures with a maximum of mode separation. The tubes constructed to date have been of the nontunable variety. A tunable magnetron of this type is now in the process of development. iii

ACKNOWLEDGEMENTS Many members of the staff of the University of Michigan Electron Tube Laboratory were engaged in the work which made this report possible. The details of design and construction were the responsibility of Messrs. H. W. Welch, Jr., and J. R. Black. Experimental data were made available mainly through the efforts of Mr. G. R. Brewer. The fabrication of tube parts was done by Messrs. T. G. Keith and R. F. Denning under the supervision of Mr. V. R. Burris, and the drawings were made by Mr. N. Navarre. Tube assembly was the work of Messrs. R. F. Steiner and J. W. VanNatter. iv

TABLE OF CONTENTS Page ABSTRACT iii ACKNOWLEDGEMENTS iv 1. INTRODUCTION 1 2. INTERACTION-SPACE DESIGN 2 3. RESONATOR DESIGN 5 4. RESONATOR-CIRCUIT ANALYSIS 6 5. OUTPUT COUPLING 15 6. NUMERICAL RESULTS FOR THE MODEL 7A MAGNETRON 16 7. CATHODE STRUCTURES AND THE CATHODE-CIRCUIT PROBLEM 19 8. PARASITIC MODES 23 9. EXPERIMENTAL RESULTS 27 10. CONCLUSIONS 34 APPENDIX A CALCULATION OF CA AND LV 39 APPENDIX B MODIFIED BAR AND VANE DETAILS 47 v

MAJOR REPORTS ISSUED TO DATE Contract No. W-36-039 sc-32245. Subject: Theoretical Study, Design and Construction of C-W Magnetrons for Frequency Modulation. Technical Report No. 1 -- H. W. Welch, Jr. "Space-Charge Effects and Frequency Characteristics of C-W Magnetrons Relative to the Problem of Frequency Modulation", November 15, 1948. Technical Report No. 2 -- H. W. Welch, Jr., G. R. Brewer. "Operation of Interdigital Magnetrons in the Zero Order Mode", May 23, 1949. Technical Report No. 3 -- H. W. Welch, Jr., J. R. Black, G. R. Brewer, G. Hok. "Final Report", May 27, 1949. Contract No. W-36-039 sc-35561. Subject: Theoretical Study, Design and Construction of C-W Magnetrons for Frequency Modulation. Interim Report -- H. W. Welch, Jr., J. B. Black, G. R. Brewer. December 15, 1949. Quarterly Report No. 1 -- H. W. Welch, Jr., J. R. Black, G. R. Brewer, G. Hok. April, 1950. Quarterly Report No. 2 -- H. W. Welch, Jr., J. R. Black, G. R. Brewer, J. S. Needle, W. Peterson. July, 1950. Quarterly Report No. 3 -- H. W. Welch, Jr., J. R. Black, J. S. Needle, H. W. Batten, G. R. Brewer, W. Peterson, S. Ruthberg. September, 1950. Technical Report No. 4 -- H. W. Welch, Jr. "Effects of Space Charge on Frequency Characteristics of Magnetrons", Proc. IRE, 38, 14341449, December, 1950. Technical Report No. 5 -- H. W. Welch, Jr., S. Ruthberg, H. W. Batten, W. Peterson. "Dynamic Characteristics of the Magnetron Space Charge", December, 1950. vi

A NEW SINGLE-CAVITY RESONATOR FOR A MULTIANODE MAGNETRON 1. INTRODUCTION A new multianode, single-cavity resonator magnetron designed for nontunable C-W operation at 14 centimeters has been under investigation at the University of Michigan Electron Tube Laboratory. Power output of 165 watts with an overall efficiency of 55 per cent and an electronic efficiency of 61 per cent has been attained from one of a number of tubes built. C-W performance data on three tubes and pulsed performance traces for two tubes are included in the experimental results. An unbalance (more than 25 to 1) of r-f potential differences between the cathode and the anode segments of opposite phase (in n-mode operation) results from the inherent geometry of this new structure. Further discussion of the cathode unbalance and the related problem of power loss through the cathode line is presented in Section 7, Cathode Structures. The single-cavity resonator magnetron, which has been designated as Model 7, consists of a section of coaxial transmission line excited at its center by an r-f voltage produced between a system of radial vane anodes and longitudinal bar anodes. The radial vane anodes extend inward from the outer conductor of the coaxial line and protrude through slots * This structure was proposed in Technical Report No. 2 (page 50), of this project.

2 bounded by longitudinal bar anodes in the center conductor. The cathode is located symmetrically within the center conductor. The essential features of the resonator geometry are illustrated in the assembly drawing of Fig. 1.1, and a photograph of one of the tubes is reproduced in Fig. 1.2. Sections 3 and 4 of this report deal with the analysis and design of the resonator. The Model 7 single-cavity resonator magnetron possesses certain advantages over most existing structures. A few of these advantages are: (a) The resonator can easily be designed for wide-range tunability. (b) The dimensions and shape of the resonator can be materially altered without changing the interaction-space design. (c) Parallel operation of anode structures is possible with a maximum of mode separation. (d) The basic geometry of the structure is readily adaptable to external-cavity magnetron construction. 2. INTERACTION-SPACE DESIGN The region of interaction between the electrons and the r-f field is located within the center conductor at its midpoint. For t-mode operation the bars of the center conductor form one set of anodes and the vanes the other. The design of the interaction space is based on conventional procedures. For the Model 7 tubes the interaction space parameters are as follows: * Quarterly Progress Report No. 3, page 56.

