THE CAVITY MAGNETRON* By H. A. H. BOOT, Ph.D.,I and J. T. RANDALL, D.Sc., F.R.S.,T Associate Member.

(The paper was frst received l5th February, and in revised form 3rd July, 1946.) ST'MMARY mid-plane sectional drawing (at right angles to the cylindrical This paper gives an account of the discovery of the cavity magnetron axis) ofFigs. 1(a) and 1(ô). The general type ofdesign illustrated in the University of by the authors, and of subsequent developments in that laboratory including the discovery by Sayers of what is now known as strapping. From October, 1939, to August, 1941, the work was carried out by the authors who, from June, 1940, received much technical help from S. M. Duke. Sayers began work on the magnetron in the summer of 1941 and his ideas on modes led almost immediately to the introduction of straps. Sayers's detailed work will later be the subject of a separate paper.

(1) INTRODUCTION (à) As the group of workers originally engaged on the production Fig. l.-End view of resorlator systens. of centimetre waves in the Physics Department of the Type (a) is based on a Hertzian dipole while (à) is based on a short{ircuited quarter University wave Iine, of Birmingham has been gradually disbanded since the autumn of 1943, it may not be inapt to recall the inception of this work in Fig. 1(a) was the first to be used in Birmingham, and a and the.early ideas concerning the magnetron. Initially, under photograph of one of the first six blocks to be made is Oliphant, a considerable attempt was made by Sayers and others given in Fig. 2. to improve the klystronl as a centimetre-wave power oscillator, (2.2) and in fact a good deal was achieved in this connection. At the Construction same time an attempt was made by the authors to use the Fig. 2 also males clear how problem (ô) was overcome. The Barkhausen-Kurz valve as a detector; before long, however, interest moved towards the central problem ofthe production of high power at or below ten centimetre . It appeared that the major clifficulty in the way of any attempts to improve the by a large factor was that of getting sufficient power into the beam, necessarily of small cross-sectional area; it was realized by the authors that a magnetron would be free from this defect. One of the outstanding advantages of the klystron was the use of internal such as had been described by Hanson2 and Rayleigh.3 Resonators of this type, turned from solid , give low h.f. losses, high frequenry- stability, and are capable oflarge hèat dissipation. The problern was therefore to design a magnetron, capable of giving a large anode current, and which also incorporated a system of suitable properties. The main investigation therefore initially resolved itself into (a) the design of a suitable type of resonator, the determination of its size, and the method of grouping a number of resonators in a device of cylindrical symmetry. (ô) A method of construc- Fig, 2.-One of the first six anode blocks made. tion which would ensure high electrical and thermal conductivity. (c) The design of an h.f. output-circuit in relation to the chosen whole anode resonator system was constructed from a single resonator system. machined copper block, the central axial cavity forming the anode,/ space. The resonator cavities were grouped (2) GENERAL REQLITREMENTS around this, heat being dissipated by conduction along the . (2.1) Type of Resonator webs or segments between neighbouring resonators. The Hanson papers were by this time available in the laboratory, but it was clear that the designs (hollow spheres, (2.3) Resonator Size cubes, and "doughnut"-shaped cavities) could not be assoiiated' The problem of resonator size for an intended of with the cylindrical symmetry of the magnetron. It was decided, 10 cm was more difficult. The experiments of Hertz (confirmed therefore, to use either a three-dimensional extension of the well- theoretically by MacDonald) had shown that the wavelength to known Hertzian loop or a corresponding extension of a be expected from a simple loop of this wire is 7'94 times the shortæircuited quarter-wave line. That either type lends itself diameter of the loop. It was assumed with some justiflcation to a symmetrical magnetron construction may be seen from the that the wavelength to be expected from a single, slotted, copper * Radiosectionpaper. f universityofBirmingham. I universityof . cylinder would be largely independent of the cylinder length, te28l BOOT AND RANDALL: THE CÀVTTY

and the unpredictable effect of electromagnetic and electrostatic 0.75 mm in diameter was used (as being more suitable for c.w.' coupling between neighbouring resonators was neglected' operation), it was also realized from the French publications available that the use of an oxideæoated cathode was desirable. The subsequent introduction ofi such by both the (2.4) Number of Resonators and Anode Hole t: Research Laboratories of the Company, and the was not known at the time to what extent the operation I It Birmingham group is referred to below. of the valve would be affected by small departures from sym- I metry; it witl be noticed that, in Fie. 2, the anode hole is the (2.O ôutPut Circuit Later ,1 same diameter as that of the surrounding resonators. The output circuit is of some interest as it was destined to be principles in the design experiments showed that the adopted first the standard for a considerable period, exgept in cases of very outstanding 1 were of veiy general application. One of the high power (or very sholt wavelengths), when wave-guide output features of the design at this stage was the use of an enclosed circuits proved more suitable. The method adopted initially i resonator-anode system, and in this feature it differed radically was to utilize a coaxial-transmission line, the inner conductor from ali earlier magnetrons known to the authors. The chief terminating in a loop,'in such a way that the magnetic flux I dimensions of the first caùity magnetron were:- parallel to the resonator axis passed through that fraction ofthe .t cavity section embraced by the loop. The ratio of the loop area Anode lensrh, slot di-"',ion,, to cavity area in the early experiments was estimated to be l I -'''c.;.-^'.â*i;. ] I I:aq:l_"-tresonators I ---.Â- -' cm I I .- I I "ff!$.t:, between 0'4 and 0'5. The ftanSmission line lies in a mid.section t plane at right angles to the cylin\er axis, and being sealed by a glass-metal seal, became a part ol\he valve system. 4.0 t-2 I 0.1 x0.1 I 6 1.2 It is perhaps useful to summari2\ the main conclusions which had been established by the trst experiments outlined above. f (i) A magnetron with a completely enclosed resonator system (2.5) Operating Conditions had been successfully opeqatèh at a wavelength of 10 cm at an The calculations on which the operating conditions of the efficiency (10-15%) comparable with that of other known first cavity magnetrons wêre based were of the simplest nature. high-frequency oscillators such as the klystron. The chief assumption related.to orbits in which the (ii) The use of a number of closely coupled resonators in the + pass from one iesonator slot to the next at grazing incidence same oscillator apparently offered no difficulty. in a time equal to half a period of oscillation under an applied (iii) The use of a combined copper anode block and resonator ï anode poteritial of Y volts and an axial of system ensured adequate heat dissipation, low electrical losses, f/ oersteds with a phase diflerence of n'* between neighbouring and the potentialities of simple manufacture. segments. Such calculations give rise to expressions lor V and H (iv) The use of a single, simple, output circuit to draw h.f. J in terms of À, the expected wavelength, D the anode diameter, power from the system was established and it was clear that such z the number ofresonators, and known physical constants. On an output circuit would enable power to be fed in a comparatively this basis it appeared that 16 kV and I 000 oersteds would be easy manner to aerial systems and wave guides. required to opèiate a magnetron of the above dimensions' The detailed expressions are referred to later. (3) FURTHER DE1IELOPMENTS $ Facilities for making sealed-off valves were not immediately The following steps in the development of the valve were available, and the ûrst cavity magnetron was completed in de- obvious but necessary consequences ofthe eariy experiments. 