NO. 2
THE BELL SYSTEM
TECHNICAL JOURNAL
DEVOTBD TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION
1 viCiX
/
The Magnetron as a Generator of Centimeter Waves.
Developments at the Bell Telephone Laboratories, 1940-1945
J. B. Fisk, H , D . Hagstrum and P . L. Hartman 1
Contributors to this I s s u e ... 189
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$ 1 Because" d rcu m stan ces have delayed the issuance of this the Bell System Technical Journal far beyond its designated d a teo f appearance, it seems desirable to record th a t issuance actually occurred on Ju y ,
C O R R E C T IO N FOR ISSUE OF JA N U A RY , 1946
Page 35: Footnote, 5 “The M agnetron as a G enerator of C entim eter W aves,” J . B. Fisk, II. G. H agstrum , and P. L. H artm an, B. S. T . January, 1946.
should read, 5 “ The M agnetron as a G enerator of C entim eter W aves,” J. B. Fisk, H . G. Hagstrum , and P. L. H artm an, to appear in B. S. T. April, 1946.
T h e Bell System Technical Journal
Vol. X X V April, 194.6 N o. 2
T h e M a g n etro n a s a G enerator of C en tim eter W a v es By J. B. FISK, H. D. HAGSTRUM, and P. L. HARTMAN
In t r o d u c t io n
A T E in the sum m er of 1940, a fire control radar operating a t 700 mega-, -*—■4 cycles per second was in an advanced sta te of developm ent a t the Bell Telephone Laboratories. The pulse power of this radar was generated by a pair of triodes operating near their upper lim it of frequency. Even when driven to the point where tube life was short, the generator produced peak power in each pulse of only two kilowatts, a q u an tity usable b u t marginal.
Although the triodes employed had not been designed for high voltage pulsed operation, th ey were the best available. This is an example of how develop
m ent of rad ar in the centim eter wave region was circumscribed by the lack of a generator of adequate power and reasonable life expectancy. M ore
over, the prospects of improvem ent of the triode as a power generator a t these w avelengths and extension of its use to shorter wavelengths were not bright. Solution of the problem by means of power amplification was rem ote. A new source of centim eter wave power was urgently needed.
For the B ritish, who were a t war, the problem was even more urgent.
They had undertaken a vigorous search for a new type of generator of sufficiently high power and frequency to m ake airborne radar practicable in the defense against enem y night bombers. T hey found a solution in the m ultiresonator m agnetron oscillator, adm irably suited to pulsed generation of centim eter waves of high power.
In the fall of 1940, an early model of this m agnetron operating a t ten cen
tim eters was brought to the U nited S tates for examination. The first Ameri
can test of its o u tp u t power capabilities w'as made on October 6, 1940 in the Bell Telephone L aboratories’ radio laboratory a t W hippany, N. J. This te st confirmed B ritish information and dem onstrated th a t a generator now existed which could supply several times the power th a t our triodes delivered a n d a t a frequency four times as great. The most im portant restraint on the developm ent of rad ar in the centim eter wavelength region had now been removed.
A num ber of pressing questions rem ained to be answered, however.
Could the new m agnetron be reproduced quickly and in quantity? Was its 107
operating life satisfactory? Could its efficiency and o u tp u t power be sub
stan tially increased? Could one construct sim ilar m agnetrons a t forty centim eters, a t three centim eters, even a t one centim eter? Could the m ag
netron oscillator be tuned conveniently? One by one, during the w ar years, all of these questions have been answered in the affirm ative. In m any in
stances, b u t not w ithout detours and delays, results have been b e tte r than expected or hoped for.
T he B ritish m agnetron was first reproduced in America a t the Bell Telephone L aboratories for use in its ra d ar developm ents and those at the R adiation L aboratory of the N ational Defense Research Com m ittee which was then being form ed a t the M assachusetts In stitu te of Technology.
Since th a t time, extensive research an d developm ent w ork has been carried on in our Laboratories, in other industrial laboratories, an d in th e laboratories of the N ational Defense Research Com m ittee. Several m anufacturers have produced the resu ltan t designs. M agnetron research and developm ent was also carried on in G reat B ritain by governm ental an d industrial laboratories.
There has been continuous interchange of inform ation am ong all these laboratories through visits and w ritten reports. M agnetron and ra d ar de
velopm ents have been greatly accelerated b y this interchange.
M ulticavity m agnetron oscillators are now available for use as pulsed and continuous wave generators a t w avelengths from approxim ately 0.5 to 50 centim eters. The upper lim it of peak power is now about 100 kilow atts at 1 centim eter, 3 m egaw atts a t 10 centim eters. O perating voltages m ay be less th an 1 kilovolt or more th an 40 kilovolts. The m agnetic fields essential to operation range from 600 to 15,000 gauss. T unable m agnetrons now exist for m any parts of the centim eter wave region. T he tuning range for pulsed operation a t high voltage is ab o u t ± 5 % . I t is as m uch as ± 2 0 % for low voltage m agnetrons. M agnetrons m ay now be tu n ed electronically, m aking frequency m odulation possible. P resen t m agnetron cathodes are rugged and have long life. E ven for high frequency m agnetrons where cur
re n t density requirem ents are m ost severe, research has m ade available rugged cathodes w ith adequate life. M agnetrons are built to w ithstand shock and vibration w ithout change in characteristics. Designs have been compressed an d in some cases the m agnet has been incorporated in the m agnetron stru ctu re in the interest of light weight for airborne ra d ar equip
m ents.
P A R T I of this p ap er is a general discussion of present knowdedge con
cerning the m agnetron oscillator. As such i t is largely a discussion of what has come to be common knowledge am ong those who hav e carried out w artim e developm ents. I t brings together in one place results of work done b y all the m agnetron research groups including th a t a t our Labora
tories. P A R T I supplies the background necessary to understanding the
M A G N E T R O N A S G E N E R A T O R OF C E N T I M E T E R W A V E S 169
discussion in P A R T I I of the magnetrons developed a t the Bell Laboratories during the war. M ore complete presentations of the experim ental and theo
retical work done on the m agnetron during the w ar are soon to be published by other research groups.