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5 X = 14 cm N = 16 anodes r =.665 cm = anode radius a r^ =.381 cm = cathode radius L =.763 cm = length of cathode ra/rc = 1.75 (1.30 has also been used) V = 355 volts Bo = 286 gauss where: m /2lc)2 2 N V0 = ra volts (n =) (2.1) 2e n\ 2 B = (Irc) - 1 webers/meter2 (2.2) 0 e lnX,,^ 2 (rc/ra) Typical operation: V = 3000 volts I = 100 ma. B = 900 gauss PO = 100 watts An axial magnetic field is supplied through copper-plated pole pieces (the parts labeled 1 in Fig. 1.1) which also serve as part of the resonator cavity. 3. RESONATOR DESIGN The electrical length of the centrally loaded coaxial-line resonator is one-half wave length, where for the models built in this laboratory, = 1l centimeters. The design parameters of' the resonator structure f'or operation at a particular f'requency are: (a) the capacitance between

6 the vanes and bars, (b) the inductance of the. vanes, (c) the length of the coaxial-line segments, and (d) the output coupling system. Calculations of bar-to-vane capacitance and vane inductance are based on twodimensional field maps. The field maps themselves are estimated to be correct to within five per cent. The calculated bar-to-vane capacitance is probably correct to within ten per cent. The calculation of vane inductance is based on the assumption of a uniformly distributed current density over the surface of the vane and is therefore only a very rough * first approximation. Flux maps and calculations based on these maps are included in Appendix A. Resonator-design equations and the effect of the output coupling are treated in subsequent sections. 4. RESONATOR-CIRCUIT ANALYSIS The following approximate analysis was developed in-order to determine the equations for (a) the resonance frequency of the cavity, (b) the external Q, and (c) the impedance between the bars and the vanes as seen by the electrons. The analysis is restricted to a lossless cavity resonator in the absence of the cathode. A sketch showing the geometry of the resonator and some of the associated notation is given in Fig. 4.1. We shall assume that the actual resonator may be represented by a lossless transmission line with lumped constant admittances as in Fig. 4.2. Here YL is the load admittance transferred into the coaxial cavity; j1, P, and are, respectively, the distance of the "T" coupling connection from one shorted end of the coaxial cavity, the distance measured from * Attwood, S. S., Electric and Magnetic Fields. ^rd ed., Chapter 7, Wiley and Sons, New York, 1949.~~

7 BARS -- l, / ii.'/-I CENTER CONDUCTOR A TRANSMISSION LINE EQUIVALENT CIRCUIT

8 the "T" to the right edge of the vanes, and the distance from the remaining short-circuited end of the coaxial line to the left edge of the vanes. For convenience in handling, the schematic circuit of Fig. 4.2 is divided into separate components as shown in Fig. 4.35. The admittances indicated on the diagrams define the notations used in the equations which follow. A-~~~~~~~~~A YAB YA' YL Be ~ B'i ~ ^_________, B' ^,13 12j FIG. 4.3 Substituting into the equations for lossless transmission lines, we obtain 13 (YAB + YL) j Y 0 tan 2 (41 YT Y- + i (YAB + Ltan (4.1)

9 YCD 2t ).3 2J( O - -jcot = -jY0 cot.2 (l) Let Y =Yg + YCD; then V ^ YL - J Y0 cot(2n11/X) + J Y0 tan(2iZ2/X) 2v 3 - YO + j YL- J Y0 cot(2nZA/X)] tan 32 - j cot Let 91 = ~__,A = v @ 5 =;t (4* 4) then IL. YL J ^Y0 (tan @2 - 1tan 1).(4I) YO Y 70(14+ tan 92/tan 91) +~ J Y^ tan'2 tan 9 Eq 4.5 represents the normalized admittance of the equivalent circuit shown in Fig. 4.4, where Y' is the admittance of the coaxial cavity plus load at the position of the bar and vane structure. ~ 93 ~^ ~ 2 ~ s ~o el ^ ~Y'^ I~ Y YL GL+jBL FIG. 4.4 We now consider the effects of the vane and bar geometry as employed in the Model 7 type magnetron. Fig. 4.5 defines the required notation which is used in the equations.

10 L v YSHUNT CA^ I I FIG. 4.5 Here LV is the total inductance of all the vanes in parallel, and CA is the total capacitance between the vanes and bars. The shunt admittance which is seen by the electrons is: Y yt - + j^WC. (4.6) "shunt 1 + j WY LV Substitution of Eq 4.5 for YV into Eq 4.6 and rationalization results in the expressions given by Eqs 4.8 and 4.9, where a =tan @1 Cc= ll+b)( 1b) ~1(1 ) a (b- d ad b = tan 92 (47) d = tan~ 9K ^= (I +) YL = +J BL, YO2 GL (ca~'+ b ~ G _________^ ^^ ^^^_________ (4.8) ^^ ^^0VY(Y03 + aBL) - (YQd - BL)] + [^Y(L - bG^

Bshunt = OCA 24 LV (y0p^aBL)2 +a0 -yo Ya[(-bBL) (YOfiaBL) -c]b - E~~LVYo(Yop4czBL) -(Yc$-bBL)2 + ELVJYOGOc-bGT] G~2] 49 Eqs 4.8 and 4.9 can be given a simpler approximate form by making use of the inequalities given below, which were determined from numerical computation. The resultant final approximate equations, 4.10 and 4.11, for shunt susceptance and shunt conductance have been checked numerically against the more exact equations, 4.8 and 4.9, and have been found to be correct to within three per cent for the Model 7 geometry coupled to a matched load. Since aBL <(< Y0 b BL < < YO' and yLY^pGj - bGj2 c< [ J0(Y03 + aBL) - bB], then GL(aa'+ b3) G (4 lo______. ^1) shunt - also, fflnce 2 (aG%)2 < < (Y03 + aBL) abG2 < < (Y0/ - bBL)(Yo + BL) bBL <K e o0' and aBL < < YoP

