JULY 1939 189

THE MAGNETRON AS A GENERATOR OF ULTRA SHORT WAVES

A magnetron consists of a cathode filament, a cylindrical anode, usually divided into anumber of sections, and a homogeneous magnetic field parallel to the filament. With sucha system two main types of oscillations can be generated:1) Oscillations with any relatively low frequency.2) Oscillations whose frequency is determined by the periodic character of the movement

of the electrons. In this case it is possible to distinguish between radial and tangentialmovements of electrons.

In the case of the first type of oscillations the frequency is subject to the same restrictionsas in a radio valve. In the second type these restrictions do not hold, and very short wavescan be obtained.

The generation of high power ultra short wavesin transmitter valves of normal constructionbecomes more and more difficult with higher fre-quencies. This is due chiefly to the fact that thetransit times of the electrons in the transmittervalves reach the same order of magnitude as theoscillation period of the waves to be generated.In addition, in the case of waves of several metresor decimetres, the necessary capacities and self-inductions of the oscillating circuits become sosmall that the required capacities and self-induc-tions in the transmitter valve and its connectionscause unwanted differences between the desiredand the actual circuit. These factors make it im-possible to generate shorter and shorter wavesefficiently, except by continually reducing the di-mensions of the transmitter valve. When this isdone, however, the voltages which may be appliedto the electrodes and the power which these elec-trodes can dissipate also decrease very much, sothat It becomes very difficult to generate reasonablyhigh powers in the range of the decimetre and cen-timetre waves.

In the above-mentioned range of wave lengths,where the transit times of the electrons spoil theaction of an ordinary transmitter valve, a quitedifferent type of generator of oscillations just beginsto assume satisfactory properties. In the case ofthese generators, which are called magnetrons, thefinite transit times are put to effective use by givingthe electrons an oscillatory motion by means of amagnetic field. This motion can be brought intoresonance with the high frequency oscillations whichwe wish to generate.A magnetron consists mainly of a straight fila-

ment as cathode, a cylindrical anode and a magnetwhich produces a homogeneous field parallel tothe axis. The anode cylinder usually consists of anumber of sections which are separated by slitsparallel to the axis, but oscillations can also begenerated in certain cases by a magnetron whose.anode is not divided.

621.385.16 : 621.396.615.14

Fig. I is a magnetron constructed by Philipswith four sections, which can dissipate 50 W. Withother numbers of sections fundamentally analogouscircuits occur.

In recent years important results have beenobtained by means of magnetrons, especially in the

Fig. I. A magnetron produced by Philips with four sectionswhich can generate 50 W.

r{lnge of decimetre and centimetre waves. At wavelengths of about 80 cm powers of the order of 100 Wcan be generated with the same degree of efficiencyas with normal transmitter valves on broadcastingwaves.

190 PHILIPS TECHNICAL REVIEW Vol. ~, No. 7

The oscillation phenomena in a magnetron showgreat variety and are by no means completely un-derstood in all cases. In most cases, however, oneis concerned with one of three relatively simpleforms of oscillation." These three forms will bedescribed in this article and in each case it will beshown how the electron motion is able to maintainan oscillation in' a connected circuit.In order to do' this, two points must first be

considered. We shall first examine' the generalconditions for the occurrence of an oscillation andthen indicate some of the laws of motion of elec-, '

trons in the electric and magnetic fields which occurin the magnetron.

The excitation of oscillations

We shall begin with a very simple mechanicalmodel, namely that of a mass hanging on a spring(see fig. 2) .We assume that the mass oscillates upand down, so that the tension on the spring variesperiodically., When l~ft. entirely to itself the os-cillation will stop after some time. When, however,the tension of the spring is changed in the correctway by suddenly shifting the point of suspensioneither upwards or downwards the oscillation willnot die out but. will increase in amplitude. Theupper curve of fig. 3 shows how the' amplitude ofthe oscil1ation can be increased. Whenever the de-viation of the oscillating mass is a maximum inthe downward direction, the point of suspensionis given it cert~in displacement in an upwarddirection and vice versa, so that the tension on thespring is slightly increased. In this way the am-plitude of the oscillation grows steadily larger.