T he m aterial w ritten up during the war has appeared as secret or confi
dential reports issued by the British Com m ittee on Valve Developm ent (CVD M agnetron R eports), by the R adiation Laboratories a t the M assa
chusetts In stitu te of Technology and a t Columbia University, and by the participating industrial laboratories. N o atte m p t has been made in P A R T I to indicate the specific sources of the work done since 1940. To fit the w ar
time developm ent of m agnetrons into the sequence of previous developments, specific references are made to publications appearing in the literature prior to 1940.
The natu re and scope of P A R T I I of the paper are discussed more fully
i n its in troductory Section, 11. Ge n e r a l Re m a r k s.
P A R T I
T H E M A G N E T R O N OSCILLATOR 1. Ge n e r a l De s c r i p t i o n
1.1 Description: The m ulticavity m agnetron oscillator has three principal com ponent p arts: an electron interaction space, a m ultiple resonator system, and an o u tp u t circuit. Each of these is illustrated schematically in Fig. 1.
T he electron interaction space is the region of cylindrical sym m etry between the cathode and the m ultisegm ent anode. In this region electrons em itted from the cylindrical cathode move under the action of the D C radial electric field, the D C axial m agnetic field, and the R E field set up by the resonator system between the anode segments. These electronic motions result in a net transfer of energy from the D C electric field to the R F field. T he R F interaction field is the fringing electric field appearing between the anode seg
ments, built up and m aintained by the m ulticavity resonator in the anode block. R F energy fed into the resonator system by the electrons is delivered through the o u tp u t circuit to the useful load. The output circuit shown in Fig. 1 consists of a loop, inductively coupled to one of the hole and slot cavi
ties, feeding a coaxial line.
To operate such a m agnetron oscillator, one m ust place it in a magnetic field of suitable strength and apply a voltage of proper m agnitude to its cathode, driving the cathode negative w ith respect to the anode. This voltage m ay be constant or pulsed. In the latter case, the voltage is applied suddenly by a so-called pulser or m odulator for short intervals, usually of about one microsecond duration a t a repetition rate of about 1 0 0 0 pulses per second. W ith suitable values of the operating param eters, the m agnetron
oscillates as a self excited oscillator w henever the D C voltage is applied.
T he energy available a t the o u tp u t circuit m ay be connected, as in a rad ar set, to an a n ten n a or, as in a lab o rato ry experim ental setup, m ay be absorbed in a column of water.
1.2 Analogy to Other Oscillators: In its fundam ental aspects, the m ag
netron oscillator is n o t unlike other and perhaps m ore fam iliar oscillators.
In particular, instructive analogies m ay be drawn between the m agnetron oscillator, the velocity variation oscillator, an d the simple triode oscillator.
In Fig. 2 is depicted schem atically the parallelism s betw een these types of oscillators an d a simplified equivalent lum ped constant circuit.
In th e triode of Fig. 2(a), as in the gap of the second cavity of the velocity variation tu b e of Fig. 2(b) and in the interaction space of the m agnetron
Fig. 1.— A schem atic diagram designed to show th e principal com ponent p a rts of a centim eter w ave m agnetron oscillator. T h e resonator system and o u tp u t circuit each represents one of several ty p es used in m agnetron construction.
oscillator of Fig. 2(c), electrons are driven against R F fields set up by the resonator or “ ta n k circuit,” to which th ey give up energy absorbed from the p rim ary D C source. In each type of oscillator there is operative a mecha
nism of “ bunching” which allows electrons to in teract w ith the R F field prim arily when the interaction will result in energy transfer to the R F field.
In the triode oscillator this is accom plished by the grid, whose R F potential is supplied by the “ ta n k circuit” in proper phase w ith respect to the RF p o ten tial on the anode. In the velocity v ariatio n oscillator, bunching is accomplished by variation of the electron velocities in th e gap of the first cavity, followed by drift through the intervening space to the second gap.
T h e first cav ity is driven in proper phase by a feed back line from the second cavity. In the m agnetron oscillator, as is to be described in detail later, electron interaction w ith the R F fields is such as to group th e electrons into
M A G N E T R O N A S G E N E R A T O R OF C E N T I M E T E R W A V E S 171
( d )
Fig. 2.—A schem atic diagram depicting the parallelism am ong the conventional triode oscillator, th e velocity variation oscillator, the centim eter w ave m agnetron an d an equivalent lum ped c o n stan t circuit. In th e figure an a tte m p t is m ade to align corresponding p a rts vertically above one another.
bunches or “ spokes” which sweep p ast the gaps in the anode, in phase for favorable interaction w ith the R F fields across the gaps. T he bunching field
is th u s the same held as th a t to which energy is transferred. In this sense the m agnetron oscillator is perhaps m ore properly analogous to the reflex type of velocity variation oscillator, in which a single cavity is used both as
“ buncher” and “ catch er” ; the electrons, after traversing the gap once, are turned back in the proper phase in the drift space so as to pass through the gap again in the opposite direction.
Each type of oscillator has a resonator in which energy is stored and which synchronizes the flow of energy from the electrons into it by the m eans of self excitation. In each type, energy is extracted from the resonator by an o u tp u t circuit a t a ra te which, under steady sta te conditions, equals th a t of influx from the electron interaction, m inus the losses in the resonator itself.
1.3 Use of Equivalent Circuits: In m any instances the understanding of electrom agnetic oscillators is m ade easier and analytic trea trnent m ade pos
sible by use of an equivalent circuit w ith lum ped constants. Of several possible types, one of the sim pler and more frequently used for the magne
tron oscillator is shown in Fig. 2. This m ay appear in the case of the multi- cavity m agnetron to be an oversimplification as it does not account for the fact th a t the resonant frequency of the m agnetron resonator system is m any valued. A m agnetron resonator, being m ade up of a num ber of coupled resonating cavities, is capable of supporting several modes of oscillation.
These modes of oscillation have different resonant frequencies and corre
spond to different configurations of th e electrom agnetic fields. B y means to be discussed, however, m agnetron resonators can be m ade to oscillate
“ cleanly” in one of these modes and m ay th u s be represented for m any pur
poses by a simple L-C circuit having a single resonance.
