unclassified 417620 - dtic loginanode structures for cold-cathode high-power magnetron by y. ikeda...
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UNCLASSIFIED
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Anode StructuresFor Cold-CathodeHigh-Power Magnetron
by
Y. Ikeda
417620
DtCSeries No. 60, Issue No. 455Contract No. AF 19(628)-324 eztt*
June 30, 1962ISA
£ £ ~
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US DEPARTMENT OF COMMERCEOFFICE OF TECHNICAL SERVICESWASHINGTON 25. D.C."
AFCRL-63-320
Electronics Research LaboratoryUniversity of CaliforniaBerkeley, California
ANODE STRUCTURES FOR COLD-CATHODE
HIGH-POWER MAGNETRON
by
Y. Ikeda
Institute of Engineering ResearchSeries No. 60, Issue No. 455
Contract No. AF 19(628)-324Project No. 5634Task No. 563402
Scientific Report No. 20
June 30, 1962
Prepared forAir Force Cambridge Research LaboratoriesOffice of Aerospace ResearchUnited States Air ForceBedford, Massachusetts
Acknowledgment
The author is indebted to the Electronics Research Laboratory,
University of Caifornia at Berkeley, for providing him with the oppor-
tunity of performing the investigatiion. The research has been carried
out under the guidance of Prof. D. H. Sloan, from whom the original idea
regarding the new structure came. The author also gratefully acknowledges
the suggestions made by Prof.- A. W. Trivelpiece and Prof. C. Susskind with
regard to the final manuscript, as well as the technical assistance by
Messrs. 0. B. Westwick and J. Tombaugh.
-ii-
SE TERY
Rf interaction properties of several structures suitable for
cold-cathode high-power magnetrons have been investigated analytically
and experimentally, with special emphasis on increasing the under-
standing of the interaction and maximizing the area of coherent
interaction with the electron beam at a given frequency. The
structures analyzed were designed for large mode separation,
mxim= interaction inedance, and easy coupling to the output
circuit.
-iii-
TABLE OF CONTENTS
Page
I. INTRODUCTION ....................... 1
II. INVERTED MAGNETRON STRUCTURE ............... 1A. Proposed Anode Structure, Symbols and Definitions... 1
B. Resonance Frequency for the Individual Cavity ........ 3
C. Measurement of the Resonant Frequency .... ......... 4
D. An Equivalent Circuit Representation .... ......... 10
E. Cavity Losses and Q ...... .................. ... 15
F. Mode-Separation Improvement ......... . . ........ 18
III. CONVENTIONAL-MAGNETRON ANODE STRUCIJRE .. .......... ... 20
A. Anode Structure, Symbols, and Definitions ... ....... 20
B. Resonant Frequency of an Individual Cavity ........ ... 20
C. Measurement of Resonant Frequencies ..... .......... 24
D. Equivalent Circuits for Linear Magnetron Structure . . 25
1. Analysis for n = 0 Mode ... ............. .... 25
2. Analysis for n = 1 Mode ... ............. .... 28
3. Numerical Results and Experiment ........... .... 29
E. Cavity Losses and Q ...... .................. .... 30
F. Improvement of Mode Separation .... ............ ... 34
G. Comparison of Structures of Secs. II and III ....... 34
IV. ANODE-STRUCT1URE CONSIDERATIONS .... .............. .... 37
A. Reduction of Outer Radius .... ............ .... 37
B. Magnetron Structure with Large Mode Separation . 38
C. Outer-Cathode Anode Structure with Short-Circulating
Bare Along Outer Edge ........ ................. 40
D. Cylindrical Cavity ...... .................. ... 41
V. CONCLUSIONS ........ ........................ .... 43
REFERENCES ......... .......................... .... 43
-iv-
LIST OF ILLUSTRATIONS
Figure
1 Inverted Magnetron Structure ....... .............. 22 Equivalent Capacitance ...... .. ................ 3
3 Graphical Determination of Resonant Frequency ......... 5
4 Results of the Calculation of Resonant Frequencies . . 65 Cavity Used in Experimental Confirmation of Calculated
Frequencies ....... .... ...................... 7
6 Alternate Inverted Structure ....... .............. 8
7 Measured Spectra and Calculated Frequencies for Unit
Cavity and for Cavities at Both Ends ..... .......... 98 Equivalent Circuit for the Structure of Fig. 1. ..... 11
9 Four-Terminal Network Elements of the Line of Fig. 8 . 12
10 Phase Characteristics and Characteristic Impedance for
the Structure of Fig. 6 ..... ................. 13
11 Equivalent-Circuit Representation for Various Resonant
Conditions: (a) Parallel Resonance, (b) Series Reso-
nance, (c) Combined Resonance .... .............. ... 14
12 Schematic Representation of Gap .... ............. ... 17
13 Distribution of Loss Density ....... .............. 17
14 Gap Modified for Improved Mode Separation. ........ 18
15 Calculation of Resonant Frequency from Eq. (14). ..... 19
16 Structure for Cylindrical Magnetron ........... 21
17 Structure for Linear Magnetron ... ............. .... 21
18 Solutions of Eq. (18) for K = 0 ... ............ ... 22
19 Comparison with the Results of Sec. II ........... ... 23
20 Test Configuration ...... ................... ... 24
21 Equivalent Circuit for n = .0 Mode .. ........... .... 28
22 Equivalent Circuit for the n = 1 Mode ............. ... 29
23 Experimental Configuration .... ............... .... 30
24 Summary of Experimental Results .... ............ ... 31
25 Schematic Representation of Gap .... ............ ... 32
26 Loss-Density Distribution over Plate Surface ........ ... 33
27 Structure Used for Mode-Separation Improvement ..... 34
_V--
LIST OF ILLUSTRATIONS (Cont.)