It is now clear where the energy comes fromwhich is supplied to the oscillating mass. The workperformed by the point of suspension at each dis-placement is equal to the length of the displacementmul:iplied by the tension of the spring in the oppo.-

;-u

SI775M

Fig. 2.Mechanical model of an oscillator consisting of a máss.Msuspended on a spring. The mass can he made to oscillate by asuitable motion of the handle H. The electrical analogy isan L-C circuit which is made to oscillate by means of an ex-ternal circuit. The velocity v corresponds to the current' i,the velocity V to the current I, the tension S of the springto the electrical potential U on the condenser.

site direction. If the motion of the point 'of sus-pension does not take place in steps hut is con-tinuous (sinusoidal for instance) the energy suppliedmay be expressed by the product of the velocityof the point of suspension and the tension of thespring in the opposite direction. In order to in-crease the amplitude of an oscillation this energymust be positive, which means that ~he velocityof the point of suspension must he in opposite phaseto the tension of the spring.

::::F-·_·_·+-·-·_·-+-·-·-1-·_·_·f-_·_a

b Sf77£;

Fig. 3 a. Deviation of the handle of the model representedin fig. 2 as a function of the time.

b. Tension of the spring as a function of the time.

If now we pass over to electriè~l oscillations, i;e.to a circuit consisting of self-induction coils andcondensers, the tension of the spring correspondsto the voltage between the plates of the condenser.The motion of the point of suspension correspondsto a displacement of charges which changes thevoltage on the condenser; the velocity of this motionthus corresponds to the current in a circuit whichis . connected externally to the oscillating circuit.'The analogy is indicated more in detail in fig. 2.The condition for the maintenance of oscillationsin electrical terms ,is now that the current in -theexternal circuit must be opposite in phase to thevoltage hetween the plates sr the condenser, Itmust therefore be possible to consider 'the imped-ance ofthe external circuit as a negative resist-,ance.

Infig. 4 it is shown by means of the well knowninverse feed back amplifier connection how a:negative resistance can he obtained.

When the potenrialof the anode obtains a positivemaximu~ value, that' of the grid is maximum neg-~tive. The' grid, voltage varies in opposite phasewith the anode voltage. The' current from the anode,varies in rhythm with the grid voltage and thusin opposite phase to the anode voltage. ,The am-plifier valve therefore actually has a negative resist ...ance for the alternating components of the anodecurrent.The energy which is supplied to an oscillating

circuit is manifested as a reduced heating of the

JULY 1939 THE MAGNETRON WITH ULTRä SHORT WAVES. 191

anode. When, there is an oscillation in the Le cir-cuit, the ele~rons in the amplifier valve pass overto the anode chiefly at those moments- when theanode voltage. is lowest. The electrons are thus forthe most part retarded by the alternating voltage,which immediately gives rise to an increase in the

. alternáting voltage. .

/ .

0++II777

Fig:'4,. Circuit of an oscillator.

In more cqmplicated cases such as that çf themagnetron, a. consideration of the energy involvedin the manner indicated above is the best way ofjudging whether an electron tube is capable of. generating oscillations. The anode voltage consists, of a direct voltage and an alternating voltage deter-mined by the ~scillation in a conneètcd circuit.The ele'ctrons receive energy from the source' ofdirect voltage. An oscillation can be maintained, ifthe motion of the electrons is controlled by the alter-nating voltage in such a way that the electrons give. offpart of the energy which they receive from the sourceof direct voltage, to the source of alternating voltage.This will be the case when the majority 'of the elec-.trons are moving' against the electric field whichis generated by the alternating voltage in the valve. '

We shall apply this principle in dealing furthérwith the different forms of oscillation of the mag-netron. We must first, however, study the motionof an electron under the influence of an electricand a magnetic field.

The motion of' an electron in a homogeneousmagnetic field

A:iJ.electron moving in a magnetic :field experien-ces a for~e perpen~icular to the direction of th'emagnetic field and to the direction. of motion ofthe electron. Such a force normal to the 'directionof motion cannot change the absolute value of thevelocity of the electron and can only cause a curva-ture of its path. Since the velocity of the electronremains constant, the curvature of the path willbe the same at aU points in a homogeneous mag-netic field, in other words the electron describes acircular .orbit.

The radius r of the cirele is given by the con-

dition that the centrifugal force of the electron isequal and opposite to the force exerted by themagnetic :field. This condition may' be formulatedas follows (see fig. 5):

m v2 ,- .!'-_ = evIl" •r ,1.- - _,

(1) ,

where e =' 1.6· 10-20 coulomb, m = 0.91 . 10-27 g;H is expressed in gauss, v in c~/sec and r in cm.

v

"

.1778

Fig. 5. Forces acting on an electron in a homogeneous mag-netic field.