T he o u tp u t circuit of the oscillator is also am enable to treatm en t by equivalent lum ped constant circuits which account for its behavior with accuracy. M ore general, four term inal netw ork theory has also been applied in the stu d y a n d design of impedance transform ations in this p a rt of the oscillator.
Finally, the electrons, which in a sense are connected to the circuit formed by the resonator and the load, m ay also be treated by circuit concepts.
T he electrons m oving in the space betw een the cathode and anode, by virtue of their presence an d m otion, induce charge fluctuations on the anode seg
m ents. The tim e derivative of these fluctuations is equivalent to an RF cu rren t flowing into the anode from the interaction space. T his current and th e R F voltage on the anode, bearing a definite phase relationship, make possible the definition of an ad m ittance called the average electronic adm it
tance, Y e = Ge + j B c. Since the electrons are being driven against RF fields in th e interaction space, this adm ittance looking into the electron stream has a negative conductance term . Unlike usual circuit adm ittances, the electronic adm ittance is nonlinear, being a function of the voltage
M A G N E T R O N /15 G E N E R A T O R OR C E N T I M E T E R IVA V E S 173
am plitude of oscillation, Vk f , as well as of other param eters governing the electronic behavior of the oscillator, such as voltage and m agnetic field.
I t is not known a priori b u t m ay be deduced from measurements on the op
erating oscillator and its circuit.
A necessary condition for oscillation, applicable to the m agnetron as to any oscillator, is th at, on breaking the circuit a t any point, the sum of the adm ittances looking in the two directions is zero. Thus, if the circuit is broken a t the junction of electrons and resonator, as is convenient, the elec
tronic adm ittance, Y c, looking from the circuit into the electron stream , m ust be the negative of the circuit adm ittance, Ts, looking from the electron stream into the circuit.
W ith these rem arks, of general applicability to all types of electromagnetic oscillators, the discussion will be continued for the centim eter wave mag
netron oscillator in particular. As far as is possible, the electronic inter
action space, resonator system , and output circuit of the device will be taken up in th a t order. T he function and operation of each p art will be described;
then the principles of its design, and its relation to previous m agnetron developm ent will be indicated.
1.4 Electron Motions in Electric and Magnetic Fields— The DC Magnetron:
Before beginning the discussion of the electronics of the m agnetron oscillator, it would be well to review briefly electron motions in various types and com
binations of electric and magnetic fields, and the operation of the D C m agnetron. 1
An electron, of charge e and mass m, moving in an electric field of strength E , is acted upon by a force, independent of the electron’s velocity, of strength eE, directed opposite!}' to the conventional direction of the field. If the field is constant a n d . uniform, the motion of the electron is identical to th a t of a body moving in a uniform gravitational field.
An electron moving in a magnetic field of strength B, however, is acted upon by a force which depends on the m agnitude of the electron’s velocity, v, on the strength of the field, and on how the direction of motion is oriented w ith respect to the direction of the field. The force is directed norm al to the plane of the velocity and magnetic field vectors and is of m agnitude proportional to the velocity, the magnetic field, and the sine of the angle, 0, between them. T hus the force is the cross or vector product of v and B ,
F = e[v X B\, F = Bev sin 9.
An electron moving parallel to a magnetic field (sin 9 = 0) feels no force.
One moving perpendicular to a uniform magnetic field (sin 9 — 1) is con-
1 T h e cylindrical D C m agnetron was reported by A. W. Hull, Phys. Rev. 18, 31
strain ed to move in a circle by the m agnetic force a t right angles to its path.
Since this force is balanced by the centrifugal force, the radius, p, of the circular p a th depends on the electron’s m om entum and the strength of the field; th a t is,
Bev = — ,tmi- P mo
yielding p = — . (1)
Fig. 3.— T h e cycloidal p a th of an electron which sta rte d from re st a t the cathode in crossed electric and m agnetic fields for the case of parallel plane electrodes. T h e mecha
nism of generation of the orbit by a p oin t on th e periphery of a rolling circle is depicted.
T he tune, T c, required to traverse the circle is independent of th e radius and hence of the velocity of the electron; T c = 2 rp /v — 2irm/eB. Thus, the angular frequency of traversing the circular p ath , the so-called cyclo
tron frequency, depends on the m agnetic field alone and is given by,
coc = 2 ir f c = 2t~ — — B . ( 2 )
1 C m
In the m agnetron, electron m otion in crossed electric and m agnetic fields is involved. Consider first such m otion between two parallel plane elec
trodes, neglecting space charge. If, as in Fig. 3, the electric field is directed in the-negative y direction and the m agnetic field in the negative s direction, the equations of m otion of the electron are:
M A G N E T R O N A S G E N E R A T O R OF C E N T I M E T E R W A V E S 175
d-x cB_ dy dl2 m dl ’
l - M s - j g ) .
T m \ d l J
d-z „
dr _ '
(3)
The particular case of m ost interest here is th a t for which the electron starts from rest a t the origin. The equations of motion then yield a cycloidal orbit given by the param etric equations:
X = I ' d — Pe sill u d = p c ( u d T S' n “ c0>]
y = pc(l — cosead), in which:
(4)
E (5)
vc - B ,
m E (6)
Pc = 1 B~’ .[
e 03c = — B.
m
(7)
This motion m ay be regarded as a combination of rectilinear motion of velocity vc in the direction of the x axis, perpend le u a r to o a , and of m otion in the x y plane about a.circular p a th of radius p, at : an angular frequency coc, the cyclotron frequency. Fig. 3 shows th e re s u n cycloidal p a th and its generation by a point on the periphery of the ro lln g circle. In the case of cylindrical geometry, it is often convenient to think
in term s of the plane case. . . . __
In the case of cylindrical geom etry with radial electric and axial n, fields, the electron orbit, neglecting space charge, approxim a es an e generated by rolling a circle around on the cvlin nca ca ioc e.
is not exactly an epicycloid because the radial motion is no simp e , which sta te of affairs arises from the variation of the D C electric field w ith radius. T he approxim ation of the epicycloid to t ie actua pa
venient one, however, because the radius of the r o ll in g circle, its angular frequency of ro tatio n , and the velocity of its center, for the eplcy c o , all approxim ate those for the cycloid of the plane case. ese appr tions improve w ith increasing ratio of cathode to anode rad.» Severa electron orbits in a D C cylindrical m agnetron are show n in i0.
magnetic fields.