Figure
28 Mode Separation end R/r Ratio at 1000 Mc as a
Function of 0 ...... ..................... 3529 Mode Separation and R/r ration as a Function of
Mean Radius (Rr)1/2 ...... ................... ... 36
30 Proposed Reduced-Size Anode ....... .............. 37
31 Structure with Iil-roved Mode Separation: (a) Proposed
Model, (b) Simplified Model ....... .............. 39
32 Anode Structure with Outer Short-Circuiting Bars .... 40
33 TE-Mode Structure ...... ................... ... 4234 End Cavities for TE-Mode Structure ........... 42
-vi -
LIST OF TABLES
Table Page
1 Resonant Frequencies for the Structure of Fig. 5 .... 72 Resonant Frequencies for Another Structure 9....... 9
3 Resonant Frequencies for the Structure of Fig. 20... 24
4 Resonant Frequencies Measured with Structures with Bars. 26
5 Calculated and Measured Frequencies ... .......... 38
6 x - 2xr/A 0 for Various t and I .. .......... .. 37
7 29r/N O (-er) for R/r = 2 ..... ................ ... 388 Resonant Frequencies in Terms of 3a.. .............. .... 39
9 Results for Fig. 32 .................. 41
-vii-
I., INTRODUCTION
This report deals with the rf interaction properties of several anode
structures for high-power, cold-cathode magnetrons. Pphasis is on under-
standing the interaction and on determining how the region of coherent inter-
action with the electron beam can be made as large as possible at a given
frequency so as to maximize the output power.
In a conventional magnetron, the number of resonators is limited by
the requirement of reasonable separation in frequency of the modes. As
the number of resonators increases, the mode separation of even the "strapped"
and "rising-sun" configurations begin to be insufficient..
The structures investigated in this report were chosen as (1) suitable
for construction in the cold-cathode magnetron experiments in this Laboratory,
(2) possessing large mode separation, and (3) having a circuit that is easily
coupled to the output circuit.
One circuit that was tried was a corrugated cylindrical wall with inter-
action bars and coupling channels. This circuit has a 60-percent mode
separation but a rather low interaction impedance for the TM0 mode, since
the minimum electric field occurs at the wall.
The new structures analyzed in this report are free from this difficulty;
however, they do suffer from the disadvantage of being susceptible to possible
multipactor action along the magnetic field resulting from the rf electric
field. This problem probably can be avoided by a careful design of the circuit.
The main assumption made in the analysis is that the axial length of
the structure is much shorter than a free-space wavelength, so that field
variations along the structure can be neglected. Further, it is assumed
that since many bars oriented parallel to the axis are to be used in structure,
the capacity between them and the cylindrical wall is taken to be uniformly
distributed along the cavity circumference. In many cases the capacity between
anode and cathode is neglected.
MKS units are used throughout and only the symbols given other than
common meaning are explained in the text.
II. INVERTED MAGERON STRUCTURE
A. PROPOSED AN1E STRUCURE, SYMBOLS AND DEFINITIONS
In the first anode structure to be discussed (Fig. 1), the points at
(II. INVERTED MAGNETRON STRUCTURE)
ZUz
Cyl dr" Plate
Bar
(radius a)
II I, tl - !nd -
RI Cavity
FIG. 1. -- Inverted magnetron structure.
which the plate electrodes and bars are connected have been indicated by
dots. The slow-wave structure is on the inside and is surrounded by a con-
centric cold cathode that depends on secondary emission for its electron
current. The TM0 mode that is excited in each cavity makes the bars alter-
nately plus and minus and consequently provides the circumferential rf fields
necessary for magnetron operation. There is a dc magnetic field in the
direction of the z axis.