12 BSe( - -A - ). (4.11) Substitution for the values of a, 3, and ainto Eqs 4.10 and 4.11, and inclusion of the relation (91 + G2) = 03, yields: Ghunt G GZ2 B i~2~l (412) shuftl0 4 cos02 LV + (Zo/2)tan ]2( Bshunt CA - 1 + (z2)tan 9 Eq 4.13, when set equal to zero, gives the condition for resonance, i.e., resonance of the cavity in the absence of the cathode. To obtain an expression for Qe for the Model 7 geometry, we assume B shntvaries linearly with wavelength in the region cJ = t (see Fig. 4.6); then dB sh'Jo or sh ) d I.= o multiplying both sides of Eq. 4.15 by W/2 yields (O (dBsh) - _ _ = e. (4.16) 2 Gshunt d(( 2( ( -L) 0

.006.....004 I I I I I I _..002....... 01 - _________________006_______ll COMPUTED SHUNT SUSCEPTANCE VERSUS WAVELENGTH FOR MODEL 7A NO. 33 3.6 13.7 138 13.9 14.0 14.1 14.2 X CM.

14 Carrying out the indicated differentiation, we obtain LV + (93Zo/2o) sec23 Qe A + (4. 17) 1V +'(Z0/2)tan 92 2shunt In the case of a "T" coupling to the output line, it can be shown that the load admittance is transferred into the cavity at the position of the "T" with very nearly a one-to-one transformation ratio. The deviation from a one-to-one transformation ratio depends on the load susceptance. The deviation for a matched load in series with the reactance of the coupling geometry used in Model 7 tubes is of the order of three per cent. For the case of the "T" coupling, Eq 4.17, after substitution for Gshunt, becomes Q = -i:_ 2 0oLVe1cos2,3 0oCAsin293 "e2 2+ GL in2 Z2 @3 2c oCA 6oLvsin @3 cos e3 + 3 + (4.18) A curve of Qe versus i, the distance of the "T" from the cavity wall, is shown in Fig. 5.2. If we substitute the resonance condition c 1'J CA 1=_________ (4 19) ALV, + (Z0/2)tan 9 into Eq. 4.17 and then let (LV go to zero, we obtain Gsh L 2in J

15 Eq 4.20 shows the division of energy storage for the Model 7 structure in terms of the lumped energy storage (JOCA. Letting 9@ go to zero in Eq 4.20 results in the relation for O. for a lumped constant circuit, i.e., "so CA Gsh 5. OUTPUT COUPLING Fig. 5.1 shows a sketch which gives the details of the output arrangement used in Model 7 tubes. A coupling loop is formed by the length ^ of the resonator cavity and the section of output-line center conductor, 5, which protrudes into the resonator. The position of the "T" junction relative to the shorted end of the coaxial line, i.e., I,, determines the relative amount of loading. However, an increase in 2^ increases not only the loading but also the series reactance of the coupling loop. laT" JUNCTION AREA ENCLOSED BY 8 J do-^ ^^d COUPLING LOOP OUTPUT LINE FIG. 5.1

16 The reactance of the part of the loop formed by the length I of coaxial line is given by X = ZO tan (2Jti/\). The reactance of the remainder of the coupling loop is estimated on the basis of the inductance of a coaxial transmission line of length 8, whose outer radius is ^ and whose inner radius is d0/2. The loop reactance is then given approximately by = Zotan + 2- ln2l (5.1) The impedance of the load transferred to the position of the "T" inside the cavity (for an output line terminated in its characteristic impedance Bo) is approximately ZL - Ro + L (3.2) Fig. 5.2 gives a curve showing the theoretical external Q (see Eq 4.18) as a function of in per cent of the theoretical external Q of the Model 7A structure. The absolute value of external Q for the Model 7A tube has been calculated to be 160. However, measurements show the actual %to be 340. For this reason, the graph shows the relative rather than the absolute Qe, so that this empirical value (340) can be extrapolated to any distance 6. NUMERICAL RESULTS FOR THE MODEL 7A MAGNETRON In order to find numerical answers for resonant wave length, shunt impedance at resonance, and external Q, certain quantities need to be obtained from the geometry of the resonator, the excitation structure, and the coupling system. These quantities, which are listed below, were approximated by employing two-dimensional field plots.

17 FIG. 5.2 ~~ RELATIVE THEORETICAL EXTERNAL 9C0\_____ Q (no cathode) VERSUS DISTANCE Jl OF "T" FROM END OF CAVITY. Qe FOR i/ =.125" TAKEN AS 100 % 80 ~ ~_~ ~ ~ ~_~_~ 0 CQ0 ~ OI 100 % CORRESPONDS TO w5O\ ~ ~~~~ A CALCULATED VALUE OF Qe OF 160 -J \ w 40 20 10 ALL MODELS EXCEPT 7D MODEL TD ___;.125".2___________ 50" i (INCHES)

18 CA = 4.88 pldf (total vane-to-bar capacitance) LV = 122.9,yxhenries (vane inductance - 8 vanes in parallel) L 800'/henries (series inductance of the outputline portion of the "T" connection) Listed below are the quantities necessary for numerical solution of the circuit equations. These values are computed for 14 cm. 91l = 8.140 Q = 47.5'92 = 39.3Z = 24.4 ohms = 13.45 x 10 radians/sec YL = 0.0185 - j.00527 (matched 5011 line) 0)LV = 1.658 ohms WCA = 0.066 mhos (J = 14.29 ohms Upon solving Eq 4.15 to find the wave length for which the shunt susceptance is zero, we find Xges to be 13-95 cm. Since the values of shunt conductance and external Q vary slowly with wave length, we use the quantities calculated above (at 14 cm) for the numerical solutions to Eqs 4.12 and 4.18. The results are 1 = 1835 ohms; Q = 160 shunt The experimental values for resonant wave length of the cavity in the absence of the cathode are 15.864 cm and 13."786 cm for the Model 7A No. 35 and the Model 7B No. 4o, respectively. Results from Q measurements give external Q's of 340 for the No. 55 tube and 230 for the No. 40 tube.