I t is clear from this simplified picture of the orbits in a D C cylindrical m agnetron w ithout space charge, th a t, a t a given electric field, an electron orbit for a sufficiently strong m agnetic field m ay miss the anode completely and retu rn to the cathode. T he critical m agnetic field a t which this is just possible is called the cut-off value, B c. F or a given voltage betw een cathode and anode, as the m agnetic field is increased, the current norm ally passed by the device falls ra th e r ab ru p tly a t B c. A cu rren t versus m agnetic field curve, together w ith electron orbits corresponding to four regions of the
Fig. 4.— Electron p a th s in a cylindrical D C m agnetron a t several m agnetic fields above an d below th e cut-off value, Bc. T he electrons are assum ed to be em itted from the cathode with zero initial velocity.
curve, are shown in Fig. 5. For the case of parallel plane electrodes, the cut-off relation betw een the critical anode potential, V c, an d m agnetic field, B C) and the electrode separation, d, for the parallel plane case, is obtained by equating the electrode separation to the diam eter of the rolling circle.
Thus,
M A G N E T R O N A S G E N E R A T O R OR C E N T IM E T E R \V A V E S 177
For the cylindrical case, the relation m ay be shown to be
in term s of cathode and anode radii, r cand ra-
2. Ty p e s o f Ma g n e t r o n Os c il l a t o r s
2.1 Definitions: T he D C m agnetron m ay be converted into an oscillator, suitable for the generation of centim eter waves, by introducing RF fields into the anode-cathode region. This m ay be done by applying between anode
Fig. 5.—V ariation of cu rre n t passed by a cylindrical DC m agnetron at con stan t voltage, plotted as a function of m agnetic field. T he orbits of electrons occurring a t four different magnetic fields are shown above the corresponding regions of the current characteristic.
and cathode R F voltage from a resonant circuit, in which case the electrons interact w ith the superposed radial R F field. Or, it m ay be done by split
ting the m agnetron anode into two or more segments between which the R F voltage is applied. Then the electrons interact with the fringing R I fields existing between the segments. The problem of understanding the electronics of the m ulticavity m agnetron oscillator is th a t ot understanding how an electron, subject to the constraints placed upon its motion by the DC axial magnetic and DC radial electric fields, can move so as to interact favorably w ith the R F field; how an electron interacting unfavorably is rejected; and why, on the average, the electrons transfer more energy to the RI- field than they take from it.
On the basis of the nature of the electronic m echanism by m eans of which energy is transferred to the R F field, it is now convenient to distinguish three types of m agnetron oscillators. 2 T he negative resistance magnetron oscillator depends on the existence of a static negative resistance character
istic between the two halves of a split anode. 3 T he cyclotron frequency mag
netron oscillator operates b y v irtu e of resonance between the period of RF oscillation and the period of the cycloidal m otion of the electrons (rolling circle or cyclotron frequency) . 4 T he traveling wave magnetron oscillator de
pends upon resonance, th a t is, approxim ate equality, between the mean translational velocity of the electrons and the velocity of a traveling wave com ponent of the R F interaction field. 5
T he m agnetron oscillator w ith which this paper is prim arily concerned is of the traveling wave type. T h e o th er m agnetron types are discussed briefly for the sake of com pleteness and because an understanding of them enhances one’s grasp of the entire subject and places the traveling wave m agnetron oscillator in its proper historical perspective.
2.2 The Negative Resistance Magnetron Oscillator— Type I: In the neg
ative resistance m agnetron oscillator, 5 the anode is split parallel to the axis into two halves, between which the R F circuit is attac h ed . T he elec
trons em itted by the cathode m ust move under the com bined action of the D C radial electric an d D C axial m agnetic fields together w ith the RF electric field existing betw een th e two sem icylinders form ing the anode.
T he tran sit tim e from cathode to anode is n o t involved in the mechanism except th a t it m ust be sm all relative to the period of the R F oscillation. The sta tic negative resistance characteristic arises from th e fact th a t under cer
tain conditions the allowable orbits for the m ajority of electrons terminate on the segm ent of lower p o tential, irrespective of the segm ent tow ard which th ey s ta rt. These electrons, being driven against the R F com ponent of the field, give energy gained from the D C field to the R F field.
In Fig. 6 are shown the p ath s, p lo tted by K ilgore, 7 of two electrons sta rt
ing initially tow ard opposite segm ents b u t both striking the segment of lower potential. E ach p a th is com pletely traversed in a tim e during which
2 T he m agnetron oscillator discussed b y H u ll, in w hich the m agnet w inding is coupled to th e p late circuit, is n o t considered as it is essentially a n audio frequency device. K- O kabe in his book, “ M agnetron-O scillations of U ltra S h o rt W avelengths” (Shokendo, 1937), distinguishes five types, b u t i t is n o t clear ju s t how his ty p es C a n d E are to be identified.
3 T hese oscillations have been called H ab an n , q uasi-stationary, or d y n a tro n oscilla
tions, a n d correspond to O kabe’s ty p e D.
4 T hese oscillations have been called electronic oscillations by M egaw, tran s it time osculations of th e first order b y H erriger an d H ulstcr, an d correspond to O kabe’s type A.
3 T hese oscillations arc th e running wave ty p e discussed by P osthum us, th e transit tim e oscillations of higher order of H erriger and H ulstcr, a n d correspond to Okabe s ty p e B.
6 T h is ty p e w as disclosed by H ab an n , Z cit f. Hochfrequenz. 24, 115 an d 135 (1924).
' G. R . Kilgore, Proc. I.R .E . 24, 1140 (1936).
