44 PHILIPS TECHNICAL REVriw VqL. 14, No. 2

MAGNETRONS

by J. VERWEEL. 621.385.16: 621.396.615.141.2

Split-anode magnetrons have already been in use for a number of years for generatingdecimetric and centimetric waves. In 1937 a radio telephone link between Eindhoven and Nij-megen (Holland) employing magnetrons and operating on a wavelength of 25 cm was estab-lishêd. During the period 1940-1945 great 'strides were made in the development of magne-trons; output power was increased by more than 1000 times and generation of waves of 1centimetre became a practical possibility. In this way the magnetron came to assume the mainrole in radar, and that this has had an important effect on war-time as well as peace-timeactivities is sufficiently well-known. In this article the working and construction of modemmagnetrons are discussed.

Some 30 years ago H u Ill) published an articleon the effect of an uniform axial magnetic field onthe motion of electrons between coaxial cylinders(fig. la). Although Hull spoke neither of oscil-lations, nor used the word magnetron, his work laidthe foundations for the use of the magnetron as anoscillator. Since 1921 a varying but none the lesssteadily increasing amount of interest was shownin the magnetron. Up to 1930 the oscillations pro-duced by these tubes were of little practical value,but from that time onwards there was a wide-spread increase in interest, as it was found that splitanodes (fig. lb) with resonators or transmissionlines between them were capable of generatingfrequencies with a high degree of efficiency. Pos t-humus 2) has contributed much towards thedevelopment of valves designed on this principleand his theory of the oscillations produced bythem is regarded as of pioneer value. In the four_years following his publication more than 100articleswere written on the subject of the magnetron, inall parts of the world.

In the period up to 1940 interest waned slightly,but in that year Boot and Ran d.al l ") carried outexperiments with magnetrons provided with cavityresonators (fig. le), and these experiments led tothe successful use of the magnetron as a transmittingtube for radar. Feverish activity ensued; outputpower was increased once more and some veryshort waves were produced. Important theoreticalwork was also submitted. To give some idea of whathas been achieved with these tubes, we may mention

1) A. W. Hull, Phys. Rev. 18, 31-57, 1921.2) K. Posthumus, Principles underlying the generation

of oscillations by means of a split anode magnetron,Philips Transm. News 1, 11-25, Dec. 1934; Oscillations ina split anode magnetron, Wireless Eng. 12, 126-132, 1935.

3) H. A. H. Boot and J. T. Randall, The cavity magnetron,J. Inst. Elec. Engrs. 93, 3a, 928-938, 1946.

that in recent years magnetrons have been madewhich operate at a wavelength of 3 cm, deliveringmore than 1000 kW peak output, and that othersoperate at a wavelength of 3 mm, supplying anoutput of several kilowatts 4). This power is trans-mitted in pulses varying in duration from a fewtenths of a microsecond to several microseconds,the repetition frequency being usually between500 cis and 4000 cis. Fig. 2 illustrates a modernmagnetron for 8.5 cm waves, delivering a powerof 400 kW peak.By far the most important field of application

of the magnetron to date is radar, after whichcomes diathermy, where centimetric waves arein some cases particularly beneficial. Anotherspecial field is to be found in the linear accelera-tor, an appliance for imparting enormous velocitiesto electrons for the purposes of nuclear physicalresearch 5).

In 1939 this Review contained an outline of thedevelopment of magnetrons up to that time 6); thepresent article is intended to provide a generalreview of modern màgnetrons which will at thesa~e time pave the way for later articles dealingwith special designs in this sphere. In the presentpaper we shall endeavour to answer the followingquestions.1) In what manner is the energy derived by the

electrons in the magnetron from the directvoltage source converted to H.F. energy?

2) To what conditions must theresonators conform?3) What kind of output system can be used to

draw from the magnetron the energy developedby it?

4) J., R. P i er ce, Millimeter waves, Electronics 24, 66-69,1951 (No. 1)

5) Philips Techn. Rev. 14, 1-12, 1952 (No. I).0) G. Heller, Philips Techn. Rev. 4, 189-197, 1939.

.__

AUGUST 1952 MAGNETRONS 45

Fig. 1. Various forms of magnetrons in cross section. K = cathode; A = anode. The fluxdensity B is perpendicular to the plane of the drawing and is uniform within the whole ofthe anode space. a) H uil magnetron. b) Magnetron with split anode, comprising foursegments (A" Az A2 and A4), Such magnetrons can have a very high efficiency.c) Magnetron by Boot and Randall. The anode is a solid block of copper with cavityresonators T cut in it.

A

KeBEI)

This will be followed by a few details regardingconstruction.It will be necessary to restrict ourselves to the

main essentials and to refer the reader to existingpublications 7) for a more detailed study.

Fig. 2. Experimental magnetron for a wavelength of 8.5 cm,400 kW peak output, with one of the covers removed. Behindthe magnetron will be seen the associated permanent magnet.

7) See e.g. G. B. Collins, Microwave magnetrons, RadiationLab. Series 6, McGraw Hill, New York 1947, and J. B.Fisk, H. D. Hagstrum and P. L. Hartman, Themagnetron as a generator of centimeter waves, Bell Syst.Techn. J. 25, 167-348, 1946.

A

T

K

c 11).1.')'