19 The disagreement between the two experimental external Q's for the aforementioned tubes is at present unexplainable in terms of the tube geometries since both tubes have the same resonator dimensions. This discrepancy will be checked as soon as the tubes are available for measurements without cathodes. The discrepancy between measurement and theory is probably the result of oversimplification of the circuit used in the analysis. Further work on the analysis of the resonator is contemplated. 7. CATHODE STRUCTURES AND THE CATHODE-CIRCUIT PROBLEM The Model 7 resonator system has been used in conjunction with a number of different cathodes, a few of which are shown in Fig. 7.1. Fig. 7.1(a) shows a thoriated tungsten bifilar helix cathode, which was used at an early stage of tube development. Operation with this cathode resulted in a power loss through the cathode line and poor oscillator performance. The cathode shown in Fig. 7.1(b) differs from that of Fig. 7.1(a) mainly in the increased diameter of the cathode stem. The enlarged section of the cathode stem, together with the inner surface of one of the pole pieces, forms a quarter-wave cathode-line by-pass. This by-pass makes the potential difference between the cathode and the bar anodes much smaller than the potential difference between the cathode and the vanes. The r-f voltage unbalance for the Model 7A No. 33 tube is conservatively estimated to be over twenty-five to one. The reactance of the X/14 cathode-line by-pass is much less than the Z0 of the by-pass over a wide frequency range. The Z0 for the by-pass is 4.05 ohms. The capacitance between the vanes an^ the cathode was computed on the basis of a flux plot giving a resultant reactance at 114 cm of 20^I ohms.

20 FIG.7.I CATHODES USED IN MODEL 7 TUBES

21 The use of the cathode-line by-pass reduces the power leakage through the cathode line but at the same time produces the aforementioned unbalance by placing a low reactance between the cathode and the inner wall of the center conductor, which, in turn, is directly connected to the bar anode segments. Fig. 7.2(a) shows the approximate space-charge-free r-f field distribution which would result from a geometry in which the cathode is at a potential midway between the anode segements of opposite phase (in the it mode). Fig. 7.2(b) shows the field distribution for the opposite limiting case, in which the cathode is at the same r-f potential as the bar anode segments. Experimental results indicate that it is possible to achieve good electronic efficiency (with thoriated tungsten bifilar helix cathodes) even though an appreciable r-f voltage unbalance exists between the cathode and the anode segments of opposite phase. The maximum-current boundary for the tubes built so far is, however, not as great as it should be with the available cathode emission. Bather unusual effects on maximum-current boundary, efficiency, and wave length are noticed near the magnetic field which corresponds to the cyclotron field, which is given by B = 2gf (7.1) e It is suspected that this behavior is related to the r-f voltage unbalance which exists in the interaction space of the structure. Operation is normal at magnetic fields well above the cyclotron field, as may be seen from the C-W performance charts given in Section 9, Experimental Besults. Fig. 7.1(c) shows a nickel-mesh oxide-coated cathode which is used in conjunction with a modified bar-and-vane geometry. The modified

22 - CATHODE AT A POTENTIAL HALF WAY BETWEEN BAR AND VANE. (BALANCED CASE) / \ ~~~~~~~~~~~~VANE CATHODE AT THE SAME POTENTIAL AS THE BARS. (UNBALANCED CASE) FIG. 7.2 SPACE CHARGE FREE R-F FIELD DISTRIBUTIONS SHOWING THE EFFECT OF CATHODE UNBALANCE.

23 z p /o FIG.l7.3 DIMNSINSUNLSSTHRWIEPECFIE MSTEELDTO TLERNC' ~-FRACIONAL DECM ____ ______________________ __ _TIT L DWG. N. ~ j FIGt. 7. UE DATET O ID OA E ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~o M-GlC TH D ^ __________ CLASSIFICATION DWG.NO. A - ^D l^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o UE DATE' ^^I^J~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~o

- ON'SMa X~~~~~~~~~~~ ^ (EC T/ON A-A FIG. 7.4 ALL DIMENSIONS UNLESS OTHERWISE SPECIFIED MUST BE HELD TO A TOLERANCE - FRACTIONAL ~ 1/4" DECIMAL ~ S0S1, ANGULAR ~ 3* En i ~~~~~~~~~DESIGNED BY /'' PRVDB [ -V -~I ENGINEERING RESEARCH INSTITUTE DRAWN BY oy. AP E FY UNIVERSITY OF MICHIGAN CHECKED BY DATE /~l 7 ] ANN ARBOR MICHIGAN - TITLE PROJECT CO -AXIALMAG/TON ~ ~zIzI M- 7 ^______2______ MO C 7C _____ I ~ CLASSIFICATION DWG. NO. B- /o 007C ISSUEl DATE *''f "I