It follows from equation (1) that

7 V= 0.57 . 10- - .' '.H

(2)

The radius is thus proportional to the velocity vof the electron, and inversely proportional to themagnetic :field. From this. it' follows that thefrequency of th ec ir cu l a r motion is independ-ent of the velocity. The' angular frequency isnamely:

v eHw = -=-= 1.76·107B.

r m(3)

If a field strength of 100 gauss is taken, forexample, a frequency of280 megacycles/seo (107 cm)is obtained. This example already shows thatphenomena of extremely high frequency can occurin the magnetron.

When in addition to the magnetic field there isalso an electric field, the velocity of the .electronis no longer constant, but is determined at everypoint of its path by the value of the electricalpotential U 2). According to the 'law of the con'ser-

1) In the ordinary circuits the voltage V is not suppliedby a battery but by an R-G circuit so that the voltage Vautomatically assumes a suitable value.

2) It is hereby assumed that the initial velocity of the elec-trons at the cathode (U =.0) can be neglected.

, 192 PHILlPS TECHNICAL REVIEW' Vol. 4, No. 7

vation of energy the following is valid everywherein space: .

mv2 = e U,

2

from which; upon substituting the numerical valuesof e and m, it follows that

v = 0.594 . 108 -VUvolt .

From this velocity a certain magnetic deflection"follows,but in addition the electron is now deflectedby the electric field.

At a great distance from the filament' wherethe potential V is high and the electric field strengthlow, this additional deflection may be neglected,.and one finds according to equation (2) a radius

. of curvature:

, ru'r = 3.38 - . . . .. (4)

H

When the potential U is known for every pointir: space, then with the help of equation (4) a picturecan he obtained of the motion of the electrons. Al-though this picture is not very accurate because ofthe neglecting of the deviationby the electric field,various properties of the magnetron can be explained,with its help. For a complete picture, however, itis necessary to consider the electric field, at leastin, approximation. We shall do this by calculatingthe motion in. the çase of a homogeneous electricfield perpendicular to the magnetic field. On the. basis of the results we' may then discuss morecomplex cases in a qualitátive manner.

The motion of an electron in a magnetic and anelectric field

Let us assume that the electron is moving ina plane defined by the coordinates x and y, and thatthere is a homogeneous electric field E in the ydirection and a homogeneous magnetic field Hperpendicular to the plane in the r direction. Theequations of motion of the electron are the fol-lowing:

dvxmat = eVyH.

dv 'm dJ = e E _ e Vx H.

By. differentiating (5b) with respect to time we',obtain:

d2 V ' . dv'm--y=-eH~

dt2' dt

and if in this expression we substitute the value ofdvx .Tt from, equation (5a) we obtain: .

The general solution of this equation is:

eHvy =~a cos - (t-to), m (6)

In order to determine the other velocity componentVx we write equation (5b) in th,e following form:

m dvy EVx =_ -- -- + _:_

eH dt H '

dv 'and by substituting here __1: according to equa-

dttion (6) we obtain

. eH . EVx = a SIn - (t _ to) +_., m H

If we neglect' the last term in equation' (7), the'velocity components V:Ï; and vy .together define áci~cular motion with a velocity a and aIJ. angularfrequency w = eH/m, which is thus independentof the electric field. Thedast- term takes into ac- .count the influence of the electric field, and in-dicates that a translaiion with a constant velocity E/Hin the x direction is superposed on the circularmotion. This translation is perpendicular to thefield E and thus fol~ows an, equipotential line.In fig. 6 different forms of paths are indicatedwhich may occur in this way.