Motion of an electron in mutually perpendicularelectric and magnetic fields

In a cylindrical magnetron the electric field ismainly perpendicular to the magnetic field. Whenthe magnetron is oscillating, the electric field hasnot only a radial, but also a tangential componentand, moreover, the space charge of the electronshas a very marked effect on the motion; in con-sequence the theory is rather complicated. As thevarious computations that have been made arevery lengthy, they fall outside the scope of thisarticle and we shall therefore confine ourselves to ageneral outline of the electronic motion.Let us first call to mind the theory relating to the

motion of electrons in a uniform magnetic field, theflux density of which is denoted by B (in the z-direction of a rectangular system of co-ordinates),and a uniform electric field E perpendicular thereto(in the negative y-direction). We are then con-cerned with the electric and the Lor ent z forces.Analytically this is represented in our system ofco-ordinates by:

m dvx/dt = eVyB,m dVy/dt = eE - eVxB,m dvz/dt = 0,

where m is the mass of the electron, t is the timeand vx, vy and Vz are the velocity components alongthe axis.It is easy to verify the general solution of these

expressions, viz:

eB EVx = -a cos-;;; (t - to) + B'

46 PHILlPS TECHNICAL REVIEW VOL. 14., No. 2

eB 'Vy = a sin- (t-to),

m

Vz = b.

a, b and to are integration consta~ts. Furtherintegration gives us the equations for the electron .paths. If we assume that all co-ordinates andvelocities are zero at t = 0, we have:

E m E eBx=-t---sin-t. B e B2 m'

, m E ( eR )y = - - 1- cos - t ,e R2 m

z = O.

These equations represent a cycloid, as describedby a point on the periphery of a circle roiling alongthe z-axis with constant velocity E/B (fig. 3). Thediameter of the circle is (2m/e) (E/B2), and thisrepresents the maximum distance of the electronfrom the z-axis. The general movement of theelectron is perpendicular to the lines of electricand magnetic force [i.e. in an equipotential surfaceof the electric field) and the electron thus describesarcs to a height of (2m/e) (E/B2).

Now let us take the case of a plane magnetron,the cathode of which is formed by the plane y = 0and the anode by·y = d (fig. 4). As long as themagnetron does not oscillate and, disregarding the

7Q44B

_X

Fig. 3. Under the combined influence of a uniform electricfield E and a perpendicular uniform magnetic field (fluxdensity B), an electron emitted with zero velocity at thex-axis follows a cycloidal path. The average velocity in thex-direction is E/B.

space charge, the field between the cathode theanode. will indeed be uniform. If, as assumed, theelectrons leave the cathode with zero velocity, theywill move along the cycloidal paths mentionedpreviously. If (2m/e) (E/B2) > d, they describe onlythe first part of the cycloid shown in fig. 3 and are.then absorbed by the anode. As soon as (2m/e) (E/B2)< d, however, the cycloidal path is completed andthe electrons do not reach the anode. The magneticfield whereby the path just touches the anode is

. known as the critical field, the flux density of which

is denoted by Bcr. Hence:

,

2mEBcr2 = --,

e d

B _ .,/2m l'vcr-Ie s '

where V is the anode voltage.For a cylindrical magnetron, in which per-

fectly cycloidal paths are obviously no longerpossible, a. similar equation applies, VlZ:

(1) (2)

where Ta is the radius of the anode and Tk that ofthe. cathode. In a non-oscillating magnetron theanode current is therefore zero when B>Bcr.

Fig. 4. Electron paths in a non-oscillating magnetron withdistance d between cathode K and anode A (both plane):a) (2m/e) (E/B2) > d: paths end at the anode;b) em/.) (E/B2) = d: paths touch the anode;c) (2m/.) (E/B2) < tl: electrons no longer able to reach the

anode.

When the electric field is no longer uniform, butnevertheless still perpendicular to the magneticfield, as in an oscillating magnetron, the motionis more complex. Assuming the magnetic field to bestrong enough, so that the radius of curvature of thecycloidal path is small compared with that of theequipotential lines, the electric field in smallareas can be regarded as uniform. In that case, too,the electron, on an average, follows an equipotentialline. It is true that in the actual magnetron theradius of the circular motion is not usually smallin comparison with that of the equipotential lines,but the approximation is close enough to justify aqualitative representation of the mechanism.

Qualitative explanation of the occurrence of oscil-lations

In the event that B <Ben the magnetron be-haves as an ordinary diode and oscillation is notpossible. It will therefore be investigated whathappens when B>Bcr. In the absence of oscillationno anode current flows and the electrons followcycloidal paths, their general movement beingparallel to the cathode and anode. When oscillation

AUGUST 1952 MAGNETRONS 47

occurs the conditions are different; the electronsare then able to follow paths which do terminateat the anode; anode current flows and the magne-tron consumes energy. Let us now assume that thecondition of oscillation has been established in oneway or another, and investigate how such oscilla-tions are sustained.Let the number of anode segments be 2n and

assume the potentials between two adjacent seg-ments to be constantly varying in counterphase, asis usually the case. Fig. 5 shows the lines of electricforce of the alternating field at a givenmoment, in theevent offour segments. According to Posthumus,this stationary alternating field is equivalent tofields rotating in opposite directions; the twofundamental components of these fields rotatewith an angular velocity win or - win, where wis the angular frequency of the oscillation. Now, itis essential to the mechanism that the electrons besynchronised with one of these fields. The meantangential velocity of the electrons, as we haveseen, is E/B, An approximate expression for thesynchronisation can be based on the velocity ofthe electrons half-way between anode and cathode,disregarding the fact that the electric field isdependent on the radius T. The angular velocity isthen:

v E/B

Equating this with the angular velocity win, wethen have:

We shall refer to this equation again presently, butassume for the moment that it is satisfied by asuitable selection of the parameters.Let us now examine the interaction between the

electron and the synchronous field, assuming thatboth rotate in, ,say, a clockwise direction. Theother rotating field passes the electrons veryquickly; as this is an alternating field it will havealternately an accelerating and a decelerating ef-fect. The electrons will, therefore, perform smalloscillations about the average path, but these willbe disregarded. Let us first see how the electronbehaves in an area where the tangential field hasa decelerating effect (at A in fig. 6). As the condi-tion of synchronisation has been met, the electronwill remain in this zone. It js true that the alter-nating field is usually smaller than the steadyfield, but the effect may nevertheless not be ignored.