M A G N E T R O N A S G E N E R A T O R OF C E N T I M E T E R W A V E S 179
the R F field changes little. Thus it is possible by applying D C potential differences between the anode segments to measure a negative resistance between them . As can be seen from the orbits of Fig. 6, m agnetic fields considerably above the cut-off value are used. W ith m agnetrons of this l ype) power o u tp u t up to 1 0 0 w atts a t 600 m c/s a t an efficiency of 25% has been a tta in e d. 7 Oscillations of frequency as high as 1 0 0 0 m c/s, (30 cm.) have been produced. 8 Because a large number of orbital loops are required,
. . cjj
however, m aking u <JC — , this type of m agnetron oscillator demands the
+ 150 V O L T S + 150 V O L T S
+ 5 0 V O L T S + 5 0 V O L T S
(0) (0)
Fig. 6.—E lectron p ath s plotted by Kilgore for the negative resistance m agnetron oscillator, T y p e I. D uring the tim e the orbits shown are being executed, the cathode is at zero potential and the anode segm ents a t the potentials indicated. I.ines of electric force on an electron are plo tted in this figure. T he two orbits are those of electrons which s ta rt initially tow ard opposite anode segments. I t should be noted th a t in either case the elec
tron is driven to th e segm ent of lower potential against the R F field component.
use of high m agnetic field in the centim eter wave region and is thus less desirable th a n other types.
2.3 The Cyclotron Frequency Magnetron Oscillator— Type I I : N o t long after the invention of the D C m agnetron, oscillations between anode and cathode were found to occur near the cut-off value of magnetic field. 9 fh ese were found to be strongest for wavelengths obeying a relation of the form:
constant
' E. C. S. Megaw, Jo u rn . I.E .E . (London) 72, 326 (1933).
■ • Zacek, Cos. Pro. Pest. M a th , a Fys. (Prague) 53, 578 (1924). A sum m ary api>eared 1,1 « a t . f. Hochfrequenz. 32, 172 (1928).
L ater, it was shown th a t the oscillation period is equal to the electron transit tim e from the vicinity of the cathode to the vicinity of the anode an d back.
This m ade it possible to calculate a value for the constant in the above equation in good agreem ent w ith experim ent. 10 The oscillation frequency is th a t of the ro tatio n al com ponent of the electronic m otion, th a t is, approxi
m ate!)' the cyclotron frequency of equation (7).
T he m echanism m ust be explained in term s of electrons m oving in the D C radial electric and axial m agnetic fields and the superposed R F radial elec
tric field. T his m ay be done as follows: An electron leaving the cathode in such phase as to gain energy when moving from the cathode tow ard the anode will also gain energy during its return, striking the cathode w ith more energy than it h ad when it left. There, such an electron is stopped from fu rth er m otion during w hich it would continue to absorb energy from the
Fig. 7.— A n approxim ate o rb it of an electron w hich gains energy from the R F field in a cyclotron frequency or T y p e I I m agnetron oscillator, shown for the plane case. The o rb it is continued as a dashed line in d icatin g how i t would be trav ersed w ere i t n o t stopped by th e cathode. T h e D C electric force on th e electron is directed from cath o d e to anode.
R F field a t the expense of the oscillation. The electron will execute an o rb it som ething like th a t of Fig. 7 for the plane case. An electron leaving the cathode in the opposite phase, on the o ther hand, loses energy when m oving tow ard the anode and again on its retu rn tow ard the cathode. As is shown in Fig. 8, it reverses its direction after the first trip w ith o u t reaching the cathode surface and sta rts over on a second loop of sm aller am plitude, rem aining in the same phase and continuing to lose energy to the field. This process continues u n til all the energy of the rotational com ponent of the electron’s m otion has been absorbed by the R F field. If the electron is not removed a t this sta^e, in its subsequent m otion the rotational component will build up, extracting energy from the R F oscillation. M eans such as tiltin g the m agnetic field or placing electrodes a t the ends of the tube have been used to remove the electrons from the interaction space when all the
1» K. Okabe, Proc. I.R .E . 17, 652 (1970).
M A G N E T R O N A S G E N E R A T O R OR C E N T I M E T E R W A V E S 181
rotational energy has been absorbed. I t is possible to m aintain the oscilla
tions and ex tract energy from them because electrons which give energy to the field can do so over m any cycles, whereas electrons of opposite phase can gain energy over only one cycle before they are removed.
M agnetrons oscillating in this m anner have been built w ith split anodes. " 1' 11 H ere the R F field w ith which the electron interacts is more tangential than radial b u t the criterion for oscillation is the same, namely, resonance between the field variations and the rotational com ponent of the electron’s motion. O perating efficiencies of 10 to 15% have been obtained.
I t was with a m agnetron of this type having an anode diam eter of 0.38 mm.
th a t radiation of wavelength as low as 0.64 cm. was generated. 12
I he cyclotron frequency m agnetron oscillator has been alm ost entirely superseded by the traveling wave m agnetron oscillator as a generator of
tig . 8.—An approxim ate o rb it of an electron which loses energy to the R F field in a cyclotron frequency or T y p e I I m agnetron oscillator, shown for the plane case. If the electron after losing all its ro tatio n al energy remains in the interaction space, it gains energy from the R F field, and its orb it builds up cycloidal scallops in a m anner directly the reverse of th a t shown here. T he DC electric force on the electron is directed from cathode to anode.
centim eter waves. In the m ain this is the result of the impossibility of removing electrons em itted from an extended cathode area from the inter
action region a t the proper stage in their orbits. This inherent drawback is not shared by the traveling wave m agnetron oscillator which m ay be oper
ated a t higher efficiency w ithout critical adjustm ent of orientation in the magnetic field or of th e'p o te n tia l of auxiliary electrodes.
2.4 The Traveling Wave Magnetron Oscillator -T y p e I I I : Oscillations have been found to occur in the m agnetron which are independent of any static negative resistance characteristic and which can occur a t frequen
cies widely different from the cyclotron frequency. In 193513 the elec
tronic mechanism of these oscillations was correctly interpreted as an inter-
11 H. Yagi, Proc. I.R .E . 16, 715 (1928).
u C- E. Cleeton and X. H . Williams, Phys. Rev. 50, 1091 (1936).
3 K. Posthum us, Wireless F.ngineer 12, 126 (1935).
action of the electrons w ith the tangential com ponent of a traveling wave whose velocity is approxim ately equal to the m ean translational velocity of the electrons. L a te r11 the role of the radial com ponent of the rotating electric field in keeping the electrons in proper phase was recognized.