(7)

E a

b

c

~---------------------------- d

e;n77!J

Fig, 6. 'Paths ?f an electron in mutually perpendicular homo-geneous electric and magnetic field, with different initialcon-ditions:a) The electron leaves point P with a vertical initial velocity.b) The electron Ieàves with zero velocity.c), d), .e):.:rhe elec,t~onleaves with increasingly great horizon_. tal initial velocities. In case d) the horizontal initial veloei-is equalto EJH. . Y

193JULY 1939 THE MAGNETRON WITH ULTRA SHORT WAVES . 'The equations of motion (6) and (7) appear somewhat

strange because they express the fact that the velocity oftranslation of the electrons increases with .decreasing mag-, netic field, and would even becomeinfinitely great if the mag-netic field should disappear. This paradox does not, however,appear if the initial conditions are taken into account in thecorrect way. Let us ,assume for example that the electronleaves at the time t = 0 a certain point with the velocityzero. The equations of motion are then:

, E ( H )V., = H 1 - cos cm t ,

E . eHVy =,H sin -;;:;- t.

Let the magnetic field become very small; the sine and cosinefunctions can then be developed and we obtain:

cE lEe"'Vy = - t + -6 -3- H2 t3 + ...m m

At small values of H these expressions behave exactly aswould be expected. When H approaches zero only one termremains which expresses the well-known acceleration of anelectron in a homogeneous electric field. ' \

If the electric field, is not homogeneous themotion becomes more complex and it is impossible,to give a general solution of the equations of motion.When, however, the magnetic field is sufficientlystrong so that the circular paths become small,and when the electric field does not yet vary verymuch in the neighbourhood of th~ circular orbits,the electrical field may be considered to be homo-geneous locally, and one may thus conclude thatthe electron will on the average follow an equi-potentialline. This is indicated in fig. 7.

Eig; 7. Motion of an' electron in a two-dimensional electric.field and a homogeneous magnetic field in the direction of thethird dimension. The elec~ron~follows the eqnipotential lines.

In the magnetron the radius of the circularmotion is in ~any cases not so small that theelectric field may be considered as homogeneousalong one circle. In this .case it is impossible to 'analyse the, motion directly into a "rotation" anda "translation". This can, however, be done withsufficient accuracy for a qualitative discussion.We shall therefore make use of these terms in thefollowing in order to characterize' the circularmotion and the displacement along an equipoten-·tial line.

The motion of the electron in the magnetron

In a magnetron the electrons' leave the cathodewith a low velocity and are accelerated by a radialfield.' They will be deflected by the. magnetic fieldand curved paths will result. The curvature oftheir paths at every point is, as we have seen, pro-portional to the field strength, and inversely pro-portional to the velocity and thus also to thesquare.root ,of the potential at the point in question.When the strength of the magnetic .field is suf-ficiently great the electrons cannot reach the anode,and describe a path like that represented in fig. Ba.

a b c .31781

, Fig. 8. Form of path of an electron in a magnetron at differentintensities of the magnetic field H.a) H> Hkr; b) H = Hkr; c) H < Hkr.

With a completely symmetrical arrangement theelectron emitted would. return to' its. startingpoint, the cathode. Due to a slight asymmetry,however; it may occur that the electron misses itsgoal; in that case it describes a second loop similarto the first in shape but turned 90°, and so' on, 'sothat a closed orbit of four loops results. '

When the strength of the magnetic field is madeto decrease, the diameter of the loops increasesuntil át the so-called critical field strength the elec-trons can reach the anode (fig. 8b and c). At thatmoment an anode current suddenly begins to flow,which current remains practically constant uponfurther decrease of the strength of th~ magneticfield.When the cathode filament is sufficiently thin

the critical field strength can easily be calculated.It may then be assumed that the potential is con-stant in the' greatest part of the space and equalt6 the anode voltage Va. The electron then ~de-scribes a circular orbit whose diameter 2r at the crit-ical field strength Hk is equal to the radius aof the magnetron. According to equation (4) thefollowing is .valid:

-v Va2 r = 6.76 -- = a of

" Hk

6.76 .Hk= -. ffa.

a(8)

It is remarkable that this formula which is derived

194, PHILIPS TECHNICAL REVIEW Vol. 4, No. 7

by approximation is satisfied exactly when theelectron leaves the axis of the magnetron with zerovelocity. Moreover it is independent ofthe.variationof the potential between the cathode and the anode,and is also valid, for instance, when this potentialchanges due to the space charge.When the anode cylinder is not continuous but

consists of a number of sections with equal potentialthe paths of the electrons will be practically thesame. If, however, there are differences in potentialbetween the sections very divergent forms of orbitsmay appear which will be discussed in the followingbecause of their close connection with the possi-bilities of oscillation of the magnetron.