25 bar-and-vane geometry (see Appendix B) was designed for the purpose of achieving a better balance of r-f potential differences with respect to the cathode. The cathode stem, in this case, was made as small in diameter as possible in order to attain minimum capacitance to the inner wall of the center conductor. Another oxide-coated cathode, an assembly of which is shown in Fig. 7.3, employs a choke and by-pass in the cathode line in order to provide a high impedance between the cathode and the center conductor. The cathode stem and inner wall of the center conductor form a quarter-wave choke beyond which a quarter-wave by-pass is formed by a copper cylinder closely spaced to an enlarged region of the center-conductor inner wall. An assembly drawing for this tube (Model 7C) is shown in Fig. 7.4. Pulsed data were obtained and are given in Section 9. 8. PARASITIC MODES Experimental data on Model 7 structures employing thoriated tungsten cathodes indicate the presence of a higher order mode near 10 cm. This mode has been identified as a resonance existing in the vane anode segments similar to the ordinary mode of conventional vane magnetrons. The "vane mode" frequency is practically unaffected by cavity dimensions and is easily changed by altering the vane structure. This has been done for the tube shown in Fig. 1.1. A backing ring, part no. 6, shortens the vanes. The use of this ring changed the "vane mode" resonance from 11 cm to 9.6 cm without appreciably altering the 14-cm desired cavity mode. In one tube (Model 7A No. 33), shown in Fig. 8.1, two outputs were provided: one for coupling to the desired 14-cm mode and one for

- ON'oMa r%) -EC T-;O, A / -A FIG. 8.1 ALL DIMENSIONS UNLESS OTHERWISE SPECIFIED MUST BE HELD TO A TOLERANCE - PRACTIONAL ~ ^.' DECIMAL *.w5," ANGULAR * x* ~ENGINEERING RESEARCH INSTITUTE DEIRAWN BY /7 / I PROE BY~ UNIVERSITY OF MICHIGAN CHECKED MY DATE [~~~ ~ ~ANN ARBOR MICHIGAN TITLE~~ __ PROJECT CO AY/ L MAGNE TOON ~I~SSU 762 /vf_______XMODAL 7A4NO B ISSUE DATE CLASSIFICATION DW.NO... B 1/,0007A ISSUE~~~~~~~~~~~~~~~~~~~~ DAT i^ ii m'

27 coupling to the "vane mode.' Thus, by selective loading of the two loops it was hoped that mode separation could be changed and effects on maximumcurrent boundary observed. Actually, the effect of loading does not seem to be sufficient to bring the two modes into competition. Mode separation is quite adequate, more than 30 per cent. The tube jumps completely out of oscillation in one mode before any oscillation is observed in the other. Data on the "vane mode" are given in Section 9 for one tube. The tubes utilizing oxide-coated cathodes show the existence of not only the "vane mode" but also of a number of other modes. Little can be said about these extra modes until more complete information is available. 9. EXPERIMENTAL RESULTS The experimental data reported in this section are not conclusive but are sufficient to indicate the results achieved thus far as well as the problems still to be solved. Table 9.1, which summarizes the performance of the tubes completed and tested up to this time, shows that power outputs of the order of 165 watts at good electronic efficiencies are attainable with this inherently unbalanced structure. The C-W performance charts of Figs. 9.1 through 9.4 show the maximum-current boundary encountered with tubes using thoriated tungsten cathodes. The reduced maximum-current boun* dary near the cyclotron magnetic field is not considered serious, since operation at magnetic fields far removed from the cyclotron field is normal. * This effect was also observed on another magnetron with the same interaction-space design but different resonant circuit. See the discussion of Model 4 in Section 2 of the interim report of December 15, 1949.

ro TABLE 9.1 SUMMARY OF MODEL 7 TUBE PERFORMANCE ~Q -Q i p ~~~~Efficienc Tube Description * QL Qo Qext B Eb bb Effcinc gauss volts amps watts 7 ^'cir% 7e% 7A-33 Two output loops. 200 460 354 14.058 Thoriated tungsten 1390 3100 0.100 105 34 57 60 cathode, with X/4 by-pass. 1550 3530 0.092 150 46 57 81 7B-40 One output. Thoriated 211 1625 241 13.916 tungsten cathode with Note: Cold-test data 1390 2890 0.070 15 7.4 87 8.5 X/4 by-pass. ra/rc taken with dummy cathode decreased to 1.5. made of solid nickel. 960 1740 0.100 220 11.3 87 11.1 7C-41 One output. Oxide- 176 790 226 13.772 coated cathode with x/4 choke and \/4 Operated pulsed only. No d-c power. by-pass. 7D-42 One output. Thoriated 64.5 658 71.3 14.59 (?) tungsten cathode with 1390 3400 0.055 102 55 90 61 x/4 by-pass. Size of coupling loop is double 1690 4300 0.070 165 55 90 61 that of all other models. 1690 4230 o.o6o 146 38 90 63 7E-45 One output. Oxide-coated cathode with small diam- Operated pulsed only. No d-c power. eter stem. Modified bar- - and-vane structure. * All tubes except the Model 7B-4O have an anode-to-cathode ratio of 1.75.

FIG. 9.1 29 PERFORMANCE CHART -COAXIAL SINGLE-CAVITY MAGNETRON FUNDAMENTAL CAVITY MODE X = 14.10 CM. 36001 ~ \ ~ \ ~ 1 ~ 1 ~ 1 ~ I ~ 1 ~I 36CC|.0...o 8:1550 GAUSS 46 EFFICIENCY _73~'' 150 POWER OUTPUT (WATTS) 3400 ~ ^73~~~ ~~~32~~ =1200 U)T~~s-r5~~~~334 uJ 30 I -_____ __ _200 1400 ~A NO. 33 12oo __0\____ _I__I_____I___\________________3 0 20 40 60 80 100 120 140 160