3 mountable fashion with waxed glass-metal seals. A view of the (a) The completion of a seaied-off version of the valve. valve removed from the pump is shown in Fig. 3. The first (à) The testing of other designs-e.g. different numbers and sizes of resonators. 't (c) The introduction of large cathodes to provide the high nç anode current necessary for high-power operation. (d) The introduction of 4 modulated power supply. (e) The adequate measurement of r.f. power. r In the achievement of (a) considerable help was obtained, J{- directly and indirectly, Ëy collaboration with the Research Laboratories of the G.E.C., Wembley, with ;vhom inlormation was exchanged in April, 1940. In this way a great deal was learned about the technique of sealing giass to copper, and of joining copper to copper by means of a gold wire under pressure $ between the two surfaces at temperatures below 500" C. In- (' directly,.great help was received from S. M. Duke, a former -r' member of the Wembley stafl who joined the Birmingham group in June, i940. An important feature in the development of the cavity mag- Fig. 3.. The first (demountable) cavity magnetron. netron was the introduction in May-June, 1940, of large oxide' coated cathodes, The French workers Gutton and Berline H tests (which were successflul) were carried out on February 21st, were already using such .cathodes in the more conventional 1940. Within a few days it had been shown that the power split-anode magnetrons just prior to the war. This information radiated was about 400 watts at a wavelength of 9'8 cm. In was already available to G.E.C., Wembley, and at about the end order to minimize delay the first valve was operated frbm a d.c. of 1939 to the Birmingham workers. Shortly after the first power suppiy, although the need for a pulsed system was clear experiments described in this paper both the G.E'C. Laboratories at the outset. Furthermore, although a . cathode and the authors produced samples embodying this feature; this fi peak-power at + Such a mode ofoperation was later referred to siDply as the æ-mode. enabled outputs of 10-50 kW to be obtained 930 BOOT AND RANDALL: THE CAVTTY I\{AGNETRON \'* -. efficiencies of 10-20% within a few months of the initial these considerations will usually work, It was found in the experiments. Birmingham laboratories, however, that more efficient operation With regard to (ô) and (c), experiments on, (1), an 8-hole, could be obtained by the use ofhiglier peak voltages and higher 5-cm design, (2),aL4-hole,5-cm design, (3), a 6-hole, 3-cm design magnetic fields than those indicatediby the formulae. On sub- and, (4), a 3O-slot 2-cm design had all been sufficiently tested sequent evidence it is not improbable that the reason for this before the end of September, 1940, to show that the principle lies in the fact that the new operating conditions bring the which had been introduced in the first cavity magnetron was of magnetrons nearer to those of the z-mode. very general application. . By the beginning of l94l it was decided to carry out work on The introduction of a modulated power supply (see d) was the spectrum of frequencies obtainable from a magnetron block recognized as a necessity, but discussion of it is omitted from this fitted with a dummy cathode.* A klystron, tunable from paper, since it will doubtless be dealt with by others. Con- 8'5-9'5cm, was used as a signal generator; the power input siderable help was received in later work from E. W. Titterton was fed to the normal coupling-loop of the valve, which was in and collaborators who constructed many modulators suitable for this case made adjustable. The output was taken from a l operation of the various magnetrons under development. similar loop placed above a resonator in a position diametrically The problem of r.f. power measurement caused most labora- opposite in the block. The output was measured by a galvano- tories engaged on this work a good deal of trouble; the initial meter or microammeter, a crystal being used as rectiter. The phase in which lamps of various types were used, was followed effect of cathode diameter and end-space depth on the various by a period concerned with the application of bolometer-type modes of ôscillation of the block kas studied. The effect of the instruments; these in turn were succeeded by the use of a insertion of rods of both conductfuk and insulating material into resonant-cavity water-filled calorimeter designed by Sayers. the resonators was also investigatel, and it was shown that a In the early stages it was thought that the resonator magnetron considerable tuning range could be o\tained. l would suffer from the disadvantages of the simpler split-anode A little later a sealed-off 9'1cm'1alve was constructed by l type in which the frequency was largely determined by the anode S. M. Duke. In this valve the cathode could be moved by a the plane containing the output and filament I voltage and magnetic field; earlier magnetrons also had known amount in a reputation of having high noise values. Experiments carried out .stems. By this means it was hoped to determine the accuracy in July, 1940, showed that the variation of frequency with anode required in mounting the cathode in production valves. The l voltage and magnetic ûeld was small and difficult to measure anode and cathode diameters were 16 and 6mm, respectively, with the equipment then available. It was only later that the and maximum efficiency was obtained when the cathode was possibility of the magnetron oscillating on different modes 0'5 mm off-centre towards the output loop. The efficiency was became evident. not, however, a sharply varying functjon of cathode position, This is not the place to discuss the theory of thè magnetron and there seemed little to be gained from mounting cathodes as later developed by Hartree, Slater, Stoner and their colla- eccentrically. borators, but it would be unfair to those engaged on the earlier (4) SECONDARY EMISSION PROPERTIES OF MAGNETRON stages of the resonator magnetron development to assume that their investigations were entirely of an experimental nature The authors were Ied to consider, during the sunmer of 1941, unguided by any theory. From simple considerations based on whether certain observed low values of efficiency could be the tangential passage of electrons close to the anode between , associated with the state of the cathode surface. A study was one resonator slot and the next, it was shown that, for a phase made of the d.c, current/voltage characteristics of a number.of difference between adjacent cavities, the d.c. anodevoltage, of{ sealed-off magnetrons in the absence of magnetic field. Numer- 4n2c2m D2 ous deviations from the well-known V3l2-lau, for voltages up (2) V: to about 200 were observed, but no obvious correlation between 1,1s-z7z6z (under For v low these conditions) and low $: then discovered that V:2-x 107D2/N2À2 volts (3) efficiency of h.f. output was found, It was all magnetrons in the Iaboratory could be set into oscillation 7.24 x 10+ with the cathode unheated at the time of switching on the anode and Ii: - oersteds {4) V^ voltage, provided that the magnetic field was previously adjusted to an appropriate value. No appreciable anode current was where D is the anode-hole diameter in centimetres and N is the observed with the cathode cold, unless the magrretic field was number of cavities. applied. Two further important observations were made at These relations, as later theory shows, are quite inadequate to this stage:- describe the detailed physical behaviour of the magnetron. (i) Magnetrons known to have high efficiency under normal Nevertheless, the relations enabled many new designs to be hot-cathode conditions oscillate with their cathodes belorv successfully completed. It should be emphasized that the wave- thermionic emission temperatures when switched on with the length is, to a first order, a function of the