The gap between the plates of the anode structure in Fig. 1 is denoted
by S , a parmeter chosen so as to minimize the multipactor problem and to
optimize the interaction impedance. In general 8 is small and as a conse-
quence the capacitance for a unit cavity is large, so that the frequency of the
cavity is insensitive to the electron beam interaction as well as to the
proximity of the cathode cylinder. For this reason no conventional "straps"
ae required for this structure.
(II. INVERTED MAGNETRON STRUCTURE)
B. RESONANCE FREQUENCY FOR THE INDIVIDUAL CAVITY
The anode structure shown in Fig. 1 is made with a large number of bars.
Their effect is therefore approximated by an equivalent uniform capacitance
per unit length in the circumferential direction (Fig. 2). The edge effect
KZZ 1rVillar-
FIG. 2.--Equivalent capacitance K.
of the plate may also be included in this equivalent capacity. It is assumed
that only the z component of the electric field exists inside the cavity
because the gap dimension 6 is small.
In cylindrical coordinates the solution of Maxwell's equations is
given by the following:
Ez = EO [Jn(kP) + ANn(kp)] cos no
H = [Jn'(kp) + ANn'(kp) ] Cos no
H = - j nEo [Jn(kp) + An(kp)] sin no
Pwherek = 2 c 0 n=O, 1, ± 2, ... and A=- Jn(kr)INn(kr). Also,
CPOr.Also,since at p = R, H 0(R)/V(R) = I (R)/V(R) = JaW, where K is the capacitance
per unit length, we have
(kR) n (kR) + An (kR) (2)Jn J(kR) + AN (kR) 110
The resonant frequency for the various modes is determined by the above
equations. It is convenient to rewrite these equations in terms of some new
- 3 -
kI. INVERTED MAGNETRON STRUCTURE)
variables. Letting kR = 2AR/X 0 = x, where X 0 is the free-space wavelength
and r/R = ,we have
, n '(x)Nn( x) - N '(x)Jn( jx) K6B n(x,1) = - =- x (2a)
Jn(X)Nn(IX) - Nn(x)Jn( rx) (OR
The capacitance per unit length between parallel bars of radius a
separated a distance d is
C0 W t 0 /log [(d + (d2 - 2 ) /2a (3)
From Fig. 1K = C0 A /d
As an example, we take R = 66 mm, = 1/8, 6 =3.5 mm, A = 5 mm,
d = 7.2 rm, and a = 2.5 mm. Then 6/E 0R 0 0.15. The resonant frequency
for the n = 0 and n = 1 modes can be determined as shown graphically in Fig. 3.The results of these calculations are given in Fig. 4. The rate of mode
separation is also given.
If the central cylinder is removed, kR is the first root of J0 (kR) = 0
for the TMo01 mode; the rate of mode separation is about 60 per cent. The
radial dimension of the cavity resulting from Fig. 4 is bigger than the
cavity for J 0 (kR) = 0 if ; > 0.45 and the mode separation is good if - < 0.14.
This structure has a large mode separation for small values of I ;
the rate of mode separation is not significantly affected by the capacitance
of the bars.
C. MEASURET OF THE RESONANT FREQUENCY
A schematic diagram of the cavity used to check the calculated frequencies
is shown in Fig. 5. The cavity was excited and the fields in the cavity
were probed by small antennas inserted into holes as shown in the figure.
The various modes of oscillation were detected by perturbing the fields
with small wires that could be inserted into the drill holes at various
places in the cavity.
The calculated and measured frequencies are compared in Table 1. The
end capacitance per unit circumferential length is taken to be 1/4 of the
-4-
(II. INVEIrED MAMVh~RON STRUCTURE)
I3 x = 455 K0 X2 for 6- 0.15
x 12 =4.95 fo 0
01 for j - = 0 .152 -- X l = 1 .5 5 1 0 O
\ r-o. 15x
I I
I I\0
B o B
- 1.8
11 } forl= 0B
-2 Xl
x02 50
B I
FIG. 3.--Graphical determination of resonant frequency.
-5-
(II. INVERTED MAGNETRON STRUCTURE)
f - f0
f£0 W
nd 21R
0
k,, Mode separation
80 4
0. .10.2--
60 3//
40 -2 .,x. 0.2
20 - 1
1/16 1/8 1 4 1/31/ 23
0.6 0.08 o.1 0.2 0.3 o.4 0.5 o.6 0.8
r/R =
FIG. 4.--Results of the calculation of resonant frequencies.
-6-
(II. INVERTED MAGNETRON STRUCTURE)
IExciter iProbe
L 68
3FIG. 5.--Cavity used in experimental confirmation of calculated
frequencies. R = 68 mm, C = 0.22. (Dimensions in millimeters.)
Table 1.--Resonant frequencies for the structure of Fig. 5
VC6/eo 1).