Oscillations of relatively low frequency

We shall consider a magnetron with two anodes~ctions (seefig. 9a); and with a given anode volt-age Va we choose a magnetic field so strong thatno anode current flows. When a difference of po- .tential is 'caused between the plates by the batteriesbI and b2 such that the average voltage remainsequal to Va, anode current is found to flow, and,remarkably enough, it flows 'to the plate with thelower potential. This ~hows directly that the mag-netron 'is capable of generating .oscillations. Ifone considers the circuit in fig.. 9b consisting of a 'magnetron, an oscillating circuit in which there is anoscillation of a certain amplitude and a battery'with the anode voltage Va,it follows from the abovethat the electrons accelerated by the alternatingvoltage always move toward that section wherebythe alternating voltage of the oscillating circuit hasa retarding action. This is exactly the conditionwhich was derived as necessary for the generationof oscillations.

•

b,. Va.3"1782

Fig. 9. a) Equivalent circuit. b). Circuit of a magnetron withtwo sections, When the magnetic field is greater than thecritical value corresponding to the voltage of the sections,a current may flow if the voltage of the two sections is dif-ferent. This current flows toward the section with l ow erpotential.

In order to complete the explanation of the os-cillation phenomenon dealt with above, we shalltry to show why the' electrons tend to choose thepath toward the plate with the lower poterrtial. In

fig. lOa the lines of equal potential and the pathsof the electrons in a magnetron with two anodesections are given.

a

b .3"17[03:

Fig. 10. Equipotentiallines and electron orbits in a magnetronaccording to fig. 9.a) Simplified scheme with' flat electredes.b) The actual magnetron.

In order to obtain a simpler picture the cathodeand the sections of the anode are drawn as flatplates, which introduces no changes in the prin-ciple of their action. Section I in fig. lOa has thehigher potential, as may he seen from the courseof the equipotential lines. Its potential is not,however, so great that an electron leaving thecathode with zero velocity could reach the plate.The path of an electron is also given in fig. lOa.

The electron is displaced in the direction of theequipotential lines as has already been explainedin detail. When the elect~on approaches the slitit enters a region where the equipotential Iines .are bent and lie closer to .the anode. The electronwill follow this course, and we see that it thereforereaches the plate with lower potential although itbegan its journey under the plate with higherpotential.In fig. lOb. the equipotential lines and the path

of an electron are given in a cylindrical magnetronwith two sections. The figure shows that the effecthere is fundamentally exactly the same, althoughthe picture is less clear. .'The above-described mechanism for the gener-

ation of oscillations resembles the mechanism inradio valves inasmuch as the oscillations are

JULY 1939 THE MAGNETRON WITH ULTRA SHORT WAVES 195 '

generated by means of a negative resistance. Justas in radio valves, the frequency is here also limitedby the transit ,time of the electrons which, withstrong magnetic fields, .will be' even longer than inradio valves, because the velocity of 'translation,v = EfH, is inversely proportional to the magneticfield. '

Therefore the considered manner of generatingof oscillations can only produce oscillations withrelatively low frequencies.

Oscillations with very high frequency

Thanks to the fact that the motion of the elec-trons' in the magnetron is periodic in nature, thereare, however, also other possibilities of oscillationwith periods which are shorter than the transittime of the' electrons. These oscillations are inducedby the oscillations which occur in the radi~l andtangential motion of the space charge in themagnetron.

The tangential motion has as fundamental period,the time necessary for an electron to run once aroundthe cathode along an equipotentialline. It is foundthat higher harmonics of this fundamental periodalso occur, particularly that period in which theelectron is displaced over the angle included byone section. The frequency of the oscillation is', determined by the velocity of the "translation",and thus by the quotient EfH. The. osciflationappears, for example, when, by changing themagnetic field, the' frequency of the tangentialmotion is brought into correspondence with theresonance frequency of the externally connectedoscillating circuit.The radial motion of the space charge varies

periodically with the' frequency of the circularmotion of the electrons.' This frequency, which' isgiven in equation (3), depends only on !he intensityof the magnetic field. The oscillation generated in'this way is more difficult to obtain than the oscil-lation which is generated by the tangential motion.'.and it has the shortest wave length which can be 'generated by a magnetron.' "We shall now .consider further the periodic

motions of the electrons, and show that it satisfiesthe conditions .for maintaining an oscillation in aconnected oscillating circuit.