dimensions of the cathode in the abnormal unheated condition. On the other resonator system alone. The above relations simply show in hand, low-efficiency magnetrons show considerable back-heating what way V and H vary with D and N for a given wavelength, À. of the cathode if switched into oscitlation with their cathodes No really adequate method of calculating the wavelength from initially cold under the same circuit conditions. first principles has been found because of the obvious difficulties (ii) Magnetrons oscillating without any cathode-heating current of representing the resonator system accurately by an equivalent show a fairly sharp cut-off as the magnetic fipld is reduced, the circuit, and the complicated nature of the boundary conditions oscillations and anode current dropping to zeto as the value of for any solution of Maxwell's equations for the cavities' Semi- fI passes througtr a value not far removed from that given by the empirical means have therefore been largely used in diferent the Hull cut-off equation. laboratories, and the predictign of wavelength has depended on These results seemed to indicate the importance of secondary the gradual accumulation of accurate experimental data. emission ,ir1'magnetrons, and the following experiment rvas has already been pointed out that relationS (2), (3) and (4) It * This work was initiated by Professor Otiphant; the injtial experiments were. should not be taken too seriously; a magnetron design based'on carrièd ôut by E. W. Titterton, ând later wotk was done by W. T' Cowhig' 931 . BOOT AND RANDALL: THE CAVTTY MAGNETRON I I carried out to distinguish between purely thermionic and oscillator by means of a small lôop in one resonator. In the (8'5 cm) secondary-emission effects. range of wavelengths that couldibe covered to 10'5 \ An aluminium cylinder, 0'6 cm diameter, and 2 cm long, was three of the block were observed. It was possible etched in caustic soda and boiled in water to give a thin coating to determine qualitatively the voltages on the segments by + of oxide. Under these conditions it was expected that the inserting a small probe, connected to a crystal detector, through a rotated I secondary-emission coefficient would be about 2' 5. This cathode hole in the magnetron end plate which itself could be was mounted in an 8-hole, E1189-type of block with adjustable to bring the probe over each segment in turn. These three I cathode and coupling loop, and the valve was operated on the modes werc originally designated by Sayers as the AB-mode, pump. The magnetron oscillated immediately and gave an the A-mode, and the B-mode; for, if the segments are labelled f then the AB-mode large amplitudes I efficiency of 260/o with a peak power output of about 20 kW. A and B alternately, in 'c Experiments with a nickel cathode (with a secondary-emission are found on all segments. In the A-mode' all the B segments coefrcient believed to be about I'2) were much less successful, had zero amplitude, whilst in the B-mode all the A segments I the measured efficiency being no greater th,an 0'51. In both had zero amplitudes. This terminology is no longer used and cases residual gas provides the primary bombardment. A modes are designated by the number, n, of complete waves of, t reflnement of the first experiment was carried out to make a potential distribution occurrin$..round the anode" Alternatively r1 sealed-off magnetron fitted with an aluminium cathode and a ihey muy be specified tv d, th" phase change in the voltage palladium tube to provide hydrogen. So long as sufficient gas pattern observed between adjàçent segments. The relation was present this valve operated normally. Later experiments, between n and { is.simply Nd : \rn, whete N is the number of particularly on 3-cm magnetrons, were made using pilot-cathodes resonators. The AB-mode was pr\bably the z (i.e. 180') mode, of tungsten and surfaces of oxide on nickel or that is n : 4 for eight resonators. i molybdenum cylinders; the use of a pilot cathode avoids the Sayers suggested that the A- .and B-modes could both be necessity for gas to provide the initial electron bombardment. eliminated by connecting togethdr all the A segments at one This work points to the possibility of making c'w. cavity end and all the B segments at the other end of the anode by magnetrons utilizing .cold secondary-emitting surfaces. (It short pieces of wire, now called straps, and when this was done should be remembered that in the first experiments described only one mode (AB) could be observed. By a different arrange- in this paper the magnetron gave 400-watts h.f. output with a ment of straps and by connecting either the A or B segments tungsten cathode which remained sufficiently hot to emit when to the magnetron end plate the A- or B-modes were apparently the cathode heating supply was disconnected.) There seems to suppressed. Various geometrical arrangements of the straps be no fundamental reason why designs cannot be produced for were proposed, but not all have come into general use. The c.w. power purposes incorporating water-cooled cathodes. two methods most used are known as double ring and echelon strapping. In the first case two narrow concentric grooves are (5) THE OSCILLATORY CIRCUIT AND TTM bITRODUCTION turned near the ends of the segments at each end of the valve OF STRAPPING and a castellated copper ring, made by bending a strip of the groove. The essential feature of the cavity magnetron is the use of a form shown in Fig. 4(a) into a circle, is pressed into each number of more or less similar resonant elements mutually coupled to each other and contained in a conducting enclosure. A quite natural result of this construction is that there should be a number of resonant frequencies of the combined system depending on the number of elements' This fact seems to have Æ:æ received little attention during the fust year or so of the develop- probably initialiy by ment of the map.etron and was obscured (a) the succqss of the magrr.etrons with up to thirty segments. Peculiarities in behaviour were frequently observed as larger numbers of a given type of 10-cm magnetron became available for Service use. It was found that some valves did not oscillate (b) at the expected wavelength, but, as these valves often had a low efficiency, their behaviour was explained in terms of construc- tional inaccuracies. , Closer examination of these valves showed that several more.or less discrete frequencies could be obtained by change of operating conditions. Valves with odd numbers of resonators had been made to work both in Birmingham and r:- in the United States, and it was obvious in such a case that the valve could not be oscillating in the simple mode where the Strap I' segments are alternatively positive and negative. The experi- I ments performed in Birmingham, at the beginning of 1941, on the effect of various internal dimensions on the resonant fre- quencies of a cold anode-block, together with the above observa- tions on oscillating valves, suggested that favourable interaction (c) between the electrons and the resonators could be obtained for strapping of magnetron segments' different modes. Fig. 4.