•704.50

Fig. 5. The alternating electric field in a magnetron with fourplates is a standing wave in the space between anode andcathode. This wave may be resolved into opposed rotatingwaves, or rotating fields. The electrons interact mainly withone of these fields.

The resultant E of the two thus forms a certainangle with the radial direction and, since theaverage motion of the electron is in the directionperpendicular to E, it will be seen that it is de-flected towards, and ultimately reaches, the anode.Disregarding the fact that the electric field strengthis dependent on the radius, the average velocityE/B of the electron, and therefore also the kineticenergy, will be constant. The potential energydissipated by the electron in passing to the anodeis thus not converted to kinetic energy as in thecase of normal motion in an electric field, but isimparted to the alternating field as H. F. energy.

(3)v~... A2

A~EW+

Ec E

E Ew

~B, <.Ec IV,

+

7()451

Fig. 6. The resultant E of the steady field E« and the alter-nating field Ew, at two points, A and B. The mean electronvelocity v is perpendicular to E. In a decelerating field Ew,v receives an outward-directed component, in an aceeloratingfield Ew, an inward-directed component.

48 PHILlPS TECHNICAL REVIEW .VOL. 14, No. 2

An electron in an area where a tangentialaccelerating field prevails (at B in. fig. 6) willfollow a path towards the cathode, since the fieldvector points in the other direction. The electronis accelerated by the H.F. field and is thrown·back to the cathode after describing one are ofthe cycloid. The paths of two such electrons aredepicted in fig. 7; it will be seen that the firstof the two describes a number of arcs (a), butthat the second completes less than a single are (b).The time required to describe one complete arc

Fig. 7. Interaction of an electron with (a) a decelerating fieldand (b) an accelerating field. Electrons (a) are in the fieldlonger than electrons (b), so that, averaging over all theelectrons, energy is supplied to the field.

is constant and is, according to equation (1), equalto (m/cB) . 2:n. Seeing that the electrons a are in thefield longer than the electrons b and thereforecede more energy than is absorbed by the electronsb, there remains a surplus, so that oscillation canbe sustained and energy can be delivered to anexternal system.It is, furthermore, a fortunate circumstance that

electrons in a magnetron are driven towards a zonewhere a field of maximum deceleration exists andwhere the energy transfer is as favourable as pos-sible; in effect, phase focusing occurs, as willbe seen from jig. 8, in which the resultant E of thesteady field E; and the alternating field Ew areshown at the points A as well as at the points Cand D, on either side of it. An electron situated át

C for example, because it lags, will be in a strongerfield than an electron at A. The mean velocity E/Bof such an electron will thus be higher until theother field is overtaken. At D the electrons arein a weaker over-all field E; they therefore movemore slowly until the field catches up with them.

In consequence of this, electron bunches occur atthe most advantageous point and impart H.F.energy to the field.

At this juncture we may point out the difference that existsbetween a magnetron, and an "inverted" cyclotron. In acyclotron the charged particles move under the influence ofa magnetic field and are accelerated twice per revolution by atangential electric field whose H.F. oscillations are synchro-nised with the circular motion. It would be possible to imaginethis process inverted, that is to say, a process of shootinghigh-velocity electrons inwards; they would then yield energyto an H.F. field at the slots and would thus he decelerated.This is certainly possible in the magnetron, but the mechanismis rather different from that just described; if the oscillationswere promoted by means of a suitable combination of potentialand magnetic field, this would result in oscillations of very lowefficiency. The angular frequency of the oscillations c?rres-ponds to that with which the cyeloidal arcs are traversedin themagnetron: w = cB/m. In the oscillatory mechanism of themagnetron this frequency is of minor importance, however;in this case it is the mean velocity E/B that is important,where E contains particularly the constant-field component,which is entirely absent in the eyclotron.

The electronic motion can be computed quantita-tively by iteration; the electron paths are calculatednumerically for given values of the direct andalternating anode voltages and of the magneticfield. From a sufficiently large number of paths thespace-charge distribution in the magnetron is thenobtained, •and from this follows a new potentialfield, which, in general, is different from the original.Further electron paths are next computed fromthis new field; these in turn give rise to a third fieldand so on. With a judicious choice of the originalfield, these successive approximations convergeupon the correct solution. In 1928 Hartree 8)employed this method to quantum-mechanicalpath computations in atomic theory and, duringthe last war, the electronic paths in magnetrons

70453

Fig. 8. The resultant field vector E at a point A, and at twoother points C and D on either side of A. Owing to the in,fluence of the radial alternating field, E is greater at C andsmaller at D than at A.

8) D. R. Hartree, Proc. Cambridge Phil. Soc. 24, 111-132-1928.

AUGUST 1952 MAGNETRONS

were computed in this manner under his guidance"].The result of such an iteration procedure as

applied to a magnetron having eight anode seg-ments is seen in fig. 9. The paths of four elec-trons emitted by the cathode in different phases ofthe H.F. oscillation are depicted in a system ofco-ordinates which rotates with the field. An elec-

co-ordinates, describes the same path within thesystem. The envelope embracing all these paths,shown by the broken line in fig. 9, represents theboundary of the space-charge cloud. This consistsof four "spokes", each of which lies roughly at thelocation of the maximum deceleration :field. Theyrotate together with an angular velocity wJ4, and

-- ........."'"I\

\\,,,,

" .....