M agnetrons of w avelength as short as 75 cm., operating a t b e tter th an 50%
efficiency, were b u ilt prior to 1940, b u t perform ance such as was later to be a ttain e d w ith this type of m agnetron a t m uch shorter wavelengths was not atta in e d then, perhaps prim arily because of th e lack of a good resonator.
I t was a m agnetron of this type which the B ritish brought to the U nited S tates in 1940. T he B ritish m agnetron was a 10 cm. oscillator, intended for pulsed operation, having a tan k circuit consisting of eight resonators built into the anode block as shown in Fig. I. 15
3 . Th e El e c t r o n i c Me c h a n i s m
3.1 Electronic Interaction at Anode Gaps: T he electrons in the interaction space of the m agnetron oscillator are the agents which transfer energy from the D C field to the R F field. As such, they m u st move subject to the con
stra in ts imposed by the D C radial electric and D C axial m agnetic fields, considering, for th e m om ent, the R F fields to be small. U nder these condi
tions, as has been seen for the D C cylindrical m agnetron (see Fig. 4 for B > B c), electrons follow approxim ately epicycloidal p a th s which progress around the cathode. T he m ean velocity of this progression, th a t of the center of the rolling circle, depends upon the relative strengths of the electric and m agnetic fields [see equation (5) for the plane case]. B y proper choice of D C voltage, V, betw een cathode an d anode and of m agnetic field, B, the m ean angular velocity of the electrons m ay be set a t any desired value.
T he R F electric fields in the interaction space, w ith which the electrons m oving as described above m u st in teract, are th e electric fields fringing from th e slots in the anode surface. These fields are provided b y the N coupled oscillating cavities of which the m agnetron resonator system is composed.
As will be discussed in m ore detail later, such a system of resonators may oscillate in a num ber of different modes in each of which the oscillations in adjacen t resonators, an d th u s the fields appearing across ad jacen t anode slots, bear a definite phase relationship. F or a system of N resonators it will be seen th a t the phase difference betw een a d jac en t resonators may assume the values n ^ radians, n being the integers 0, 1, 2, • • • , ~ .
N l
A dopting ano th er p o in t of view, one m ay consider th e potentials placed upon the anode segm ents by the resonators. T h e variation of the potential
11 F. H erriger and F. H ülster, Zeit. f. H ochfrequenz, -19, 123 (1937). p 15 T h e use of such in tern al resonators is reported in th e literatu re by N . T . Alekseiell an d D . E. M aliaroff, Jo u rn . of T ech. Phys. (U .S.S.R .) 10, 1297 (1940); republishedm English, Proc. I.R .E . 32, 136 (1944). A. L . Sam uel h as o b tain ed U. S. P a te n t % 2,063,34- Dec. S, 1936, for a sim ilar device.
M A G N E T R O N A S G E N E R A T O R OF C E N T I M E T E R W A V E S 183
from one segm ent to the next depends upon the mode of oscillation of the system as a whole. The restriction on the phase difference stated above requires the sequence of anode segment potentials a t any in stan t to contain
t + 1 / 4 T t + £ / 4 T
t + 3 / 4 T t + 4 / 4 T
t t 5 / 4 T
t + 6 / 4 T
t + 7 / 4 T t * 8 / 4 T
t * 9 / 4 T
t + I 0 / 4 T
t + I I /4 T
t + 1 2 / 4 T
t + 1 3 / 4 T
t + I 4 / 4 T
t + 1 5 / 4 T
t + 16/4 T
\ / ' \ \ '/ \ / \ / \_
\ \ ' \
|K| = 2 8 2 0 12 4
Fig. 9.—A plot showing tlrj ir mode anode potential wave a t several in stan ts in an eight resonator m agnetron and the m ean p a th s of electrons which in teract favorably with the I Fehl. T he p lo t is developed from the cylindrical case, the shaded rectangles a t the top representing the anode segm ents. T he anode potential variation is a standing wave, shown here for a sequence of in sta n ts one q u a rte r period ( T / i ) ap art. N ote th a t the po tential is co n stan t across the anode surfaces and varies linearly betw een them . E lectrons interacting favorably w ith th e R F field cross the anode gaps when the field there is m axi
mum retarding as indicated by th e filled circles. T he lines for | k ) = 4 ,1 2 ,2 0 , 28, • • • rep
resent m ean p ath s of electrons traveling with m ean angular velocities — , 7^7,
2, / 4 1 2 2 0
2g 1 ' • ■ around in the interaction space. Since the field is a standing wave, it is clear th a t electrons possessing these velocities in either direction m ay in te rac t favorably w ith the R F field.
n complete cycles in one traversal of the cylindrical anode, n still denoting the integers 0, 1, 2, In general, these anode potential waves m ay be standing waves or waves traveling around the anode structure in either direction w ith angular velocity — radians per second, where / is the R F
frequency. F or the two modes in which adjacen t resonators are in phase (n = 0) and it radians out of phase (« = ~ , the so-called r mode), however, N only standing potential waves on the anode are possible. As examples of
w -
p i
//rA
A
A ' / A AW / ' AA
W '' ZA
A
t + 1 / 4 T t + 2 / 4 T t + 3 / 4 T t 4 4 / 4 T t + 5 / 4 T t + 6 / 4 T t 4 7 / 4 T t + 6 / 4 T t + 9 / 4 T t + 1 0 / 4 T t + 11 / 4 T t + 1 2 / 4 T t 4 1 3 / 4 T t 4 1 4 / 4 T t 4 1 5 / 4 T t 4 1 6 / 4 T t 4 1 7 / 4 T t 4 1 6 /4 T t 4 1 9 / 4 T t 4 2 0 / 4 T
I p
\ \ .>_
\ \ '
11 V 1 '
-+ -V
a / v a r
I KI —2M _ V \ ______ 7 ^
|k| =18
Fig. 10.— A plot sim ilar to th a t of Fig. 9 for the standing wave com ponent of anode potential of periodicity it = 2 in a m agnetron having eight resonators. Electrons which
. , . . . . . . 2 t t f 2 i r f 2tt/ 2 i r f
in te rac t favorably have m ean angular velocities - r r , —jr , T7T> ~7T>
L 0 1U 1 4
in the interaction space.