-Illustrating During August 1941,Dr. J. Sayers, who until then had been pitch working at Birmingham on high-power , became The distance between the castellations is twice the segment interested in the problem and, using an 8-hole block of the so that alternate segrnents are 'bridged together. Echelon small E1198-type, examined the waveiengths of the principai modes strapping is shown in Fig. 4(b) and here. fhe straps are jig punched of oscillation. This was done by feeding jnto the anode block U-shâped eopper bent to shape in a and into depicts another aûange- a sma1l amount of c.w. radio-frequency power from a tunable small holes in the segment. Fig' 4(c) 932 BOOT AND THE CAVITY MAGNETRON ment of straps for an eight-segment valve. The dotted straps mately inversely proportional to its length whilst the capacitances are those at the remote end of the valve and it can be seen tliat would be nearly proportional to the length; and, if the frequency the amangement is symmetrical about a diameter through the of oscillation depended on these factors alone,. it snouta Uê cathode leads. Such symmetry is desirable to avoid capàcitive nearly independent of the anode lêngth. In the course of a pick-up ofr.f. power on the cathode leads. very comprehensive series of experiments, kofessor J. C. Slater These suggestions were quickly put practice . into at Birming_ has shown that this is not the case. In.a typical experiment on ham by using a modification arrângement of the shown t an 8-hole block it was found that for an anode length of 2 Fig. 4(c) but suitable for cm a l0-hole valve already under con- and an end-space depth of 6rnm the waielengths ôf the fo* struction. From tve samples an average efficiency of 40/" was modes were:- obtained. The lowest efficiency obtained was 33/, u.,d the n: hieùest 501. The average efficiency of a number of unstrapped I Z 3 4 valves of this type wâs below 10 and such valves were p.oUabty \- ô^ t r\: t.0 9.6^i 9.7 9.78cm not working in the n-mode. When applied to an E1l9g_typè valve, efficiencies .of up to 65yowere obtained giving peak outjuts - Fof an anode length of about 4.4cm, the wavelengths of all of over 150kW, whereas the highest efficiencies àbtained with four modes lay between 10.3 and 10.35 cm whiÈ for 'an this type of valve uns{rapped were 4045i/.. anode 6 cm long the wavelengths were:- These increases of output-power were perhaps the most ti, striking outcome of the use of strapping, but the môst important tt: I z 4 effect was the almost complete freedom from mode jumping (frequency jurnps). À: 10.8 10.6 llfsz to.5ocm The increase in power is really a seco.râar! \ effect of strapping for, due to the removal of other modes, it is It will be noticed that the order of th\modes in the wavelength possible increase to the anode current and voltage without spectrum has been reversed and a sirnilar effect is produced coming too near to the operating if conditions for anoiher mode. the anode length remains fixed whilst the depth of end space is {. Ilh9l the steepness ofthe current/voltage curve at fixed magnetic increased, l teld is considered it is obvious that a comparatively small .huog" This behaviour has been explained qualitatively from considera_ ' i" t!" wavelength of the adjacent mode and its âccompanyiig tion of an equivalent lumped-constant circuit at Birmingham. small change of threshold voltage ' may make un enormoui It was found, by variation of the magnetic coupling coeffiiients change to the power input possible. between resonators, that reversal of the order: of the modes Numerous types of 9-10 cm , valves were tried using straps and occurs when the coupling coefficient reaches a critical value . rn most cases were successful; experiments at 3 cm however were depending on the ratio of the slot capacitance to the segment_ not initially successful. ÊIere the problem was far more diffcult, "earth" capacitance. because at that time 3-cm valves were larger in terms of thé A valve in which all the modes have almost identical wave- operating wavelength, and it was thus impossible to make the lengths is unlikely tô be efficient for, if only one mode is excited straps short compared with a quarter wavelength. AIso, due directly by the electrons, ihe frequency produced will give,rise to the uncertainties concerning the electronic behaviour of 3_cm to large oscillations of the block itself in other modes, and the valves, designs were produced and strapped for the z.mode r.f. voltages produced'on the segments will react back on the when actually it was almost impossible to reach the zr-mode electrons. Also, from electronic calculations, it is known that operating conditions later established by Hartree's work. When tw9 modes n, apd n., wavelengths- À, and à2, will th-is was realized, attempts were made Jhe lqu-g to strap valves for the have similar operating conditions if zrÀ, : nrÀr. tn thii' case nl2modeby" earthing" each -oieration end of one set of alÈrnate segments. trouble due to mode jumping, or continual the This too failed, due possibly in to the fact that such strapping unwanted mode, may result. These represent the two conditions could oniy be effective if a standing wave alone existed in thé which should be avoided in the design of any néw magnetron block, as it did in the cold-block resorrunc" experiments of and it becomes more difficult, when valves of large size are Sayers. For these reasons the fust 3-cm valves used by the required, because increase in anode length usually reJults in less Services were, like the first 10-cm Service valves, unstraiped. mode separation, and increase in diameter (often accompanied Successfully strapped 3-cm magnetrons are, of-course,-iow by more resonators) produces the same effect. available, but these have only been made possible by a reduction Consider now the effect of strapping alternate segments by ln physical size so as to approximate to a scaleôdown 10-cm echelon strapping. When oscillating in the z-mode each valve. strap joins.a pair of segmelts having equal potentials and crosses à For completeness it is worth considering, , irr more detail, the segment of equal but opposite potential. There will thus be behaviour of an 8-hole unstrapped block in terms of its various no net current along the strap but a reactive cuûent will flow dimensions, so that the effect of strapping on the wavelength into each end to the small condenser formed between the centre distribution of its principal modes .nay Èe àemonstrated. If we of the strap and the segment below it. The only effect of the regard the block in terms of ordinary lumped circuit con_ current will be to increase the wavelength of the mode above its stants then we should expect the wavelengths to depend on unstrapped value by an amount depending on strap the foilowing:- the capacitance. If the length of the strap was infinitely small ihii (a) Resonator inductance, determined by its length and would be the onty effect of strapping and the'other modes would diameter. not exist. (ô) Slot capacitance, determined by its length, width and. With tnite strap length the next mode, say 3 for an g-seg- radial depth. n: ment block, must result in a difference in potential between the (c) Capacitance between each segment and cathode and to ends of some of the straps and consequently current will flow other segments, etc. along the strap in addition to the reactive current. If the strap (d) Coupling coefficients k arising from mutual inductances length is small its inductance will be small and, in order tô between each resonator and other reJonators. maintain the required potential difference between its ends, (e) The mode of oscillation specified by $ or n. either a very large current must flow in the strap or else the The resonator inductance would be expêcted to be approxi_ frequency must be increased. The current is limited bv the ) t. Tr{E cAwrY MAGNETRON 933 BOOT AND RANDALL: i i (6) THE CV64 MAG.NETRON I .relative impedances of the two alternative paths pfovided by the Tneed arose a strapped t straps and the resonators and so the wavelength of this mode In the autumn'of 1941 an urgent for airborne A'I. equip- will tend to be reduced. The reactive current will tend to increase 9.l-cm magnetron for,use in an improved power available in an aircraft the wavelength as for the a'-mode but to a lesser extent due to ment, A.I. Mark VIII. Since the + the smaller potential difference between the centre of the strap is necessarily limited, and as it is destable to have the minimum and the segment below it. Thus the final wavelength of this possible adjustment in the event of a valvé having to be replaced, I outset. mode will depend on the relative values of the two effects but the operating conditions were closely specified at the I should be less than even if no change in wavelength is produced an increased separa- It had been decided that the anode voltage t( peak-power more than tion between the n : 4 arrd n: 3 modes is obtained. 