Frequency (Mc)
Mode Measured Calculated
0 957 950
1 1326 1287
2 2010 -
capacitance of a coaxial line that has an inner radius of 3 mm and an outer
radius of 6 mm. The calculated and measured values agree to within 3 per cent.
In the calculation of the resonant frequency for this case it was possible
to assume the effective radius R to be equal to 1/2 the distance along the
gap in the cross section of Fig. 5; it is also assumed thatAK is equal to
0. In addition to the tabulated results a 1308-Mc mode was found. This is
a weakly excited n = 1 mode that exists in the coupled structure.
These measurements were repeated with the structure shown in Fig. 6.
The results of these measurements are given in Fig. 7. This structure has
many resonances because of the complicated coupling of the structure. These
frequencies are shown in Fig. 7 in relation to the resonant frequency for the
single cavity, and will be given more detailed consideration below. Results
of another experiment with a similar structure but of different dimensions
are shown in Table 2.
-7-
II(II. I1WEHTED MAMIETRON STRUCTUJRE)
Exciter j be
Bars (60 are used)
II g I il
, 66._4. 66.7.iJI .
K ' 72
FIG. 6.--Alternate inverted structure. (All dimensions inmillimeters.) 6 = 3.5, A= 5.0, d = 7.2, a, 2.5,K6/c 0 R = 0.15.
-8-
( j. ~ . £~iiJiIED MGIf-TRO STRUCTIU.RU,
n=1ln-2I n=1n12
n I n=J.I I of Levels of:. modes of normal strength
... ... ... I II I ' .. . wt _m _d _. ..l l l,-wkI nt modes ij L I wea modes li600 6W 100 0 1200 1400 1600
Frequency (Mc)
FIG. 7.--Measured spectra (solid lines) and calculated frequencies for
unit cavity with R = 66.7 mm(.-. ) and for cavities at both ends withR=72m ( ---- ).
Table 2.--Resonant frequencies for another structure: R = 60,
i 0.125, 6= 3, &= 12, d = 10, a = 3, C6/c 0 R 0 0.2; 40 bars.
Measured frequencies marked by an asterisk are caused by end
cavities (cf. Fig. 6).
Mode(measured Frequency (Mc)
circumferent ially) Measured Calculated
0 660 716
(1) 750* (890)
0 975* (890)
1 1125 1175
0 1230
0 1270
-9-
(II. INVERTED MAGMETRON STRUCTURE )
In Fig. 7 the detected frequencies are classified into three levels
according to the amplitude of the oscillation. The amplitude depends on
the method of excitation and thus the classification is not particularly
valuable, although the probes were situated at the correct positions to
measure TM modes. The agreement of theory and experiment is perhaps better
than would be expected in view of the approximations used in determining
the constants.
The end-cavities that were installed for the purpose of terminating
the structure have a resonant frequency different from that of the main
cavities. Therefore they are detected as a different group and are shown
both in Fig. 7 and Table 2. These additional modes are characterized by a
certain number of voltage nodes p of the voltage between adjacent bars in
the z direction. In Fig. 7 the mode for 758 Mc has one node for the value
of p and the configuration given in Table 2 has two nodes for the value of
p. This is a result of the axial length of the latter structure being twice
as long as that of the former.
These additional modes can be avoided by selection of an even number
of main cavities. Then the end plates of the main cavities are connected
with the same bars. It is also important for the number of main cavities
to be even from the viewpoint of eliminating the additional end cavities,
which generally have different resonant frequencies. In general an un-
symmetrical structure at both ends introduces extraneous modes. Care must
be taken to introduce the detecting probe and exciting antenna so as not
to excite extraneous modes. For instance if the probe and antenna are in-
serted in the radial direction separated by an angle of 1200, the usual
n = 1 mode-region has several n = 3 modes apparently excited. Similarly
when the angle is 90 some of the n = 2 modes are excited.
D. AN EQUIVALENT CIRCUIT REPRESENTATION
We can synthesize an equivalent circuit for the structure of Fig. 1
if we assume that the two bars constitute a parallel-wire transmission line
periodically loaded by the reactance of the cavities between the parallel
plates. This equivalent circuit is shown in Fig. 8. The symbol L denoteseq
the reactance that changes from inductive to capacitative as the frequency
is changed. The expression for L iseq
- 10 -
(I. INVERTED MAGNETRON STRUCTURE
L L L
FIG. 8.--Equivalent circuit for the structutre of Fig. 1.
-1 fCO R 6 ±OR Jn(X)Nn(Cx) - Nn(x)Jn(Cx) _ 6L 0Req Mi B 2'XC (4)() xeq Ceq X2Ceq xd Jn'(x)Nn(Cx) Nn'(x)Jn(Cx) xd n
where x = 2R/ X 0 and C = r/R.