.,.r--""

/

/.-/

'" /

Fig. 9. Paths of four electrons (a, b, c and d) emitted by the cathode K in different phaseswith respect to the rotating field, plotted in a system of co-ordinates that rotates with thefield. The actual field is constant with time. From a point on the cathode which rotateswith the system of co-ordinates, the same path is traced each time. The envelope of all thepaths is shown by the broken lines; this is the boundary of the space charge. The areas ofthe tangential field of maximum deceleration are shown by the lines .NI. The radial distancebetween the dotted circle and the curve fluctuating around it represents the rotating alter-nating field. (From an article by J. B. Fisk, H. D. Hagstrum and P. C. Hartman, BellSyst. Techn. J. 25, 195, 1946).

tron a emitted at an unfavourable instant returnsto the cathode; the three other, favourably emittedelectrons b, c and d proceed to the anode and, in sodoing describe a number of loops, Since the systemof co-ordinates is rotating, the :fieldis' constanE~Wi.th

. ~.time; hence every electron emerging fromf"'ihecathode surface at a point which rotates with the

9) C. V. D. Report, Mag. 36 and 41.

constantly pass those parts of the anode that arejust about to become positive, intensifying thecharge by reason of the induction. In this way theoscillation is sustained in much the same way asthat of a pendulum to which a pulse is appliedeach time at the correct moment. It is thus clearlyseen that the potenrial energy dissipated by the.electron and not converted to kinetic energy,becomes available as H.F. energy.

49

50 PHILlPS TECHNICAL REVIEW VOL. l4., No. 2

Characteristics' of the magnetron

In this section we shall trace the relationshipsthat exist between current, voltage, magneticfield, flux density, etc. . .We have already mentioned the cut-off condition

indicating the smallest flux density necessary foroscillation, viz:

1/8m 'iv

I Bcr = -;- Ta(1-'--'--Tk-2-jT-a-2-)....

Further, we nave derived the approximatecondition for synchronism.

A more accurately defined condition for syn-chronism (which will not he discussed here) is asfollows:

Hartree formulated a condition that has tohe met if the electrons are to reach the anode inthe case of an infinitely small H.F. field. Thisstates that:

W 2' (Tk)2/ m (WTa)2V>-TaB)l- - ,-- - .2n ( Ta) 2e n

In fig. 10 all these lines are shown diagrammat-

(2)

v

t c

//'

/'/'

/'/'

/'/'

""./'/'

/'/'

/'/'

a

B, -B

Fig. 10. The curve (2) representing the critical flux densityand the Harti:ee line (5) divide the V-B plane into threezones a, band c. In (a) the magnetron passes no current andno oscillation occurs. (b) is the oscillation zone; here thecurrent rises steeply with the voltage. In (c) the magnetronis no longer cut oITso that no oscillation occurs.Lines (3) and (4) represent the simple and the more accurate

conditions for synchronism respectively.For the equations oflines (2), (3), (4)and (5) see the formulae

of the same numbers.

(2)

ically, with the flux density B as abscissa and thevoltage V as ordinate. The "cut-off curve (2) is aparabola; the "simple" condition for synchronism(3) is a straight line through the origin, andHartree 's condition (5) produces .another straightline, parallel to the other and tangent to the para-bola. The more accurate condition for synchronism(4) is represented by a line located between the-other two straight lines and also lying parallel tothem.

(3)

A

70716

(4)

Fig. 11. 'Electron paths in a plane magnetron with cathodeK and anode A. .a) B slightly higher than Ber. The electron describes a largearc. As its velocity is zero at P, and as it can cede only littleenergy to the field mi its way to the anode, a large propor-tion ofthe potential energy which it possesses at P is convertedto heat. The efficiency is therefore only low.b) B much greater than Ber. The electron describes a smallarc. Onlythat potential energywhich the electron still possessesat P' can be converted to heat. The efficiency is now high.

(5)Lines (2) and (5) divide the V-Bplane into three

zones a, band C; if the voltage he increased for agiven value Bl ofthe flux density, each of these zoneswill be traversed in turn. At low potentials zonea is involved; the magnetron is then cut off, butoscillation is not possible, for the voltage does notconform to condition (5). When the voltage israised so that zone b is entered, oscillation canoccur. With further increases in potential the anodecurrent rises rapidly and, with it, the amplitudeof the oscillation. Usually a limit is then encoun-tered owing to, the fact that the cathode is unableto deliver more current. The oscillations, which areat a maximum in the region of line (4), decreasewhen the voltage is raised, seeing that the condi-tion for synchronism is then not met. In zone ccurrent may flow without H.F. voltage, the magne-tron is no longer cut off and no further oscillationoccurs.The efficiency of the oscillation is found to rise

when the flux density is increased (hence withincreasing voltage in order to remain on line (4)which represents the condition for synchronism).'This will be readily appreciated from the figure. Ifthe flux density B is but slightly higher than thecritical value Bcr, the conditions will be as showninfig.lla. As is seen from equation (1), the heightof the arc of the cycloid is not much less than the

AUGUST 1952 MAGNETRONS 51

distance from anode; to cathode. An electronleaving point P roughly at zero velocity stillpossesses much of its potential energy and canimpart only a small proportion of it to the H.F.field;' a large proportion is thus dissipated oncollision with the anode. The efficiency is thenrelatively low.