14 kV at I 350 gauss, the input not Similar arguments can be applied to the z : 2 and n: 7 150 kW, and the peak output not less than 35 kV/. modes. For n : 2 an even larger potential difference between A general investigation of 10-cm strapped valves had already the ends of some straps is required than for n : 3 and the been undertaken by the authors and in the light of the above reactive currents will be smaller so that this mode is more easily requirement the programme was directed towards designing a reduced in wavelength. For z: 1, the' potential difference suitable valve, resulting in the 8-segment echelon-strapped valve, along the straps is on the average similar to that for n : 3, but 8M717. This valve was later given the type number CV64, since been manufactured extremely large numbers. lo in the z : 3 mode each strap crosses a segment of opposite and has in designed t" polarity whilst for n: I the strap is of the same polarity, but The CV64 was the first strapped malpetron specifically I not potential, as the segment which it crosses. Here the reactive for a Service application. \ general different current will be much less and considerablereduction inwavelength In the course of the investigation, thirteen All were p'f the hole-and-slot type I' results, designs were investigated. The increase in mode separation is a measure of what is known having from eight,to twelve resona{ors, and anode diameters most 1., as "the tightness of strapping." A valve may be more tightly ranging from 10' to 28:mm. The type which seemed strapped by the following changes:- suitable CBM717) had eight resonators and anode and cathode )t. diameters of 16 and 6 mm respectively; all other designs being (a) Reduction of strap length. rejected as a result, either of unsuitable operating conditions, l' jig- t (ô) Increase of strap cross section (to reduce strap inductance). or of mode jumps in the operating range. By the use of Y (c) Attachment of straps near the inner ends of the segments. made echelon straps of 24 s.w.g. copper wire it was possible (d) Reduction of anode length. to make the wavelength of then:3 mode as low as 7'5cm. This alone was an indication that the valve was fairly tightly Slater investigated the effect of (c) and (d) on mode separation 'strapped, arid consequently variation in strap dimensions pro- and some typical results of varying the point of attachment of duced comparatively large changes in operating wavelength. the straps are shown in Fig. 5. It should bé borne in mind This difiiculty was at first met by jig-mounting all the straps, and the output-loop size was also accurately determined by r1.o means of jigs. This last process was made necessary because it was intended that the A.I. set should use the same aerial and mirror for both transmission and reception' During the i to.5 quiescent period between outgoing pulses the cold impedance I 'i of the magnetron, viewed from the coaxial lead, had to lie within certain close limits, because the position of the mixer tapping L and T.R. on the aerial line was dependent on the mag- i to.o L netron cold impedance. In developing a method of measuring the cold impedance Ë I t) suitable for use under factory conditions, S. Devons of the I - 9'5 Telecommunications Research Establishment introduced a i -c D magnetron by bending l: t], method of adjusting the wavelength of the I É the straps. ) g'o * In the case of the CV64 a small amount of c.w. power is fed from a variable-fïequency oscillator into the magnetrot output 6 - lead through a short length of attenuating cable (about 10 db). I = The magnetron output circuit, which in this case was â short \ length of I;f-in concentric line fitted with a single quarter-wave slug, has a longitudinal slot cut in its outer conductor. The I probe of a crystal standing-wave detector projects through this slot, and from a knowledge of the position of the standing-wave minimum and the standing-wave ratio it is possible to measure the cold input impedance of the magûetron as a function of 7.5+ frequency. (a) As the frequency of the oscillator is varied over a range containing the resonant frequency of the magnetron block, the Fig. 5,-Wavelengths of resonant modes of 8-pole magnetron. position of the standing-wave minimum changes by something (a) U$trapped. the actual amount depending on (àHe) with increasiag tigbtness of straps' iess than one halfa wavelength, the coupling to the block and the impedance transf,ormation that this experiment necessarily involved some change of strap occurring in the output stem. A curve relating the position of length, but it can be seen that the modes are well spaced and the standing-wave minimum against wavelength shows an that the wavelength increases with n, making it easy to avoid inflection at the cold-block resonant wavelength and enables its the condition nrÀy: n.r\r. value to be found, A curVe of standing-wave ratio against 934 BOOT AND RANDALL: THE CAVITY MAGNETRON wavelength shows a minimum (i.e, most nearly matched) con- It is impossible to deal fully here with the work of any one of dition at the wavelength. these teams but a brief outline olProfessor Hartree's work cannot is fortunate that the It operating frequency of a magnetron is be omitted. i appreciably different from the resonant frequency of the block. The discovery of the so-called hig$-field operating conditions In the CV64 the operating frequency is roughly 0.5/" lower for a magnetron at Birmingham ha{ enlarged the discrepancy than the resonant frequency; as a result, the rate of change of between the experimentally observed operating conditions and cold impedance with frequency is not large, as it would be at the those expected from current theory, and the question arose as block resonant frequency, and it is not difficult to fix the position to whether the circulating cloud of electrons produced a magnetic of the T.R. switch along the output line to obtain correct opera- field comparable rvith, but in opposition to, the applied field. tion for all valves of a particular type. This position can be This problem was one of the first tackled by Professor Hartree's obtained from the curves. team, and whilst.it was shown that the fleld was small (not more The method may be used for pre-setting the wavelength than 3l of the appiied field) the calculations were of use in generated by a strapped valve before the end-plates are sealed deciding the potential distribution in the anode-cathode space of on if both the difference between operating wavelength and a single-anode non-oscillating magnetron rvorking under con- block resonant wavelength and the shift in wavelength due to ditions of space-charge limitation. Unless this potential dis- removal of the end plates are known. It is then only necessary tribution were known it would not be possible to calculate to bend thè straps until the position of the minimum reaches a electron orbits in either a non-oscillating or an oscillating predetermined point when the oscillator frequency is equal to the magnetron. required block resonant frequency. A somewhat simpler method The method by which orbits, anfl consequently electron dis- uses a fixed standing'wave detector and then, if the oscillator tributions, were found involved the aË6umption of the dimensions power is constant, the straps are bent causing the minimum and operating conditions of the mdgnetron together with the in the coaxial line to approach the crystal probe until the crystal amplitude of oscillation of the segmilnts. Most of the early current reaches a minimum value. calculations were done for an 8-hole iO-cm magnetron of the Both of the methods have been well tried on many thousands E1198-type as the operating conditiond for this valve were well of mapetrons by comparatively unskilled female labour. In established. To derive the potential distribution in the presence Table I are given the results of the first batch of CV64 mag- of a large space-charge involved a process ofsuccessive approxi- mations. The method of calculation is now well known and was Table 1 originally devised by Hartree for the study of electronic orbits in atoms. It is usually termed the "self-consistent ûeld method." Predicted transmirting wavelensth e.o, (cm) I JLllÏ; i . In the magnetron problem-.an initial distribution of electric l*i,il,iii,tË,nl ;;;;:d- | !:l=lser and. teid is assumed