1 in either direction
standing an d traveling anode p o tential waves in an anode stru ctu re having eight resonators (A7 = 8), the standing wave for n = 4 an d standing and traveling waves for n — 2 are shown in Figs. 9, 10, and 11 respectively.
From w hat has been said ab o u t the R F field and the electronic motion in the interaction space of the m agnetron oscillator of T y p e I I I , it is possible
M A G N E T R O N .i.Ç G E N E R A T O R OF C E N T I M E T E R W A V E S 185
to understand its fundam ental electronic mechanism. As in any oscillator, the criterion for oscillation is th a t more energy shall be transferred to the Rh field by electrons driven against it than is taken from the R F field by electrons accelerated by it. T his can be accomplished in the traveling wave
i
1&
'¿A&
2 2 2 2 VeA• X V 7 ' \ _____ ^ k = / = -
t+ 1 /8 T --- V -t^.--- —
.
t + 1 /4 T — ■ il
n a
y
U-
t + 2 /4 T
t + 3 /4 T
t + 4 /4 T
t 4 5 /4 T
t + 8 /4 T
OA-
11 '' r
\ / \
- Z Z \ " r f
---
\ - U
---
i »
T +-
-l-i . . ...X L __I
^ T T \ / A _____
t + 7 /4 T
t + 8 /4 T
t + 9 /4 T
t +■ 10/4 T
I 1 1 A
f \ v
_____,\= f= P \
v \ _ y \ _____
\ ______/ \ ± = / T ~ \ ~
K = 1 8
-6/
Fig. 11.—A plot sim ilar to those of Figs. 9 and 10 for the rotating wave of anode potential of periodicity » = 2 in a m agnetron having eight resonators [see equation (13) in the text).
The field a t the in stan t t + I T is p lotted as a dashed line to show th a t the traveling wave does n ot preserve its shape a t all instan ts. W hereas the wave travels in one direction with the angular velocity electrons which travel with velocities • • • in the
2. 1 1U lo
9 f 9 f
sam e direction or w ith velocities • • • in the opposite direction in teract favorably with the R F field. D irections of electron motion m ust now be distinguished. Electrons whose velocity is opposed to th a t of the rotatin g field are said to be driving a “ reverse” mode.
m agnetron oscillator only if the mean angular velocity of the electrons is such as to make them pass successive gaps in the anode a t very nearly the same phase in the cycle of the R F field across the gaps. T hen it is possible for an electron which leaves the cathode in such phase as to oppose the tangential com ponent of the R F field across one anode gap, to continue to
lose energy gained from the D C field to the R F field a t successive gaps.
E lectrons which gain energy from the R F field are driven back into the cathode afte r only one orbital loop an d are rem oved from fu rth er motion detrim ental to the oscillation. T h is process of selection and rejection of electrons forms the groups of bunches, shown in Fig. 2(c), which sweep past the anode slots in phase to be retarded by the R F field com ponent. The criterion th a t the electron d rift velocity shall be such as to keep these bunches in proper phase is analogous to the condition th a t the drift angle in a velocity v ariatio n oscillator [Fig. 2(b)] be such as to cause th e bunches to cross the gap of the second or “ catcher” cavity in phase to lose energy to the R F field across the gap.
T he condition placed upon th e m ean angular velocity of the electrons may be discussed ihore readily by reference to Figs. 9, 10, and 11. Consider first, however, only Fig. 9 for the standing p o ten tial wave of the n = 4 mode, and focus a tten tio n on an electron which crosses the gap between anode segm ents 1 and 2 a t the in sta n t t when the R F field is m axim um retarding, th a t is, th e potential on segm ent 1 is m axim um an d on segm ent 2 minimum.
I t is clear th a t this electron can cross th e n ex t gap in the same phase if the tim e required to reach it is (|/>| + \ ) T, in which p is any integer and T is the period of R F oscillation. In Fig. 9, four lines are draw n representing the mean p a th s of electrons m oving w ith such velocities as to make p = 0, 1, 2, and 3. E ach line crosses a gap when the R F field is maximum retarding, th a t is, when th e p o tential has the m axim um negative slope at the center of the gap. As will be seen later, a more convenient parameter, to be called k, is th a t whose absolute m agnitude, |*|, specifies the number of R F cycles required for the electron to move once around the interaction space. 1*1 is then the num ber of cycles betw een crossings of successive anode gaps, which for the ir mode of Fig. 9 m ust take on the values:
= \P \ + 2 ’ Z’ = °) =hl, ± 2 ,- • - ,p = 0, ± 1, ± 2, • • ■
or the values given by the m ore general expression, applicable to any mode:
p = 0, ± 1, ± 2,- • •.
In this expression, ”, is the phase difference between adjacen t resonators, expressed as a fraction of a cycle, k m ay th u s assume the values given by
k = n + p \ , )
The m ean angular velocity which the electrons m ust possess is then given by
dd 2tr 2x f j.
I t = k T = * ’ in which 0 is the azim uthal angle.
For the x mode (« = ~ ) i t is seen th a t the negative integers, p, give the same series of values for | k \ as do the positive integers including zero.
The sequence is | * | = 4, 12, 20, 28, • • • . Reference to Fig. 9 indicates th a t electrons m ay travel in either direction around the interaction space and in teract favorably w ith the R F field, provided their m ean angular velocity is given by equation (1 1) w ith values of k specified by equation (10). T h a t this should be so is clear from the fact th a t the anode potential wave is a standing wave w ith respect to which direction has no meaning.
Fig. 9 also m akes clear ho\Y an electron moving w ith velocity different from th a t corresponding to the lines shown, will fall out of step w ith the field, and on the average be accelerated as much as it is retarded, thus effecting no net energy transfer.
In Figs. 10 and 11, diagram s for the n = 2 mode similar to th a t of Fig. 9 for the x mode are shown. Fig. 10 is for electronic interaction w ith a stan d ing wave of periodicity n = 2 and Fig. 1 1 for a traveling wave of the same periodicity. Again, as in the case of the x mode, the values of k for fa\ orable electronic interaction are given by equation (1 0).