However, if B is much greater than Bcr, we seefrom fig. llb that the electron cannot lose morepotential energy than it still possesses at the point P'and as this is much less, less is dissipated and theefficiency is higher.A magnetron for a wavelength of 3 cm may in

this way yield efficiencies of 50%, which is muchhigher than is the case with klystrons or travelling-wave tubes. Electron bunching takes place inmagnetrons in the same way as in these othertypes of tube and, moreover, the bunching is syn-chronised with the wave in magnetrons as intravelling-wave tubes. The difference, however, isthat in the magnetron the magnetic field hasa phase focusing effect. As with an ordinary top, aforce in the one direction, in this case tangential,is converted to a displacement in the perpendiculardirection, i.e. radial. The velocity in the directionof the field remains the same; there is no dissolutionof the bunches, but the potential energy lost by theelectron on its way to the anode is imparted, inthe form of H.F. energy, to the alternating field, asalready stated above. Accordingly, almost thewhole of the D.C. energy is effectively used.The charaeteristics which are usually plotted for

magnetrons are combined to form what is known asa performance chart; the anode current is plottedhorizontally and the anode voltage vertically. Byvarying the voltage and the magnetic field thevarious points in the diagram are obtained. Theoutput power and efficiency are measured, andlines of constant flux density, power and efficiencyare drawn in after the manner of fig. 12. The dif-ferent phenomena which we have just describedthen become apparent. The anode voltage isroughly proportional to the flux density and de-pends but little on the current strength ..Efficiencyis increased with the flux density, as already pointedout. Further, the efficiency is to a certain extentdependent on the anode current; with high valuesof the current, efficiency is impaired, since thespaoe-charge then disturbs the phase focusing.

In the direction of higher voltage and current theperformance of the magnetron is restricted by thecathode emission, disruptive discharges in the tubeand by the maximum magnetizing force which themagnet is capable of producing. For normal use,

magnetrons are equipped with a permanent magnet(fig. 2), for which reason only those points in theperformance chart can be attained which lie on aline of constant flux density.

7()4.9

kV "",t.~~ _40%30 O.62Wb/m2~~_ , ...~. _

V \ ...:. .....

t O.55Wb/~ ...,__ -- ---- %. ', .............-._ ' "" ---_ ....".,..20".__ ....::-:..-::_-

20 41Wbjm2 .................... ........ ....... .......

O'27Wbk2 __ .......... ---- ..... ------~~-~-_10

~~---~~n-----4~0~---~ro~---~OO~---~700~---~7~A-1

Fig. 12. Performance chart of a magnetron for a wavelengthof 3 cm. The current is plotted horizontally and the voltagevertically. Lines of constant flux density (expressed in Wb/m2),

constant power (in kW) and constant efficiency (%) areshown in the chart. This particular chart was prepared froma magnetron having 18 cavities; rk = 0.32 cm; r, = 0.52 cm;anode length = 2 cm.

Resonators

The H.F. energy occurs mainly in the resonators,where it oscillates in the form of electric and mag-netic energy. The resonators determine the wave-length and also serve as reservoirs for the energy.A portion of the energy in the resonator is fed tothe aerial or to another form of load.

Prior to 1940 the preferred form of resonator wasa two-wire transmission line. In two-plate magne-trons the two anode sections were connected directto the two wires (fig. 13a), whereas in magnetronswith four or more plates connection was establishedin pairs by means of the shortest possible leads, tokeep the pairs at the same voltage; the transmissionline was then connected to these leads (fig. 13b).

L

70458

Fig. 13. a) Two-plate magnetron with transmission line L.Tuning is effected by means of the shorting bridge k.b) Four-plate magnetron with plates connected in pairs:The transmission line is welded to these connections.

52 PHILlPS TECHNICAL REVIEW VOL. 14-, No. 2

Present-day magnetrons usually work with severalresonators in the form of cavity resonators, cutout of a solid block. of copper which serves asanode. The dissipative and radiation losses in suchresonators are smaller, the dissipation of heat isgreatly simplified and the resonators can be mademore easily with a sufficiently high degree. ofaccuracy for use on short wavelengths. Conven-tional forms of magnetron anode are depicted infig. 14.

certain limit. In any case IJ must be greater thanHcr and accordingly cannot he reduced ad libitum.E must not be too high' either, or wc run intoimpractically high voltage "values (50-100 kV).A fairly large. number of cavities is thereforeunavoidable.

As the cavities are mutually coupled via theend chambers and the central hole, the wholesystem has a series of natural frequencies, number-ing n + 1 in a magnetron with 2n identical cavities.

Fig. 14-, Anode blocks for magnetrons (shown in cross section). The cavities consist of(a) holes and slots; (b) sectors; (c) slots.

In the case of resonators consisting of holesand slots it is still permissible to speak of lumpedinductances and capacitances. The capacitance iseoncerrtrated particularly in the slots and we mayalso refer to a certain potential across the slots.The inductance may be localised in the holesthrough the walls of which the current flows. Inother forms of resonator it is not possible to makethis distinction.: but it is still true that the elec-tric :field is concentrated mainly in the region of theopen end, whereas the current is highest at theclosed end, the magnetic field therefore beingstrongest in the latter area. (The fact that thecapacitance and inductance cannot therefore heclearly distinguished, naturally does' not implythat ;the natural frequency and impedance of thecavity resonator cannot formally be defined byan '~effective" capacitance and inductance.)The number of cavities in a modern magnetron

is fairly large, being usually eight or more. In orderto deliver the required high current strength, thecathode is given a large diameter. The diameterof the anode is then also large, but the spacing ofthe cavities, which is roughly equal to (EjH) timesthe half-cycle, cannot be increased beyond a

70459

A system of two coupled circuits is able to oscil-late in two different ways; the oscillations may beeither in phase or in antiphase similarly, the modesof oscillation in a system of more than two coupledcavity resonators are distinguished by their mutualphase displacements. The phase displacement cpbetween two successive cavities is always constant;if there are 2n cavities, we find 2n times that phasedifference over the cavities in turn, round to thestarting point again, and this value must be a wholemultiple of 2n:

n2n cp = k·2n, or cp = k - ,

n

where k is any whole number. We then speak ofthe mode number k: For every value of k there isa natural frequency; for k = 0,1, 2 ...n, there aren + 1 different natural frequencies. When k =.n, cp = n and this is usually referred to as then-mode. Two adjacent cavities are then in anti-phase. When k > n, other modes of oscillationoccur, but the oscillation n + m has the samenatural frequency as n - m. Such modes of.oscillation are known as degenerate. The occur-rence of degenerate modes is due to the circular

AUGUST 1952 MAGNETRONS 53

symmetry of the anode block; the two field con-figurations are at a given moment images of eachother with respect to a given plane through theaxis. Under conditions of oscillation which aredegenerate, that oscillation may easily be excitedthat is not coupled with the electronic motion, andfor this reason magnetrons are designed to oscillateat the (non-degenerate) n-mode.

f

r

70460

1

'---<

II

Io 2 3 4 5

Fig. 15. Natural frequencies of a magnetron with twelveidentical cavity resonators. The number k of the mode ofoscillation is plotted horizontally and thc frequency i verti-cally, the unit being the frequency in of the :n:-mode(k = 6).In the vicinity of the zr-modethe frequencies are close together.