and orbits are calculated for this These mea-sured field. at 400 crs I initial orbits enable the charge distribution to be found, giving After ad- Àfter andl3j0 lwavelengtù, justment clamping rise td a field of its own which, superimposed on the initially assumed field, gives the final field. This process is repeatéd with the corrected field until the initial and final fields agree 107 I 9.00 9.095 9.095 sufficiently well. In Fig. 6 the electron distribution found in an 106 9.08 I 9.097 9.097 eight-segment magnetron is shown one particular instant. , rr0 I 9.18 9'105 9'103 at 108 I 9.11 9'095 9.097 The square-shaped is found to rotate in the direction r 11 I 9.21 9. r05 s.110 9.105 indicated by the arrow and whilst the distribution does not 112 I 9.1 I 9.095 9'100 9.098 change greatly, individual electrons move relative to the whole 109 9.09 I 9.093 9'092 pattern. Each curve shown in Fig. 6 represents the position 114 9.095 9.099 of IS.OS points 1r3 I 8.85 9.102 9.103 9'1,O4 electrons leaving diferent on the cathode at a particular r05 I 8.95 9.098 9.098 9.097 instant previous to that depicted by Fig. 6. The curve nearest r15 I 8.78 9.A99 9.102 9-097 the cathode represents electrons which were emitted one quarter 118 I 8'99 9.102 9.110 9.108 of a period earlier.and consequently have not yet reached the 116 I 9.16 9'100 9-104 9.104 t17 I 9'01 9.102 9.105 9'104 region in which there is much effect from the oscillating segments. rle | 8'ee 9. 101 9. 105 9.106 The curve showing maximum radial extension at the corners of the charge cloud is for electrons emitted two periods earlier and these have already reached.the anode, as have those starting netrons which were made early in 1.942 by the British Thomson- lf, periods earlier. Houston Co., Ltd., and in many ôases it can be seen that errors In Fig. 6 the amplitude of oscillation of each segment about its of only one megacycle/second are involved between predicted mean d.c. potential has been taken as one half the d.c. anode and observed operating wavelengths. potential, the anode and cathode diameters are 16 and 6 mm A considerablç number of the early samples of this valve respectively and the anode potential and magnetic field were were made by the Magnetron Production Unit in the Birming- taken as 10 kV and 1 050 gauss respectively. ham University Physics Department and tested in the laboratory The methods used to obtain Fig. 6 are not, ol course, con- before despatch to the Telecommunications Research Establish- venient to use in predicting the operating conditions for a new ment, but pre-production quantities were supplied by the electrical magnetron and no explanation is given as to how electrons industry within a remarkably short time. reach the anode lvhen the oscillation amplitude is very small- as it must be during the initial build-up of oscillation. (7) THEORETICAL WORK This problem was later disposed of by Hartree by considering Since the early part of 1941, a very large amount of theoretical the effect ofthe rotating electric field on the rotating space-charge work has been carried out,-ilainly by two teams in this country cloud. It is known that in an oscillating magnetron there is a under Professor rD; R. Hartree, F.R.S., at Manchester and fairly extended range of operating conditions over which the Frofessor E. C. Stoner, F.R.S., at Leeds, and by Professor J. C. magnetibmsi'will work.in a given mode. The extent of this Slater in the United States. r range depends on many points, some of which are dealt with BOOT AND RANDALL: THE CAVITY MAGNETRON 935

t

) ; t

I t. - !., I

L

1 i l

I t, x I ù I

Fig. 6.-Electron distribution in an 8-segment magnetron. Iater. lt was shown mâthematically that exact synchronism between, say the outer edge of the space-charge cloud and the rotating potential wave was not required, but that operation would continue, when started, over a range of angular velocities È1.È of the cloud. The lower limit depended on the amplitude of tlE oscillation and it was possible to find a value for rvhich electrons i l; would reach the anode for vanishingly small segment amplitude l for any particular mode number z. Thus an anode voltage was l$ determined below which no cunent could reach the anode for a "" l^i given magnetic teld and this voltage has been called the threshold l.$ voltage. Fig. 7 shorvs the relation between the threshold voltage, mode number n; magnetic fieid /1, anode and cathode radii a and b and the wavelenglh À. f Alternatively the threshold relation may be expressed in lr equation form by:-

V,À, 2H^ (1 b2la2) 1 r miooæ:;:zim--fr- (5) where l', is the threshold voltage in kilovolts and n is the effective r-number of the mode. It is possible to use this diagram to determine the mode in which a magnetron is working; in this case the threshold voltage is taken as the anode voltage for which current just starts to flow although it is now known that the load connected to the T magnetron output has a small effect on this voltage. By the middle of 1942 the calculations of Hartree's group had given considerable insight into the operation of -.,magnetrons eH)\(l b2ldz) I1(gauss) x (l bzldzJ : ------in the 9- to'12-cm wavelength,region but large"disçrepancies ; .., - nlnê- 600 -- * bdtween calculated and meaiured bperating conditions existed "t 'magnetrons. Fig. 7.-Relation betweel threshold voltage and circuit constants for for 3-cm The angular velocity of the rotating vanous mode numbers. 936 BOOT AND THE CAVTIY, MAGNETRON

1 I space-charge cloud calculated from the observed operating con- SeomenLs ditions was found to be far lower than the angular velocity of I "i\r the rotating electric-field wave-pattern set up by the oscillating segments. This was so, even for the most slowly rotating wave corresponding to the z-mode and the discrepancy was much LJ Ll LJ greater possible I t] I] LI I for all other modes. of oscillation. ill iL] In May 1942, J. Sayers and H. Sixsmith measured the phase ,4r : ol e r3 : relation between adjacent segments in an oscillating 3-cm mag- netron having either 12 or 16 segments. A special valve was used which had, in addition to the normal output lead, auxiliary I output leads loosely coupled either three o to or five segments, j The magnetron was loaded in the usual way by feeding a circular 5, wave gulle ôl il via a coaxial line from the main output lead of the -l valve. The wave guide was telescopic and ter- wai carefully f. I minated by a radiation load so that no appreciable standin! èlot ll. wave was produced in the guide, A fraction of the power transmitted along the guide was taken from a small probe t. 8 ': extending into the guide, at a fixed distance from its open I (loaded) end, and was fed into a resonant crystal detector. The l, detector could simultaneousiy be fed with power from any one i of the auxiliary output leads of the magnetror. By variation of I' \ the length of the telescopic section of wave guide the rectified I I current from the detector could be adjusted to minimum, \ I indicating that the two r.f. currents feeding the detector were in I