Tangential oscillations

Let us assume that there ~s an alternatingvoltage from an oscillating circuit on thê sections',of fig. 11 in addition to a direct voltage. The phaseof the oscillation must be such that at the momentwhen the electron passcs from section I to section 11

along' its path as given in the figure, sector I is at'its maximum and sector 11 at its minimum poten-tial. The. electron therefore gives up energy to theelectric field between the sections, and the oscil-lation in the electrical circuit is hereby reinforced.

I , n m

-~~ .. ".~3'1784

Fig. 11. Electron orbits in a flat magnetron when the timenecessary for the electron' to pass froin one slit to the nextone is equal to half a period of the oscillation generated. Thephase of the electron is chosen so that it passes each time froma place of ma;cimum potential to one of minimum potential.

Because of its loss of energy the electron willno longer be able to return to the 'cathode, but willbe further displaced along a line closer to the anode.If the time necessary for an elect~on to be displacedfrom one slit to the following slit, corresponds. exactly to half a period of the oscillation the elec-tron will again give off energy to the field andagain _approach the anode more closely. Thisprocess will be repeated until the electron rea'chesone of the sections. 'We see thus that with a suitable frequency

the condition for the generation of oscillations canhe satisfied. Whether or not this 'takes place doesnot depend only upon the ..frequency, but also onthe phase of die oscillation at the moment when anelectron passes the slit.When section I has the higher potenrial at the

moment when the' electron passes from section Ito section 11, the electron will give off energy tothe oscillating circuit; if, however, the electronspass the slit at random times no energy will betransferred on an average.From a closer consideration it is found that the

electrons do not pass the slit at random moments,but .show a certain preference to pass it in the"correct" phase. In this connection we recallequation (7) from which it follows that 'the velocity'

I u

3'1785

Fig. 12. Continuous line: varration of the strength of theelectron field as a function of time for an electron whose pathis given in fig. 11. Dotted line: variation of the field strengthfor an electron which passes the slits slightly later. Theaverage value .of the field strength is somewhat higher.

196 PHILIPS TECHNICAL REVIEW Vol. 4, No. 7

of the displacement is proportional to the strengthof the electric field.

Infig. 12 the continuous line shows schematicallyhow the field strength varies for an electron inthe "correct" phase. At the moment t = 0 when theelectron begins to move in section I this sectionhas the highest negative value of. the alternatingvoltage and therefore the field strength is at aminimum. When the electron is' about to passover from section I to section 11, section I has mean-while reached the maximum potential and thepotentialof section: 11 is at its lowest value. Inthis way the variation in the field strength alongthe path of the electron is obtained ,as shown.

The dotted line shows how the field strengthvaries for an electron which arrives too late at theslit between section I and section 11. The fieldstrength in section I has already passed its maxi-mum and is beginning to fall. The potential jumpat the boundary line t = :re/(JJ is therefore smaller,but in the case here represented it still has the cor-rect direction. It is' striking that the field strengthin the case' of the dotted curve lies higher on theaverage than in the case of the continuous curve.This means that the ,translation of an electron whicha~riv'es too late at the slits is more rapid than inthe electron which arrives in the correct phase.The tardy electron will therefore overtake the elec-, tron in the correct phase. '. In the same way it is easy to understand thatan electron which reaches the slits too early movesmore slowly than an electron 'in the correct phase,and is therefore also made to approach the' correctphase.

The frequency of the tangentlal oscil1ations canbe calculated from equation (7) for the velocity"of translation. If s is the length of path which theelectron must cover from one section' to the next,then the time T in which this distance is coveredis also equal to the time of one period. Thus:

n sT = _'= -,'

co v

where v is the velocity of translation., , E Va'According to e~uation (7) v _:_H = aH' where

a is the distance 'between anode and cathode. Inorder to find an expressión for s we again assume themagnetron to be circular; s is then equal to thelength of the path diyided by the number ofsections, .As length of path the outside ciroumference must

not be taken, but the length of a path with an aver-age radi~s which will be' about equal -to half the,

maximum radius. Thus s = :re aln. By filling in sand v in equation (10) the ,angular frequency of theoscillation is obtained:

:rev n Vaco=-=--

, s a2 H(11) ,

Equation (11) is very well confirmed experimen-tally. When with a given value of Va the magneticfield is allowed to increase, it is found that 'oscil-lations suddenly appear ai the value of H given byequation (ll). The efficiency may amount to50 per cent. When the field strength is allowed toincrease still further the efficiency decreases. T~evariation 'of the efficiency can be satisfactorilyexplained by a detailed theoretical consideration 3),which lies outside the scope of this article,