30 FIG. 9.2 PERFORMANCE CHART -COAXIAL SINGLE-CAVITY MAGNETRON 520 ________ _______ SHOWING HIGHER ORDER MODES ______________ 480C Xs 9.494 CM. 4400 ~~~~~~ (0 \~ 3.603 J BI59O GAUSS 0 W32 0 0 >2800 w 0 0 z 2000 1600 1200 ~ ~~~~~~~ ~ NOV~,19600 G.R.B 7A NO. 33 8oo _____________________ ______________________ ______ O 20 40 60 80 100 120 140 160 18 ANODE CURRENTr-MA

31 ca -.-1740 GAUSS 3.4 ~~~~~ 14.26 j ~ ~__~1 ^^I6 30. ~ ~~ ____ ____ __ 10000, 14.20 3.2 -A 3.0 ^~~~~~~~ 1390 ____________ _ FIG. 9.3 ~ PERFORMANCE CHART _____ _____ ___ ____ COAXIAL SINGLE- CAVITY MAGNETRON. 2.6 f ~ ~FUNDAMENTAL CAVITY MODE > ~ ~ ~ ~ ~ ~ ~ ~ Ifi * 14 AMPS, MATCHED LOAD 1200 X INDICATES MODE BOUNDARY ^ 2.4 ~ ~ ~ ~^ ^^.~ ~ CYCLOTRON FIELD a 760 GAUSS WAVELENGTH-CM ^ ~^^ ~ ~ ~ ~ ~^.~~~~~1080 z /ox ^^^MODEL 7B NO. 40 ^ ^ o / ___ ____ ^^^___^^____ THORIATED TUNGSTEN CATHODE 0 2.2 ~ ^^^^ ~ ~ ~ rc c 445 CM U ra/rc z 1_ ^____________ _____ ro,'rc = 1.5 ____ 0 z__ 1 2.0 ~ ~ ~ ~ ~ ~ WO-X 960- ~ ~~~ ^^^^ ~~~13.74 1.8 X 320 MA i ^ _____ _____ _____ ____ ^ ^. ^ ^ ~ ""^" 13.84 __ ___ __ ___ __ ___ ___ 390 MA ^^^^ ^___^~ ~~~580 052550 7565100 ANODE CURRENT MA

32 4400 -X B s1690 _______ ^ ________ __ ___4.07613.076 / 14.242 35 14.052 13.912 4000 _____,33.588 13.140 13.974 c600 14.12 ___ 14.148 32 9. 0 -^' ^ ~^ ~ ~ ^^Q 13.760 POWER OUTPUT-WATTS B 131185 UJ B =J0( 8^10 80 > ^ ^-~A O8.7E2 2N

33 However, the maximum-current boundary is, in general, lower than would be expected in view of the available cathode emission. The question of how to increase the maximum-current boundary is one of the subjects of another investigation being carried on at this laboratory.* A comparison of the performance chart of Fig. 9.3 with the other performance charts shows the effect of a change in interaction-space design on the maximum-current boundary. The anode-to-cathode radius ratio for the tube whose performance is given in Fig. 9.3 is 1.5, whereas the ratio for all other tubes built thus far has been 1.75. Since the amount of data available is very limited, any conclusions based on the comparison mentioned above cannot be considered as final. Fig. 9.2 gives the performance for the Model 7A No. 33 tube, showing operation in modes other than the desired 14-cm resonator cavity mode and indicating the degree of mode separation. The lower wave length modes are both presumed to be "vane" modes. The effects of heavier load on the operation of the Model 7 tubes are indicated in Fig. 9.4. The output coupling loop for this particular tube (Model 7D No. 42) is twice as large as that used in any of the other tubes. A power output of 165 watts at 55 per cent efficiency was obtained from this tube at a higher magnetic field and plate potential than those used for the Model 7A No. 33. It seems reasonable to expect that the power output from the latter tube would be greater than 165 watts if it were operated at the higher magnetic field. Comparison at the same magnetic fields shows that the Model 7A No. 33, in general, gives more power output, but at lower efficiency. * See Technical Report No. 5).

34 ~~~~~~~~~~~~~~~(a) ~~~(b) B = 1600 GAUSS 1600 GAUSS AMPSfiI = 7.0 AMPS MATCHED LOAtP LOAD ADJUSTED FOR MAX. BOUNDARY ~~~~~8:=~~~~~~~~~~1600 GAUSS ~(d) 8: 1600 GAUSS Ifil=z 6.5 AMPS iI= 6.5 AMPS MATCHED LOAD LOAD ADJUSTED FOR MAX. BOUNDARY I'~: ID1V, = 25MA

35 FIG. 9.6 PULSED PERFORMANCE FOR MODEL 7C NO. 41 (OXIDE CATHODE) 8- 1390 GAUSS 1 Ifil 6.5 AMPS (THRTE TN MATCHED LOAD (0)~~~~ Wh

36 Oscillograms showing pulsed performance for two different tubes are given in Figs. 9.5 through 9.7, inclusive. These figures show the effect of load on maximum-current boundary and also indicate the presence of spurious modes of operation. The effect of cathode temperature on leakage current and maximum-current boundary is indicated in the pictures of Fig. 9.5. The current calibration (25 ma per division) is the same for all oscillograms. Tubes employing oxide-coated cathodes have been tested under both pulsed and C-W operation. The C-W power output from these structures has been of the order of five to ten watts at very poor efficiencies. Further work with oxide-coated cathode magnetrons is required before any definite conclusions can be drawn as to the causes of the aforementioned poor operation. 10. CONCLUSIONS The Model 7 single-cavity resonator magnetron has been shown to be capable of producing significant power output at good efficiencies It is relatively simple to construct, and the resonator can easily be designed for wide-range tunability. The basic geometry of the structure is readily adaptable to external-cavity magnetron construction as well as to parallel operation of anode structures. Resonator shapes and dimensions can be varied over a wide range without requiring a change in interactionspace design. Performance of tubes constructed and tested so far indicates the necessity of further development in order to attain (a) greater maximum

37 current boundary, and (b) a more complete understanding of the cathodeleakage problem and the effects of cathode unbalance. These subjects may or may not be directly related to each other. The C-W power-output limitation observed with'magnetrons employing oxide-coated cathodes is of interest and also requires further investigation.