Fig. 15 gives an idea of the natural frequenciesof a magnetron with twelve cavity resonators;the frequency unit is the frequency of the n-mode.It will be seen that the natural frequencies arevery closely spaced in the region of the n-mode, andthe risk that the required oscillation will excitethe system in such a way as to produce other modesof oscillation is very great. This is detrimental toboth. the energy transfer and the efficiency, andefforts have therefore been made to find means ofincreasing the difference between the natural fre-quencies of the n-mode and neighbouring modesof oscillation.

Improvements Ln cavity resonator systems

One method of effecting such improvementconsists in fitting "s tra ps" between .those anodesegments which carry the same H.F. voltage, forthe zr-mode; in other words, all the even segmentsare strapped with' copper wires or rings and like-wise the uneven segments. Two methods ~f strap-ping are illustrated infig. 16.

From the aspect of the .zr-mode, these strapsincrease' the capacitance of the segments withrespect to each other. Only the charging current ofthe capacitance flows in the segments, since theextremities are at the same potential. Let the

combined effective capacitance of all the cavrtiesbe denoted by Ct and that of the straps by Cs;the wavelength is now increased in proportionwith 1"1+ (Cs/Ct), which immediately followsfrom the well-known expression for the resonantfrequency Jo of an L- C circuit, VIZ:

(1)2 LC= 1,

where (I) = 2nJo = 2nc/ Á (c = velocity of propaga-tion, Á = wavelength).

For other modes of oscillation, the voltage be-tween adjacent segments is lower and the effectivecapacitance Cs therefore smaller. (The same applieswhen extra capacitance is added to a transmissionline; the effect of this capacitance is greatest at thevoltage antinode and decreases towards the node.)Furthermore, current now also flows in the straps,seeing that the extremities are no longer at thesame potential. Effective self-inductance thenoccurs in parallel with the original inductance andthus reduces the overall inductance. Since bothcapacitance and inductance are lower than in thecase of the zr-rnode, the wavelength is also smaller.In this way it is possible to make a fairly clear

distinction between the natural frequencies of then-mode and those of other modes of oscillation,amounting to 5% or more, and it is accordinglypossible to prevent oscillation in undesirablemodes.Another method of modifying the spectrum of.

natural frequencies consists in making thecavities of unequal sizes, the most usual

\:

A

I

l2. '0401

Fig. 16. a) "Echelon strapping". Each anode segment isconnected to two others by means of a wire.b) "Ring strapping". The cross section AA is also. shown. Thering misses one segment, its bight being reduced at that point,and is attached to the next where it is higher. The ring abovethe anode block connects the segments p, and that below itthe segments q.

54 PHILIPS· TECHNICAL· REVIEW VOL. 14, No. 2

arrangement being tlie "rising sun" system depictedinfig. 17, which has ten large and ten small cavities., .

Fig. 17. "Risi~g sun" anode system with twenty cavities,alternately large and small.

Here, the 'wavelength of the n-mode lies betweentwo groups, one of which is roughly representedby the natural frequencies of the large cavitiesonly and the other those of the small ones. Fig. 18illustrates this in the case of a magnetron havingeighteen segments.

It is very difficult - or even impossible - tomake strapped magnetrons for wavelengths of lessthan 1 cm, because the straps would then have tobe less than 0.1 mm in thickness. For these milli-metric waves, "rising sun" systems are normallyused.

cm15

Àe 14x

t 130

12

11

10

9

8

'1

60

o

oo

o

2 3 5 6 '1 84_k

Fig. 18. Natural frequency ..1. as a function of the numberk of the mode of oscillation, for two different anode systemsconsisting of eighteen cavities, which have the same zr-modewavelength. The crosses refer to an unstrapped magnetronand the circlesto a "rising sun" system. (From the previouslymentioned article in Bell Syst. Techn. J. 25, 229, 1946.)

Output systems

The H.F. power is taken from one of the cavityresonators usually in one of the two followingways.

The first of these employs a loop coupled to oneof the cavity resonators and. connected to theinner conductor of a coaxial line. Between the innerand outer conductors there is a glass seal-which notonly provides the output terminal, but also hermet-ically seals the tube. Often, the coaxial portionis -coupled into a waveguide; sometimes, again,the end of the waveguide is soldered direct to the

. magnetron in the man~er shown in fig. 19.

7Q464

Fig. 19. Coaxial output system. The loop l is connected to aninner conductor which is attached to the outer conductor bby glass. The waveguide w is soldered to the magnetron.

70463

9

According to the second method a slot is providedin the rear wall of one of the cavities and the poweris taken from here direct to a waveguide, which,forming an integral part of the magnetron, alsocontains a "windo,v" which functions as vacuumseal. This method is illustrated in fig. 20 and it isemployed in many instances, e.g. when the poweris so high that there would be some risk of flashoverto the probe in the waveguide, owing to the highfield strength. Or it may be used when the wave-length is so short that it would be difficult to in-corporate a loop in the resonators.The coupling between resonator and waveguide

should preferably be such that the greatest possibleamount of power is delivered. It should not be tootight, however, for the frequency shift due to smallvariations in the impedance of the aerial systemmust remain sufficiently small. Many radar sys-

AUGUST 1952 MAGNETRONS 55

terns employ a rotating aerial and the rotationalways results in some fluctuation in the impedance.