Very short waves can be generated by thetangential oscillations. If Va is measured in voltsand H in gauss, it, follows from equation (ll) that

600 :re H a2À = ----.

n Va

Just as with low-frequency oscillations the fieldstrength H must have at least the critical value.If this value is substituted according to equation(8), one finds for the wave length:

. 12740aÀ> ~--,--",=-

. n iVa. . .. (12)

If Va is taken equal -to 1500 volts, a to 0.2 cm,,n to 4, one finds' À 16.5 cm.

(10)

Radial oscillations

We shall now aseume that the external oscillatingcircuit is tuned' to the radial oscillations of. theelectrons, the frequency of which is given by therotating motion of the electrons in the magneticfield. According to equation (3) the frequency ofthe rotation: co= 1.76 . 107,H, and from this we'find a wave length:

10700À=-- cm"

H(13)

In order to find out whether the rotating motionof the electron is' able to generate -an oscillation,we begin once more with a magnetron with flatparallel plates as cathode and anode. In this casethe. anode need not have slits.

When the anode voltage is constant an electronwhich leaves the cathode with zero velocity willdescribe an orbit like that shown in fig. 8a.

3) K. Posthumus, Wirel. Eng. 12, 126, 1935.

JULY 1939 T:ij:EMAGNETRON WITH ULTRA SHORT WAVES 197

Let us now assume that there is, in addition to thedireçt voltage, a small alternating voltage on theanode which corresponds in frequency to thenumber of revolutions of.the "rotation" and whosephase is such that the total anode voltage is ata minimum at the moment when the electron is ata maximum distance from the cathode. The' alter-nating field is then so directed at every momentthat it exerts a retárding action on the motion ofthe electron. The electron thus passes on energy ,to the oscillating circuit, and would therefore inthis special case reinforce the oscillation. If, how-ever, the electron had left the cathode in theopposite phase of the alternating voltage, it wouldnot have reinforced the oscillation but, on thecontrary it would' have damped.it, and the ayeragetransfer- of energy over all phases wouÎd be zero.

It is actually. impossible to start an. oscillationdirectly in a magnetron of the type represented.To do this it is necessary to apply some kind' ofselection which provides that on the average thereare more electrons in the magnetron with a "cor-rect" phase than with an incorrect one.

Such selection can be obtained for instance byapplying the magnetic field at an angle of a fewdegrees to the axis of the valve. The radial electricfield can now be resolved into a component perpen-dicular to the magnetic field .and a componentparallel to it. The first component causes the well-known' loop motion of the electron', while thesecond .component 'will accelerate the electron inthe direction of the magnetic' field, and since themagnetic field is oblique, the' electron reaches 'theanode after a short time.The selection is based upon the following' fact.

Electrons which started in the wrong phase arecaptured by the anode after a shorter .time than

eleetrons which started ir{the correct phase. Whenan electron starts in the correct phase the circularmotion of the electron gives off energy to the os-cilating circuit. If, however, the phase is incorrectthe oscillating circuit gives off energy to the cir-cular motion and the amplitude of this motion is "thereby incre~sed. This leads to the fact that elec-trons 'with incorrect phase reach the anode muchmore quickly than electrons with the correct phase(see fig. 13), and are thereby removed from themagnetron.

. 3'1786

Fig. 13. Electron paths in a flat magnetron with obliquemagnetic field, when there is an oscillating circuit in theexternal connections oscillating with the frequency of theradial oscillations.1. The electron is in the correct phase. The amplitude of its

radial oscillation decreases. ., 11. The electron is in an incorrect phase. The amplitude of

its radial oscillations increases and the electron quicklyreaches the anode.

When the emission of the cathode is so greatthat the space charge begins to play a part, theabove described selection is disturbed. Since more'electrons are present in the immediate neighbour-hood, of the cathode in the correct phase for theemission of electrons than in the ,wrong phase, the'emission of electrons in the correct phase will alsobe more hindered .hy the space charge. The spacecharge thus works against the selection, and thisis .the explanation of the observed fact that radialoscillations can only be obtained with very weakemission currents.

Compiled by G. ~ELLER.