39 APPENDIX A CALCULATION OF CA AND LV

40 APPENDIX A CALCULATION OF CA AND LV The use of field maps for calculations of bar-to-vane capacitance and of vane inductance is considered to be justified, since the dimensions of the vanes and bars are small relative to the wave length. The error incurred by considering the field distributions in two dimensions rather than in three dimensions is assumed to be greater than any field-mapping inaccuracies. The calculated bar-to-vane capacitance is probably correct to within ten per cent. This is a rough estimate because the answer is obtained on the basis of two-dimensional maps* Calculations of vane inductance are based on the assumption of a uniformly distributed current density over the surface of the vane. This is, of course, only a very rough first approximation, since the edges of the vanes looking longitudinally into the coaxial line segments are essentially integral parts of the line terminations. The current density in the vanes should therefore be greater at these edges than anywhere else on the surface of the vanes. Although the distribution of current density is not directly available, we can obtain at least an order of magnitude by the approach used herein until a more detailed study of the true distribution can be made. * Attwood, S. S., Electric and Magnetic Fields. 3rd ed., Chapter 7, Wiley and Sons, New York, 1949.

41 The capacitance is obtained from the two-dimensional maps by using the relation: C = g Number of squares along an equipotential Number of squares along a flux line (Capacitance is then in farads per meter measured perpendicularly into the paper.) The inductance is obtained by using the relation: L Number of squares along a magnetic equipotential line'~ Number of squares along a magnetic flux line (Inductance is then in henries per meter measured perpendicularly into the paper. ) C omputat ions Vane-to-Bar Capacitance: From the map of Fig. A-1 we have: _o 7.75 squares (farads per meter of map So 0o 2 squares depth into the paper) The map depth into the paper is equal to the vane height, which is 0.300 inch or 7.62 x 10-3 meter. Then: C1 = ~ 775 x 7.62 x 10-3 (farads for one 22-1/2-degree section 0 2 of the full sixteen-anode picture). We now consider the top and bottom edge capacitance from the map of Fig. A-2. Cedge = o 7 (farads per meter of vane thickness) Taking half the vane thickness as the dimension required in the 22-1/2-degree section in the map of Fig. A-l, and considering both the top and bottom edges of the vanes, we get:

42 \ o~d s \ \\ \'.os\ \ FIG. A-I ONE SECTION OF THE MODEL 7A VANEAND-BAR EXCITING STRUCTURE.

43 CENTER CONDUCTOR 2 3 4 5 1 \ VANE 0 VANE FIG. A-2 FLUX PLOT FOR THE COMPUTATION OF END CAPACITANCE BETWEEN CENTER | VANES AND BARS CONDUCTOR MODEL 7A SCALE X 20

44 7.5x x 10-3 (farads per 22-1/2edge x 1.3 x 10 degree section) The total capacitance per 22-1/2-degree section, then, is: C/section = C1 + Cedge = 0.305 /f ~ Since there are sixteen of these 22-1/2-degree sections in parallel for the complete system, we obtain; CA = 16 (1 + Cedgel) = 4.88 f. Vane Inductance: From the map of Fig. A-3, we obtain: Lo = 4 suares henries per meter of map depth (for 1/4 of the Lo = /Lo 6.5 squares L, = O,6.5 squares ^vane periphery) Taking the entire periphery into account, we obtain: L0 (henries per meter of vane L1 = T depth into the paper) Since the vane depth into the paper is approximately 0.200 inch or 5.08 x 10O3 meter, the inductance for one vane is Lv = 5.08 x 10 L = 9.83 x 1010 henries The total inductance for eight vanes in parallel is LV = v - 122.9?/~ henries Note: The distance between adjacent vanes has been taken as the average for the map of Fig. A-3.

FIG. A-3 FLUX PLOT FOR THE 45 CALCULATION OF VANE INDUCTANCE __K.051' L1. I l VANE' z w w3 I-Z ~ AVERAGE DISTANCE 2 0 _____ _ _____ _______ 11' 2' 3' 4' 2 4 5 6~~~_

47 APPENDIX B MODIFIED BAR AND VANE DETAILS

48 /,00/ A A 5 / A /\ / /// f/ ~43 5', ~.6/0.7~ 75010 C.1 "T5f \r, i\H/ 11A J-~ C N, a SECT/ION AA OFHC COPPER / RLQD ALL DIMENSIONS UNLESS OTHERWISE SPECIFIED MUST BE HELD TO A TOLERANCE - FRACTIONAL ~'/4," DECIMAL~.005," ANGULAR ~:O ENGINEERIG REsEC N E DESIGNED BY Asr/ APPROVED BY I IENGINEERING RESEARCH INSTITUTE I.DRAWN BY 7 SCALE ZX UNIVERSITY OF MICHIGAN CHECKED BY -:' DATE / -/-5O0 ANN ARBOR MICHIGAN TITL~ PROJECT |0C ILL A TOR F1SGEPS M-7^ 05C/LLATO2 F//VG~~S CLASSIFICATION DWG.NO. A- 5 )P ISSUE T DATE 5 |.025