The quantity C in Fig. 8 denotes the capacitance between the bars in a
length A and should also contain the effect of the plate edges. In this
calculation we shall include only the capacitance between the bars because
the effect of the plate edges is small compared to the other terms in Leq.
Thus
C - A log- [ d _ 4a} CO (5)
The quantity L in Fig. 8 is given approximately by
L = (6)
The circuit of Fig. 8 is a lumped continuous tranamission line made up
of elementary four-terminal networks such as shown in Fig. 9. The reactance
- 11 -
(II. IWERTED MAGNETRON STRUCTURE)
Jul
2 2
FIG. 9.--Four-terminal aetworeIements of the line of Fig. 8.
Z is given by
z = COq/(1 c2 CLo) L /I - (C/Ceq)] (7)
The characteristic impedance Z and the phase delay P of the waveC
propagating along the bars can be expressed in terms of the open-circuit
and short-circuit impedance of the transmission line:
cos 0 = cos A= [I - (z/Z O )11/2
where
2A2 + 4ZaL + 2L2Zo=J 2(2Z +L)
(8)
z = cuL(2Z + L)(4Z + l)2(2z2 + Z + 2L2 )
Equation (8)is a good approximation for the n = 0 mode; however, it is
not a good approximation for higher-order modes because of the voltage
variation along the circumference of the plates.
From Eqs. (4) through (8) the phase characteristic diagram and the
characteristic impedance as a function of frequency have been calculated
approximately for the structure shown in Fig. 6. The results of this calcu-
lation are shown in Fig. 10, where the n = 0 (TM001 and TMo02) and the n - 1
(TMOil) modes are shown. The frequency f is the ordinate and the abscissa
- 12-
(II. IfNERTED HAG M RTON STRUCTUJRE)
Frequency(kMc)
n=OI
3
0 1 3 Qnd/
o =l
Z/N~ohms
FIG 10 -hs haatrsisan hrceisi meac
for te strctur of Fg. 6
- 13
(II. INVERTED MAGMKTRON STRUCTURE)
LL
L/2 L L
(a)
L L
cCc \\cI = ___\_\ •/\
2 It
L/2 L L
(b)
L L
L/2 L L
(c)
FIG. l1. -- Equivalent-circuit representation for various resonantcondit'ions : (a) parallel resonance, (b) series resonance, (c)ccumbined resonance.
14-
I
(II. INVERDED MAGNETRON STRUCTURE)
is P =&. Also on the abscissa is the characteristic impedance Z dividedc
by the number of bars N (here, 60).
The points AO and A1 denote the conditions where the wave velocity along
the bars is zero and C and L have the value corresponding to paralleleqresonance for each mode (Fig. lla). The points B0 and B1 are at the place
where the conditions for series resonance exist (Fig. llb). Two groups of
circuit elements are possible for such series circuit, as shown in Fig. llb
by the solid and dotted lines. The points C and C are another resonant
condition that can occur for each mode (Fig. llc). The phase difference per
section is X in Fig. llb and 231 or zero in Fig. llc.
The resonances of the structure of Fig. 6 are easily determined from
the result shown in Fig. 10. Since seven main cavities are used, the
resonant conditions are given by A = q/7, where q is an integer. Thus,
from Fig. 10, f = 1250 Mc for q = 1 and f - 1755 Mc for q = 2 for the n = 0
mode. These frequencies are a little higher than the lowest cutoff frequency
for the n = 1 mode, which explains the spectrum of Fig. 7.
E. CAVITY LOSSES AND Q
In this section we shall obtain an estimate of the value of Q for the
unit cavity and the distribution of losses along the cavity surface, assuming
the bars to be absent. The power dissipated per unit area is given by
R= o0 (koEo02 l(koP) - J0 (k0r) N (k0 2
(9a)
R/(k0 E0 2 JO(kr) ]2
~= # w ) L ( ko r ) - N 0 (k- r 1( ~ )
The maximum value of the time-average stored energy density is given by
Ik0 oEo [J1 Jo(kor) N2
T= 2 'O&)- No-k- r 1 kOP (b)
The surface resistance is
Rs 2a
where a is the conductivity of the cavity material,
- 15 -
(II. n ED MAMTRN STRUCMU )
Total power dissipated in the structure is given by
R
PL 2 1 2tp a p +2rr 66a (10)r
The total stored energy isR
= ~ 1 p qnpo dpr
Using the relation between the constant E0 and the voltage at the gap V0 (Fig. 12)
VJ(kor) -1
E= [Jo(kol) - Jo(kor)No(kor)]
we can determine the cavity losses from (9a) and determine the cavity Q from
WoW
Taking the conductivity of copper as 108 mhos/m, we have for the cavity Q
1 = 8.26 x 10- + 18.8 x lo 6 for1 6 -6 -7 R 1
= 9.18 x 10-6 + 20.7 x 0- for =
If we use the values R = 60 mm and = 1.5 mm
Q=697 ( =1/4)
Q=636 ( =1/6)
The distributitsof losses on the plate surfaces are shown in Fig. 13
where the small contribution from oa has been neglected.a
The expressions for the total losses can be simplified as follows
PL 3.o6 x lO-8 R3/2 + 6.92 x lO " ) Vo2 1/4)
and
-8 R3/2 -8\' 2= 3. 6 9 x lo " + 8.33 x 10- Vo(= 1/6)
For a value V0 = 5000 v and the same dimensions (R = 60 mm and = 1.5 umm),
- 16 -
(II. DMERTED MAGERON STRUCTURE)
z
V 0 r
(crest)
FIG. 12.--Schematic representation of gap.