T he sequence of positive integral values of p (including zero) and the sequence of negative integral values of p do n o t each give the same sequence of values for [ k | as was the case for the x mode. l o r p §: 0, | k \ — 2, 10, 18, • • -, and for p < 0, | * | = 6, 14, 22, • • • . For the standing po
tential wave (Fig. 10) each of these values of | * j does specify the velocity of possible electron m otion in either direction for favorable interaction with the field. F or the traveling potential wave (Fig. 11), on the other hand, only the positive values of k {p ^ 0) correspond to electron motion in the same direction as the traveling wave, the negative values of k (p < 0) cor
responding to electron m otion in the direction opposite to the tra% cling w'ave. T he sign of k has significance. If the electrons arc m o \in g w ith velocities specified by equation (1 1) with the negative values of k from equa
tion (10), and are th u s moving counter to the traveling R I field wave, the electrons are said to be driving a “ reverse” mode.
T he actual electron orbits do n o t correspond to simple translation but, as has been discussed, to rotation superposed on translation. 1 he epi
cycloid-like scallops in the orbit are of no significance to the fundam ental electronic mechanism. I t is the mean velocity of the electron^ motion around the interaction space, specified by the relative values of V and B, th a t is of im portance. T he m agnetron m ay operate, for example, a t such
M A G N E T R O N .15 G E N E R A T O R OF C E N T I M E T E R W A V E S 187
high m agnetic field, provided V has the proper value, th a t the scallops be
came relatively small variations in an otherwise sm ooth o rb it (see Fig. 18).
In the cylindrical m agnetron, the radial variation of the D C electric field, resulting in a decrease in the m ean angular velocity of the electrons as the}' approach the anode, would m ake it impossible for an electron to keep step w ith the fields across the anode gaps were not a m echanism of phase focusing operative. T h a t such focusing is inherent in the interaction of electrons and fields will be seen later.
3.2 The Interaction Field: The electronic m echanism which has been discussed in term s of electron motions through th e fields a t the gaps in the m ultisegm ent anode, m ay also be discussed in term s of the traveling waves of which the R F interaction field m ay be considered to be composed. The R F interaction field corresponds to anode p o ten tial waves like those plotted in Figs. 9, 10, and 11. T he interaction fields for the several modes of oscil
lation of the resonator system are thus to be distinguished by the number, n, of repeats of the field p a tte rn around the interaction space. Since the p o tential a t the anode radius is nearly constant across the faces of th e anode segm ents and varies prim arily across the slots, the azim uthal variation of the field cannot be purely sinusoidal b u t m ust involve higher order harmonics.
F or a mode of angular frequency co = 2x/, corresponding to a phase differ- 2tt
ence between adjacent resonators of n — , the anode potential wave is of periodicity n around the anode and m ay be w ritten as a Fourier series of com ponent waves traveling in opposite directions around the interaction space:
V „ = Z A k ^ ul~kl+y) + Z B k ^ t+kM\
k k ( 12)
k — 11 -(- p N , p — 0, rfc 1, rb 2, • • • .
N ote th a t the sum m ations are taken over all integral values of k given by equation (1 0).
T he interaction field for any mode of periodicity n is thus represented by two oppositely traveling waves, whose fundam entals are m oving with angular velocities - = — , and whose com ponent am plitudes, A t and Bk, co
n n
in general are n o t equal, y and 5 are a rb itra ry phase constants. The ex
pression (1 2) m ay be reduced.to the form : VRF - Z (A k ~ B k) cos (co/ - hd + y )
k
+ Z 2B k Costco/ + ^ - y - ^ c ° s^ £ 0 - ^ k = n + p N , p = 0, ± 1, ± 2, • • ■,
*
which shows th a t the complete field p attern m ay be considered to consist of a ro tatin g wave superposed on a standing wave, each having a fundam ental com ponent of periodicity n.
The fact th a t the periodicities, k, of the harmonics in the expressions (1 2) or (13) are those for which k has the values given by (1 0) m ay be de
term ined from a Fourier analysis of the complete anode potential waves like those of Figs. 9, 10, and 11. Only those harmonics which specify the same p a tte rn of potentials a t the centers of the anode segments as the fundam ental are adm itted in the analysis.
As has been mentioned before, the complete field p attern s for n = 0 and n = — are standing waves. T hus for these modes of oscillation / I t = l hN in the expressions (12) and (13). For the other modes, n = 1, 2, 3, • • •, N-=• — 1, the electrons m ay interact with the traveling field com ponent of expression (13) or w ith.the standing field components which, in case Ak = lh , is the only com ponent present (see Figs. 10 and 11 for the case n = 2, N = 8).
The term s in expressions (12) and (13) for which | k \ = n are the funda
m ental com ponents; those for which | k | ^ n are called the H artree h a r
monics. The com ponents of field strength corresponding to these harmonics in the interaction field p atte rn fall off in intensity from anode to cathode more rapidly the higher the value of k. The variation w ith radius is of the
/ r V
form I — 1 . T hus the farther from the anode one samples the field, the more like the fundam ental sinusoidal p atte rn it appears.
For each value of k in expression (12), whether or n o t A k = Jh, there are two oppositely traveling sinusoidal wave com ponents of periodicity k.
Since each requires k cycles of the R F oscillation to complete one trip around 'lirfr the interaction space, the linear velocity a t the anode surface is { ° cor-
k responding to an angular velocitv of . Thus, as seen in Fig. 11 for the
k
instant t + T /8, the change of shape of the to tal traveling wave indicates th a t the com ponents of which it is composed travel w ith different velocities.
In Fig. 23 are shown instantaneous R F interaction field p a tte rn s for the fundam ental com ponents (p = 0) of the n = 1, 2,3 , and 4 modes of an anode block having eight resonators.
3.3 The Traveling Wave Picture: I t is instructive to discuss the operation of the T ype I I I m agnetron oscillator in term s of electron interaction w ith the traveling wave components present in the interaction field. T his m ight a t first appear to be difficult in view of the m any com ponents of several possible modes. B y mode frequency separation, as discussed later, it is
M A G N E T R O N A S G E N E R A T O R OF C E N T I M E T E R W A V E S 189