L anti-phase. This condition can be found for each ofthe auxiliary _ tt , outputs in turn and the differences between the lengths of wave , guide required in each case gives a measurement of the phase Fig. 8.-Potential distribution for a l2-segment magnetron, difference between the corresponding segments. means By this it was shown that the 3-cm magnetrons were same direction as the whole pattern but the next spaciçl harmonic, not operating in the zr-mode, but equally important, that the n: 9, rotates in the opposite direction rvith one third of the direction of the rotating anode-potential wave was opposite to angular velocity. The complete wave is made up by the spacial that of the rotating space-charge cloud. As the condition for harmonic n : 3,9, 75,27, etc., and theharmonics n : 3,n: 15, the maintdnance of oscillations was at that time assumed to be etc., travel in the direction of the resultant wave while n : 9, that'electrons should pass successive slots around the anode n:21, etc., rotate in the opposite direction. The angular phase at the same instant, two very different angular velocities velocity of each component is inversely proportional to its value were ii' . required depending on the relative directions of rotation of n. The waveform obtained by taking only the trst two com- of the potential ir wave and the space charge. With the opposing potents n:3, and n : 9 is shown by the dotted curves in directions ofrotations found, a lower space-charge velocity was il, Fig. 8 and this waveform.was taken by Hartree as sufficient required for modes other than the a.-mode and these velocities I approximation. corresponded much more nearly with the observed operating On computing the electron orbits when the rotation of the conditions. l space charge was opposite to the n : 3 wave it was found that This new viewpoint was quickly investigated by Hartree and the favourable interaction occurred with the n: 9 component I the exact mechanism of the interaction of the electrons with the I rotating with the charge cloud, and the counter-rotating n:3 rotating . l: field investigated in more detail. wave had very little effect on the orbits. The factor of three eariier iii In calculations of electron orbits it had been assumed thus gained in the value of the angular velocity of the electrons ,l that ) a sinusoidal variation of electric field round the anode was adequately accounted for the observed operating conditions of ii a close enough approximation to the truth. This was shown to 3-cm valves or for any valve working in modes other than the I be untrue at the anode surface itself but against this was the fact z-mode when the appropriate I vaiue for z was inserted in that higher spacial harmonics of potential distribution would equation (5). diminish pSeat I with rapidity on reieding from the anode towards The modification required by Hartree's earlier resonance the cathode. Also, it could be shown that a sinusoidal potential I criterion is simply that for electrons to be able to reach the wave rotating in the opposite direction the l to electrons had little anode for magnetic flelds well above cut-off and for vanishingly ll effect on the electron orbits and was certainly not capable of small r.f. amplitude, a certain degree of synchronism is extracting appreciable I energy from the electrons. required between the rotating spaæ-charge and one ol the Together with the above phase measurements this fact directed l spacial components of the rotating electric field in the anode- attention to a more exact expression for the potential wave in cathode space. i the anode. Fig. 8 shows the form of this potential 1l distribution It had been assumed in all the above orbit calculations that I at the anode surface of a 12-segment magnetron operating in the magnetron was already osciliating and the behaviorir of the the rl2 mode at three different instants separated by S periods. space-charge cloud examined undei the action of an impressed . The number of compiete waves round the anode will be three rotating electric field. This attack was justifled by the need for and so this mode is often called the n : 3 mode. The wave is explaining the existence of anode current in the oscillating shown advancing from right to left and since its form changes as magnetron at anode voltages far beiow the Hull cut-off value, it rotates it is not a very exact approximation to represent it by but the method was unlikely to give information concerning a simple sine wave.. .r, the mode of build-up of oscillations. ln a magnetron in which a If Fourier analysis of this spacial variation;of potential is a nuniber'of different oscillation frequencies are possible an made it is found that the fundamental n : 3 wave rotates in the exact knowledge of the build-up me€hanism is of great im- \ BOOT AND THE CAWTY MAGNETRON 93? bf tte possible modes of the portance in that it determines the mode-selection behaviour of (f) The values of the loaded C's resonator system. the valve. + preceding Section it is shown that relations between v From an investigation of the stability of the space-charge In the anode voltages and magnetic field have I cloud to small perturbations from axial symmetry, such as would d.imensions, wavelength, both for build-up of oscillations and for the com- be produced bi a vanishingly small rotating:field, Hartree was been obtained Less labour is generally involved ablè to show that a further criterion, other than the resonance or mencement of anode current. anode and measuring the frequency threshold criterion described above, had to be satisfied if oscilla- in making ait e;'r'rrmental modes than in attempting to calculate it and .tions were to build up spontaneously' distribution of tlie previous is of great assistance. The same Under certain cooditiôns the space-charge cloud was found to experience of loaded of the diferent modes but the be unstable to such perturbations and, in addition, to show is true for aetérmning @'s in strapping, etc., giving rise negatlve resistance Characteristics. The anode potential at effect of small dimensional changes wlich this occurred was found to depend on the dimensions, to asyrffnetry can be extremely complex. of the effect of these many variables has been magnetic field, frequency and the n-number of the pertuôation Some corrèlation provided and Copley and it is now considered that wave. by Willshaw phenomena during pulsed operation are somewhat . lf we consider the electrons rotating at a different speed from ihe occurring the rotating field each electron will be subjected to a periodic as--ifr"-uppfi"O follows:- the instability voltage for force ofangular frequency equal to n times the difference between voltage increases r\til reached. tlAt this point spontaneous i the two rotational angular velocities. .the relevant mode z is I space-charge clori$ will be produced and for ?i Also, it is well known that, for an eleætronic space-charge cloud, oscillations of the current to flow to the I there exists a critical frequency for €lectromagnetic waves these to be maintained it is necessarfrfor !:j This was earlier shown by Hartree to be impossible for impinging on the charge cloud. This liequency depends gnlV 9n anode. amplitude until the voltage is reached thË spice-charp density and a resonance effect occurs when the small oscillation lhreshold hiehei or lower than the instability criticàl frequency is equal to that ofthe periodic force acting on and this voltage may either be no current will flow until this voltage is r. the electrois paising throuefr the rotating field' When this con- voltage. If iiis higher, l' increase of anode potential the current dition is satisfied it ii found that the cloud tends to show negative- rea"h"d and on further t' gradually The current will be nearly resistance characteristics, so tending to cause oscillations to will increase from zero. between applied voltage and increase in amplitude. Thus a critical anode potential was proportional 1o the difference which oscillations may build up from zero threshold voltage. determined for than the instability amplitude. This potential is known as the instability voltage' If, however, ihe threshold voltage is lower passed the voltage at which the current Thâ relation between the instability voltage' dimensions, wave- voltage, we shall have the oscillation is there' 'length and mapetic field cannot be conveniently expressed in Ii-o* with small osôillations before "uo the instability voltage is reached-the current" an équation buiwhen plotted on a diagram similar to that shown Consequently rvhen at a value depending on the excess in Fig. 8 a number of slightly curved lines lying near'the corre- *iff tt"tt, rrôt nto, but ^t As the anode voltage and current are sponding threshold lines are obtained. voltage above threshold. - charge may become unstable for a The above conclusions were arrived at by Hartree's team by increàsed further the space as to prevent further a more detaiied process than outlined above' The actual diferent mode and may become so distorted If the threshold voltage for the impedance ofthe sface+harge cloud as seen at the anode surface operation in the original mode. opèration will commence imme- was matched to the impedance looking