Relativelossdensity
8
6r 1
4
2
0o 0.2 o.4 0.6 0.8 1.o
FIG. 13.--Distribution of loss density.
- 17 -
(II. INVERTED MAGNERON STRUCTURE )
PL = 499+283w =1/4)
PL = 6010 + 340 w ( =1/6)
The first loss term is the plate loss and the second the losses on the
cylindrical portion (p - r).
From Fig. 13 it is obvious that the losses are largest near the central
cylinder. This may present a difficult problem for cooling a high-power
magnetron structure. The problem will be worst for small values of ,which give good mode separation.
F. MODE- SEPARATION IMPROVEMENT
Mode separation can be improved by changing the gap length as a function
of radius, as shown in Fig. 14, since the frequency for each mode changes
differently from the uniform-gap case.
z
t16
r
FIG. 14. -- Gap modified for improved mode separation. r/R = r ,
rl/R = r.' 6 4G r.
We assume as approximate boundary conditions for the TM0 mode
J$Ez = bEzl
I, at pJI = 0 at p - R (13)
where the subscript 1 denotes the region r1 < p < R.
The expressions for the electric and magnetic field are similar to
Eqs. (i) and (2). The characteristic equations for the cavity resonance are
- 18 -
aI. INVERTED MAGN RON STRUCTURE)
n'(X) TIN (N x- )(14)
wherea . J n'(Cx)Nn(Cx) Jn(Cx)Nn'(CIx)
- Jn ( 1X)Nn (Cx) - Jn(X)Nn(C 1x)
and x = kR. It is easily seen that Eq.(14) reduices-to(2b) for TI 1 and
k 0.
For the case I = 1/8 and Ci - 6/8, the resonant frequencies for the
n = 0 and n n 1 modes were calculated from Eq. (14) as a function n. These
results, which are given in Fig. 15, show that a better mode separation is
obtained for small TI.
fl1"fo1 2R
0.5 1
0 ,! gil I . , ii ,0.2 0.3 0.4 0.6 0.8 1 .5
PIG. 5.--(lculation of resonant frequency frcm Eq. (4) withr =/8and 1 = 6/8.
1-192
III. CONVENTIONAL-MAMTRON ANODE STRUCTURE
A. ANODE STRUCTURE, SYMBOLS, AND DEFINITIONS
In this section we shall analyze the rf properties of structures such
as shown in Figs. 16 and 17. These configurations are of a conventional
magnetron design where the anode is the outer structure. The configuration
shown in Fig. 16 is a cylindrical one, similar to that analyzed in Sec. II.
The configuration shown in Fig. 17 is suitable for a linear magnetron
amplifier. A direct current flowing along the central structure can produce
a dc magnetic field, so that electrons move in the axial direction owing
to both dc electric and magnetic fields.
B. RESONANT FREQUENCY OF AN INDIVIDUAL CAVITY
Following the analysis given in See. II the resonant frequency for a
unit cavity is calculated with the assumption of uniform capacitive loading
to replace the effects of the bars and the edges at the inner opening. The
resonant frequency is determined from the following formula:
Jn (x)Nn (Cx) - N n(x)Jn (gx) K(n(X, 9 ) = - x (15)
N()Jn(9x) - n(xNn( X) 0
where x = kr = 2Xr/ X 0, 9 = R/r, and K is given by the same expression as
in Eq. (3). For k = 0, the resonance condition is given simply by
Jn '(x)Nn(gx) = Nn'(x)Jn(gx) (16)
The solutions of Eq. (16)for n = 0 and n = 1 modes are shown in Fig. 18.
The mode separation is better for high values of 9 . However, this means a
snaller value of r for a particular R value, and therefore the interaction
space for the electron beam is limited.
Figure 19 gives the relation between rg and the rate of mode separation
for a fixed resonant frequency. For comparison with Fig. 4, Fig. 18 is also
replotted in terms of kR instead of kr and - (r/R) instead of - (R/r).
The resonant frequency of a cavity for a given value of outer radius and
inner to outer radius ratio are much higher-and the interaction space is
maller.