Fig. 20. Cross section of slot coupling (diagrammatic). 1 =vacuum-tight window, 2 = slot, 3 = waveguide, 4 = oneof the cavity resonators.

A compromise between the condition for effectivetransfer of power (tight coupling) on the one handand that which promotes stability (loose coupling)on the other, is established by suitably dimension-ing the coupling gap. In principle it would bepossible to provide some matching arrangementoutside the magnetron, somewhere in the wave-guide, but the great objection to this is that it wouldproduce standing waves in the waveguide, be-tween the magnetron and the matching arrange-meD;t;such would tend locally to increase the fieldstrength, which in turn might lead to flashovers.Moreover, it is often required that the magnetroncan be replaced quickly, without the necessity ofhaving to make readjustments.The characteristics of an output system are

shown in a so-called Rieke diagram in whichthe frequency and output power of the magnetronare plotted as functions of the load. Every pointin the diagram corresponds to a certain load im-pedance "seen" from a fixed point in the outputline. A rectangular diagram could he employed forthis purpose, with the real and imaginary compo-nents as co-ordinates,' but it is preferable forpractical reasons to use the reflection factorand the phase of the reflected wave as variableswith polar co-ordinates 10)., The reflectionfactor and phase can, in fact, be measured direct-ly and, moreover, care can he taken in the designof the H.F. lines and aerials that the reflection

10) P. H. Smith, Transmission line calculator, Electronics 12,29-31, 1939.

factor does not exceed a certain value: The impe-dance is then kept within a given circle in theRieke diagram, the importance of which may heexplained as follows.Infig. 21 the reflection factor is plotted as radius

vector and the phase as an angle. Measurements of ,power and frequency are taken at numerousdifferent values of the impedance (i.e. differentsizes of radius vector and angle), and the Riekediagram is constructed by plotting the' curvesthrough the points of constant power or frequency.Itwill he seen fromfig. 21 that the power is high

in a certain zone, but that the variation in fre-quency with the impedance is also large. Theseconditions easily lead to instability. By varyingthe size of the coupling gap, the zone in question

Fig. 21. Rieke diagram of a magnetron for a wavelength of3 cm. The impedance of the load is plotted in a circular diagramThe reflection factor is represented by the radius vector;the phase of the reflected wave at any point is given by theangle between the radius vector and a fixed direction. In thisdiagram, lines of constant frequency (in Mcfs) and constantpower (in kW) are drawn. The overall frequency variationoccurring within the circle for a reflection factor of 0.2 isknown as the "pulling figure" (in this case approximately 12Mc/s).

can be displaced towards the centre, or away fromit. The amount of frequency shift is usually indi-,cated by the pulling figure, which is in effect thetotal frequency variation occurring in the magne-tron when the impedance value is moved roundthe circle representing a reflection factor of 0.2 inthe Rieke diagram. Both the pulling .figure andthe. output power are reduced when the width ofthe coupling gap is decreased. The particular corn,promise adopted depends on the application.

56 PHILlPS TECHNICAL REVIEW VOL: 14, No. 2

Constructional details

The cathode

The cathode of a magnetron has to meet somevery high standards. In the first place the currentdensity is great; in pulsed magnetrons cathodeloads of more than 30 A/cm2 are common. Further,at such current densities, in conjunction withanode voltages of 30 kV or more, the cathodemust not are, and it must be possible to dissipatethe heat generated by electronic bombardment inthe wrong phase (see above). These requirementsbecome so much the more rigid according as theoutput power is increased and the wavelengthreduced.

Oxide-coated cathodes are found to withstandloads of 10 A/cm2 surprisingly well, provided theseare applied in the form of pulses of about 1 fLsecduration; a cathode life of 1000 hours or more is byno means unusual, but it should be rememberedthat if the duty cycle is, say, 1 : 1000, a life of 1000hours means that the cathode has actually emittedonly for one hour.

In the case oftubes for still higher cathode loadsuse is often made of a cathode having metal gauzein the oxide coating, or a metallic powder sinteredover it which is coated with another oxide layer. Itis actually found that, if this is not done, heavycurrents result in such a large potential differenceacross the cathodc that disruptive discharges arclikely to occur in the coating 11). In consequence,the oxide coating will generally sputter; the gauzeor metallic powder more or less short-circuits thecoating and thus limits the potential differenccs.The L-type of cathode mentioned in an earlier

article 12) is particularly suitahle for magnetrons.Not only is the specific emission high, but theresistance of the whole system is,moreover negligible.Arcing is very much less in this type of cathodethan in others and the cathode is hardly heated hythe pulsa tory currents, in contrast with oxide-coatedcathodes, in which considerable heat is developedby these currents because of the high resistanceof the oxide coating 13).

In some tubes it is a disadvantage of the L-cathode that it consumes more heater power thanan oxide-coated cathode. For the magnetron,however, this is a decided advantage. Once the

") R. Loosj es, H . .J. Vink and C. G. J. Jansen, Thermionicemitters under pulsed operation, Philips Techn. Rev.13, 337-34.5, 1952 (No. 12).

12) H. J. Lemmens, M. r. lansen and R. Loosjes, PhilipsTechn. Rev. II (341-350, 1950).