IL:::' I' 3Lva I fns! 93Q7 -~j.ON.Ma _____ NOI~YDIOI1SSYO ~ ~ CIVD 7070(NV ^^ ^ ~~ dll. rc^ -0 g \^/' y ________________JLoaromd ~3~111H M NV91H:OIV UMOIMV NNV' Q9__ - t'_-Z/ / 3~YaI W<, ^ A a3)03HoH | NV91H:)IW.0 AISS13AINn _ X Z 3nt S As I NMA inlIUSNI HDIY3S38 9N133N19NIN3 AS a3AOiddV /|' i/Aa a O3sN9Is3a o% 1T mVneNV,,sOO' F ivw13I3a,,'l T VNOIJIOVMJ - 3:NVU310J. V OJ1 a13H 38 Lsnw fa3l31I3ds 3SIMW3HLO SS3hNn SNOlsN3wIla - V /VO/JddO DH O' VV NOllOh^ / 0/9' 1oo, \ Ii \ ~b00' 6*, \* tZ5'- - /0<7a z~~~~~~~~~~~~~~ ~ ^ "~'l i~~~ ~ 3~~~~ \^/\^ 6b~~ ^r^

50 0 tool +.oo/ 0 { I L I j "^, _......025 X.025 00., o I!1 I! t' —! OF/HC COPPER 8 FOQ'D ALL DIMENSIONS UNLESS OTHERWISE SPECIFIED MUST BE HELD TO A TOLERANCE - FRACTIONAL 4," DECIMAL.005," ANGULAR i % ENGINEERING RESEARCH INSTITUTE DESIGNED BY r4 r APPROVED BY I I CN E IF CE DRAWN BY 7 SCALE 2 X UNIVERSITY OF MICHIGAN CHECKED BY'~- t-A | DATE /2 / 50 ANN ARBOR MICHIGAN TIL M-762 ANODE VANE CLASSIFICATION JW ISSJIE | DATE | |~DWG. NO. A- 5 7,S.,30,T E.0

51 DISTRIBUTION LIST 20 copies - Director, Evans Signal Laboratory Belmar, New Jersey FOR - Chief, Thermionics Branch 10 copies - Chief, Bureau of Ships Navy Department Washington 25, D. C. Attention: Code 930A 10 copies - Director, Air Materiel Command Wright-Patterson Air Force Base Dayton, Ohio Attention: Electron Tube Section 10 copies - Chief, Engineering and Technical Service Office of the Chief Signal Officer Washington 25, D. C. 2 copies - H. Wm. Welch, Jr., Research Physicist Electron Tube Laboratory Engineering Research Institute University of Michigan Ann Arbor, Michigan 1 copy - Engineering Research Institute File University of Michigan Ann Arbor, Michigan W. E. Quinsey, Asst to the Director Engineering Research Institute University of Michigan Ann Arbor, Michigan W. G. Dow, Professor Dept. of Electrical Engineering University of Michigan Ann Arbor, Michigan Gunnar Hok, Research Engineer Engineering Research Institute University of Michigan Ann Arbor, Michigan J. R. Black, Research Engineer Engineering Research Institute University of Michigan Ann Arbor, Michigan G. R. Brewer, Research Associate Engineering Research Institute University of Michigan Ann Arbor, Michigan

52 J. S. Needle, Instructor Special Development Group Dept. of Electrical Engineering Lancaster Engineering Section University of Michigan Radio Corporation of America Ann Arbor, Michigan RCA Victor Division Lancaster, Pennsylvania Dept. of Electrical Engineering Attention: Hans K. Jenny University of Minnesota Minneapolis, Minnesota Magnetron Development Laboratory Attention: Prof. W. G. Shepherd Power Tube Division Raytheon Manufacturing Company Westinghouse Engineering Laboratories Waltham 54, Massachusetts Bloomfield, New Jersey Attention: Edward C. Dench Attention: Dr. J. H. Findlay Vacuum Tube Department Columbia Radiation Laboratory Federal Telecommunication Labs, Inc. Columbia University Dept. of Physics 500 Washington Avenue New York 27, New York Nutley 10, New Jersey Attention: A. K. Wing, Jr. Electron Tube Laboratory Dept. of Electrical Engineering Microwave Research Laboratory University of Illinois University of California Urbana, Illinois Berkeley, California Attention: Prof. L. C. Marshall Dept. of Electrical Engineering Stanford University General Electric Research Laboratory Stanford, California Schenectady, New York Attention: Dr. Karl Spangenberg Attention: Dr. Wilbur Hull National Bureau of Standards Library Cruft Laboratory Room 203, Northwest Building Harvard University Washington 25, D. C. Cambridge, Massachusetts Attention: Prof. E. L. Chaffee Radio Corporation of America RCA Laboratories Division Research Laboratory of Electronics Princeton, New Jersey Massachusetts Institute of Technology Attention: Mr. J. S. Donal, Jr. Cambridge, Massachusetts Attention: Prof. S. T. Martin Dept. of Electrical Engineering Pennsylvania State College Collins Radio Company State College, Pennsylvania Cedar Rapids, Iowa Attention: Prof. A. H. Waynick Attention: Robert M. Mitchell Document Office - Room 20B-221 Dept. of Electrical Engineering Research Laboratory of Electronics University of Kentucky Massachusetts Institute of Technology Lexington, Kentucky Cambridge 39, Massachusetts Attention: Prof. H. Alex Romanowitz Attention: John H. Hewitt Dept. of Electrical Engineering Bell Telephone Laboratories Yale University Murray Hill, New Jersey New Haven, Connecticut Attention: S. Millman Attention: Dr. H. J. Reich Department of Physics Document Office for Government Research Cornell University Contracts, Harvard University Ithaca, New York Cambridge, Massachusetts Attention: Dr. L. P. Smith Attention: Mrs. Marjorie L. Cox

UNIVERSITY OF MICHIGAN 3 901111111 115 03483 5549111111 3 9015 03483 5549