- 20 -
(n.CUM-ANODE S'M~cWZ)
athode
Bar ~ H 2a
6 -A
ci FIG. 16. -- Structure for cylindrical ngnhtron.
M-G 17.-8tructure for linear agmtron.
-21-
(III. oMM-ANODE STRUCTURE)
Mode 2xrseparation 0
M x 0
75- \ 3
2x -Tfor n 1
' 0 P'te of mode separation..-50- 2 - ----- -
n 0
1.5 2 3 4 5 7 10 15
=R/r
FIG. 18. -- Solutions of Eq. (18) for /C =0.
-22-
Mobde (iii. ourEE-AnoDE sTRUen)separati A/!
70 14
6o -124
60 12 \
50 -10
40 8 Rate of mode separation
30 -6-
0.7 1 2 3 4 5 7 10 15
2RFIG. 19.--Comparison with the results of Sec. IL.
80 - 4
20 4 0r
...... -
10 2 .. . I"-
n =0 e-
0 I 0 1 1
0.7 1. 3/R 0. 05i r t of e si80 4
0.0/5 0 fo = r/K. .- 2 - -
(III. OUrE-ANODE STRUCrURE)
C. MEASUR1240T OF RESONANT FRI UENCIES
Figure 20 is a schematic diagram of the experimental setup used to test
the theory presented in this analysis. Table 3 is a tabulation of the
measured results compared with the theoretically calculated values of
resonant frequency. 2 n
Metal cylinders. 1imm
..... ...... " "7In ///../.H, 7 mm
r
R =60m-
FIG. 20.--Test configuration.
Table 3.--Resonant frequencies (in megacycles) for the
structure of Fig. 20.
r n - 0 mode n = 1 mode Mode
(am) Measured Calculated Measured Calculated Note separation(%)
6 1935 1980 2980 2900 No metal 54cylinder
10 1975,1968 2055 2915,2900 2830 " > 46.8
12.5 2017,2027 2080 2820,2845 2810 > 39.8
15.7 2082,2099 2105 2765,2793 2790 > 31.715.7 1920,22 2768,2800 With metal > 37.6
cylinder
15.7 1865,2070 - 2785,2855 - "(somewhat -
eccentric)
- 24 -
I
(III. OUM-A0iDE STRUCTRE)
Measured values for the structure are in good agreement with the critically
calculated values. The metal cylinder has little effect on the resonant fre-
quency because of the capacity it introduces. The next step in the measure-
ments was to investigate the effect of a snall number of connecting bars. The
results of these measurements are tabulated in Table 4. It was expected that
the addition of the bars would reduce the n - 0 mode frequency and improve the
mode separation; however, the addition of the bars did not produce this result
as may be seen from a comparison of Parts A and B of Table 4.
If a metal shaft is inserted along the axis, it is expected to produce
the same effect as the bars insofar as their influence on the mode can be
included in the equivalent capacitance. According to Table 4 the mode
separation is worse with the shaft in place whenever the value of R/r is less
than 4 or 5, and the mode separation is better if this ratio is larger. The
resonant frequency calculated for a Type C structure in Table 4 assumes no
capacitive loading and gives f0 2500 Mc and f 1 3380 Mc. The capacitance
of the bars is thus seen to cause a considerable reduction in the resonant
frequency. The Q of some of the cavities was measured approximately from
the resonant curves. The Q for smaller gap lengths was found to be the order
of hundreds and for larger gap lengths, of the order of 1000.
D. EUIVAIZ1 CIRCUITS FOR LINEAR MAGNERTON STRUCTURE
The equivalent circuit for the structure shown in Fig. 16 is the same as
that given in Fig. 8. The equivalent loading reactance in this case is
eq _-1 r Bn-1 (17)
eq
Since the circuit is the same, similar phase characteristics for the two cases
are expected.
The analysis will be carried out for the linear magnetron structure
shown in Fig. 17.