13) E. A. Coomes, The pulsed properties of oxide cathodes,J. appl. Phys. 17, 647-654, 1946.

tube is working, the cathode remains hot when theheater voltage is reduced to zero, owing to the elec-trons striking it; it is therefore able to dissipate anamount of power equal to the heater power in theform of back-bombardment heat, which is a certainfraction of the input power. Owing to the higherheater power consumed by the L-cathode, theamount of D.e. input power of a magnetron withthis type of cathode can also he higher.

In the case of oxide-coated cathodes, good useis often made of the high secondary emission result-ing from the returning electrons. Magnetrons withthis type of cathode can he operated at a currentthat is a multiple of the primary emission. Sincethe coefficient of secondary emission of the L-typeof cathode is very much lower, the use of thiscathode means that the dependence on the pri-mary emission is greater.

Fig. 22 depicts the L-cathode as employed in amagnetron suitable for a wavelength of 3 cm. Theflanges at the ends are provided in all magnetronsto prevent electrons from straying towards theend spaces of the magnetron itself. Currents arisingfrom such electrons cannot produce any H.F.oscillation and thus result only in detrimentalheating of the end plates.

Fig. 22. L-type of cathode for a magnetron for a wavelengthof 3 cm.

The anode system

The manufacture of anode systems for magnetronsfor wavelengths of 3 cm or less is difficult becauseof the small dimensions of the system, especiallywhen the magnetron is strapped; the straps,which are not more than a few tenths of a milli-metre in thickness, have to be soldered in positionvery carefully. It will be appreciated that special

AUGUST 1952 MAGNETRONS

methods of manufacture have had to be evolvedfor magnetrons suitable for a wavelength of only1 cm, the linear dimensions being one third of thoseof a tube for a wavelength of 3 cm.

There are several ways of making magnetronswith cavity resonators in the form of sectors.The walls, which divide one cavity from the next,can, for example, be soldered to a copper outer ringwith the aid of special jigs or, again, the systemsmay be produced by electrolytic or casting pro-cesses, using a suitable matrix.We shall, however, describe III more detail

another method which is particularly suitablewhen large number of precisely similar anodesystems are to he made, even if these be of extreme-ly small dimensions, the method in question beingknown as hobbing. The anode shown in fig. 23 hasbeen made in this way. The "hob" consists of a steel"negative" very accurately ground to size. This"hob", mounted in a press, is forced into a solidblock of copper, the height of which is roughlyequal to the desired length of the anode, and thecopper is thus made to flow into the details of thehob, which is subsequently withdrawn.

57

a

b

The grinding of a taal of this kind is a lengthyprocess; it can be done automatically and withgreat precision on a machine which each timerotates the hob to the extent of one slot, after

Fig. 23. "Rising sun" anode for a magnetron [or a wavelengthof 3.2 cm, drawn three-fourths of actual size in cross and long-itudiria 1 section s.

which a high-speed grinding disc grinds out theslot to a certain depth. When the hob has completedone revolution the feed is automatically increasedand each of the slots is deepened. The leading endof the hob terminates in an obtuse point and theblock of copper to be hobbcd is recessed to receive

c d

Fig. 24. a) Hob. b) Copper block to be hobbed. c) After hobbing. cl) After turning. Thewaveguide is connected to the aperature in the side in (cl).

58 PHILIPS TECHNICAL REVIEW VOL. 14, No. 2

this. In fig. 24 the hob is seen at the rear and, infront of it, from left to right, blocks of copperbefore and after hobbing, and the same block afterhaving been turned down to the required dimen-sions for the magnetron. In order to protect thecavity walls from damage during the final machin-ing, the hobbed anode is filled with a thermo-plas-tic substance known as "Lucite", the essentialfeature of which is that it sets without the inclu-sion of any air-bubbles. After the turning operation

the "Lucite" is removed by means of a solvent. Somehundreds of anode systems can be made with asingle tool of this kind. Incidentally, waveguidesand coupling slots can also be produced comparati-vely easily by the same process.In conclusion we reproduce in fig. 25 two photo-

graphs of a hobbed magnetron with L-type ofcathode, for a wavelength of 3 cm. The performancediagram in fig. 12 and the Rieke diagram fig. 21,relate to this magnetron.

Fig. 25. Magnetron for a wavelength of 3.2 cm, to deliver 1000 kW peak. The right-handillustration shows the waveguide output connection; the coupling slot is seen through thewindow. The cathode of this magnetron is depicted in fig. 22 and the anode in fig. 24d.

Summary. This introductory article on magnetrons explainsthe motion of electrons when influenced by mntually perpcn-dicnlar electric and magnetic fields. A quantitative explanationof the occurrence of oscillations is given, based on the consid-era tions formulated by Pos th u m u s. A brief account isalso given of the useful effects of phase focusing, or formationof electron bunches, and of Hartree's met.hod of iterationas applied to the computation of electronic paths. Differentrelationships between the direct anode voltage V and theflux density B set a limit in the V-B plane to the zone in whichoscillation is possible. Mention is made of the performance chart.

The resonators employed with magnetrons now usuallytake the form of cavity resonators incorporated in the anode.Details of the spectrum of resonant frequencies resulting from

the coupling between the cavities are discussed, as well asmeans of increasing the difference between neighbouringresonant frequencies in order to avoid possible unwantedmodes of oscillation (strapping, or the use of the "rising sun"system of alternate large and srn al l cavities).

Output systems for magnetrons generally take the form ofa coupling-loop or slot in one of the cavities. The character-istics of such systems (inter alia the pulling figure) are ex-pressed in a Rieke diagram, an example of which is given.

Details regarding the design of magnetrons include thestringent requirements to whieh the cathode must conform(these being adequately met by the L-type of cathode), andthe method of manufacture of the anode block with cavityresonators by the hobbing process.

AUGUST 1952

PART OF THE PHILIPS VALVE FACTORY AT SITTARD (HOLLAND)

Photograph \Vuiter Nürnbcrg

59