outward to the resonators, nèw mode has been reached then due to the voltage-regulation and its behaviour to perturbations ofthe cloud as a function of diately at a flnite current; ifnot, the voltage will suddenly jump to frequency was determined. The frequency was considered as properties of the modulator being complex in order to simulate oscillations of increasing the new threshold voltage. pulie the anode voltage is decreasing, amplitude. At the end of the where a different behaviour may result, giving rise to a f (8) MODE-SELECTION BEIIAVTOUR effect. Once oscillations have started it is only necessary that À Despite the great increase in knowledge of the mechanism of the anode voltage shall be above the appropriate threshold I determine with the applied t magnetron opération, it is still impossible to ' value of voltage so that oscillation will continue until cerâinty the iange of operating conditions over which a single voltage dropsio this value' If, in doing so, an instability voltage I oscillati,on frequency will be generated during successive pulses' is palsed, mode jumping may again occur if the conditions for At certain conàitioos the valve will suddenly jump to a different anode current in this mode are also satisfied. mode of oscillation and, in addition to the fact that the new Thus it is apparent that, in general, operation in any particular frequency will be useless in a deviæ using a sharply tuned mode is only pôssibie over a limited range of voltage and current ,..éiu..,-u large drop in output power occurs and is generally depending ô" ttt" relative values of all the possible threshold f aæompanied by a Jonsiderable increase in cathode bo1b-ard- and instability voltages. the magnetron may result from which Copley was a member, have deter- t- . ment. Permanent damage to ' Ilartree's tèam, oi this bombardment and, as the anode voltage may rise consider- mined the relation between the dimensions, wavelengths, and may I abiy due to a change in anode impedance, puncture of the fllament both threshold and instability voltages, and these relations stems may result in high-power valves. be used to determine what changes should be made to a valve )i It is now known that mode

are numerous cases in whicf, a.Vuive was found to work differently found that one of a degenerate mode-pair only produced very when feeding a water load in the laboratory from when it was small-amplitude oscillations in the 4esonator containing the loop. feeding an aerial through a Iength of transmission line or wave In terms of circuit constants, this id equivalent to saying that the guide. It is also known that the threshold and instability coupling coefficient between the oûtput loop and the block was voltages depends to some extent on the loaded @ of the parti- very small for that mode and consequently a high loaded e cular mode in question. In certain cases, occurring mainly in would result. Such a lightly loaded mode *ould be easiÇ .numbers magnetrons with. larger of segments, the relative excited once the critical potentials were reached and.Hartree's positions of closely-spaced critical voltages may be changed by calculations show that these potentials will be lowered by raising alteration of the load impedances, but it has so far been impossible the Q, making this mode even more probable. to calculate precisely the relation between them. In order to verify that variations in coupling coefficients were In order to visualize what may happen it is necessary to occurring, their values were measured in the normal way by reconsider the behaviour of the resonator system and outpuf determining the resonant frequency of each mode when the loop loop. terminals were effectively short-circuited and open-circuited. Taking firstly the N resonators alone,- either strapped or The values of coupling coefficient obtained for the u-mode unstrapped, we shall find Nl2 separate resonant frequencies (n: 6) were fairly constant for a qiven loop size and, in general, characterized by the number, n, of complete waves of potential were not greatly affecied by the rèmoval of one or two straps. existing round the anode. The value of z may take on values For the two degenerate n :5 modes, one was found to be from 1 to N/2 inclusive, the latter being the n -mode. If now a ioaded as heavily as the z-modelwhilst the other had a small coupling loop is inserted into one of the resonators, an asymmetry coupling coefficient ranging from zbo upwards. is introduced and each of the modes except n : N/2 will occur By removing one strap it was foùnd that either n : 5 mode at two frequencies separated by an amount depending on the could be heavily loaded depending crg the position from which size and type of asymmetry produced. These modes have been the strap was removed and if the corrçç-t two straps were removed called degenerate modes. The two members of a degenerate both z : 5 modes rvere loaded. These effects can be accounted pair gives rise to different distributions of voltage and current for qualitatively by observations ofrthe voltage pattern excited in the block as may be observed experimentally in a block being in the block, but as yet trial and error seems the only method of fed from a low-power variable-frequency oscillator. Each of tnding which.straps to remove. these separate modes has its own threshotd and instability voltage When applied to the working valve, in conjunction with an and as the wavelength separation for a pair is usualiy small output circuit having the correct frequency characteristics to their voltages are nearly equal. assist in loading the unwanted modes, the range of opeiation in Jt was known, as an experimental fact, that the omission of one the z'-mode was increased by a factor of nearly three over the or two straps round the anode at certain points often eliminated original valve. an unwanted mode. This was believed to be due to the large from the above it can be seen rhat the iarge numbei of lactors asymmetry produced, so distorting the potential distribution on controlling magnetron operation can sometimes be arranged to the segments that efficient operation in this ,mode was unlikely, act in a complementary manner in the flnal design. but it had been shown by Hartree that the efliciency of operation was quite insensitive to large departures from an ideal dis- tribution. (10) ACKNoWLEDGMENTS A more likely effect of missing straps has been found during the The work described in this paper would not have been possible design of a very-high-power 10-cm valve having 12 segments. but for the initiative of Profêssôr M. L. Oliphant, F.R.3., who IniJially, operation in the z-mode could only be obtained for very in the autumn of 1939 persuaded the authorities of t|e impoitance critical values of load impedance which involved high standing- of centimetre waves, ànd collected a team of research workers wave ratios obviously unsuited to high-power operation. expressly for the improvement of methods of producing such Methods were devised for measuring the impedance transforma- waves. The authors owe a great deal to him foi his encourage- tion occurring between the output wave guide and the terminals ment and inspiration througliout a difficult period. The authors ofthe coupling loop, and it was hoped to design an output circuit also u,ish to àcknowledge the valuable assiitance of R. E. Clay, sufficiently frequency sensitive that greatly increased .loading .W. T. Cowhig, T. Gardiner, J. p. Keene, H. Sixsmith, S. È. (i.e' iower Q) was produced from all the unwanted modes. A Smerd, G. Voglis, and C. S. Watt, as well as the technical staff great improvement in behaviour resulted but consistent operation of the Department so ably guided by S. F. Cornick, the laboratory in the z-mode could not be guaranteed from valve to valve. steward. A factor which could not be closely controlled, however, was the segment potential distribution, particularly for modes other (1I) REFERENCES than the z-mode. Experimental observations on e'cold" blocks (l) Journal of Àpplîed Physics, 1939,10, p. 321. showed' wide variations in this distribution and it was often (2) Journal of Applied Physics, 1938, 9, p. 654.