1. AXALYSIS FOR n - 0 3601. Figure 21 gives the equivalent circuit with
the gmp length assmed to be much maller than a wavelength. The equivalent
inductance for a unit cell is
- 25 -
-26-
Table 4.--Resonant frequencies measured with structures with bars
Type A Type B
Schematic
viewof thestructure(all dfmen- 32 21 42 120sions inmillimeters)
R/r 3, 6 1.5, A 7.5 R/r m 3, 6 = 1.5, A 7.5
Schematic cross- Frequencies Schematic cross- Frequenciessection view measured section view measured
Basic- Probe Excite n = 0 mode Probe . Excite n- 0 modemeasure- . 2205 Mc 1934 Mcments n = 1 mode n = i mode
2580 Mc240M~ ~ ~~ f-fO . flO
i fo - 0.170 I fo - 0.257
Miscellaneous n = 0 n = 0 modemeasurements 2055 Mc: 1920 Mc
2276 mc n w 1 moden 1 Mc 2400 Mc
End cavities 2692 Mc 1 0.250ZCathode cylinde f = 0.250
2020 5Mc 1918 mc(weak mode) LJ 214o.0me2155 MC I (faint mode)2276 Mc n=in-End cavities 2410 Mc
Both probes in 2685 Mcend cavity 2700 Mc
eB n - 0 -M 021140 me 1918 me (weak)
(very 2142 Mc-- strong) n = 1i
n = 2402 MC (weak)2405 K 66mOne probe in 2710 Mc Both probes in 2710 Mcend cavity end cavity 2726 Mc
-27-
Table 4 (Continued)
Type C TypeD
Schematic A 4.5viewof the4structure
(all di- 8 28 42mensions
in milli-meters)
R/r 0 5, 6 =7.5 and 12 mm R/r =2.5, 6.= 9.5 min
Schematic cross- Frequencies Schematic cross- Frequenciessection view measured section view measured
Basic f'o = 2020 14c fo - 1490 Mcmeasure- fl = 2920 Mc fl . 1896 Mcments i fl-fO E- fl-fO
5o- f o-f .446 9 5- = 0.2720 "fo
Miscel 7withoutiscel- 7. cylinder fo = 1386laneous --
Measure- f0 = 1854 W fl - 1670merts fl-fO 0
fo - i fl-f_0 0Cathode cylinder with cylinder cathode f013(diam.) x 13 P0 = 1821 W cylinder
19d56 21.5 (diam. ) x 30
foifO = 1348 mc Ctoefo - 1380
fl = 2162 cylinder fl-f0f,2098 21.5 (Aiam.) o.21B jflBfo =x 50 if
_7- 058Cathode fo . 146o
hd cylinderylnde
f(W2098d12528) p o0i.lonO
x 30 fo
Cathode34 cylinder f 1
Z 2x 3D _: 1: O a 0.237
Cathode cylinder Eccentric, fO 0.313(diam. x 28 position
(III. OUIM-ANODE STRUCrURE)
L L L
g 0 L 0 L02 o 0 0
FIG. 21.--Equivalent circuit for n = 0 mode.
The capacitance between cathode and anode per section is
CO = 21E 0 A/log (rla)
and the corresponding inductance is
LO log (r/a) (19)
The phase characteristics for waves propagting in the axial direction are
given by
cos 0=1-9 (20)2
where 3 A = 0 and 0 = o(L + L ) The characteristic admittance is
Yx -- (21)
2. ANALYSIS FOR n = 1 MODE. A good equivalent circuit representation
is more difficult to obtain in this because of the field distribution. An
equivalent circuit that is a good approximation to the structure is shown
in Fig. 22. The quantity (0 is the resonant frequency of the TE coaxialc
line mode and is given by the first root of
J '(ka) N '(ka)
' (kr) - (22)(kr
where
k. 2/X o = c o
The effective capacitance C is determined from the electric stored
energy :
- 28 -
(II. OUTER-ANODE sTRuCTuRE)
(2/JOC1 ) 1 - (CO /C)2] (l/jac)[1 -C (/W)2]
FIG. 22.--Equivalent circuit for the n = 1 mode.
1 V12 dv (23)
so thatC1 ", ( E - 8)/2 log (rla)
where VI and E, are respectively the voltage and field between the anode
and cathode for the n - 1 mode. The circuit of Fig. 22 has its cutoff atW 3
CThe effective inductance can also be determined fron energy considerations:
Lx, = -&- B11 (x, ) (24)
The propagation characteristics of the circuit are given by
cos 0 = 1- - (25)2
where 0 - A and - .C [l - (co/)2]
The characteristic admittance is
ch - l (1 - (a) (26)
3. NtJURICAL REULTS AD EPERIMME . The phase characteristics and
the characteristic admittances for the n - 0 and n - 1 modes for the
-29-
(III. OTER-AN01E STRUCTURE)
/6
- a- 12 r =15 Jr 60
A ---- - -- -- -- --FIG. 23.--Experimental configuration.
structure shown schematically in Fig. 23 are shown in Fig. 24 for the case
R/r 4. These results were obtained by using Eqs. (17) through (26)
and the impedance for the mode from these equations is the order of a few
tens of ohms.
Selecting an axial length of q A , where q denotes the total nunber
of sections, we can predict all the resonances of this structure from the
phase characteristic diagram of Fig. 24. Table 5 gives the results between
calculated and measured resonant frequencies for a structure having six
sections. As can be seen there is good agreement between the calculated and
measured values of the resonant frequency. Not every frequency was measured
because of superposition of same modes or difficulty of excitation of sme
modes.
E. CAVITY LOSSES AND Q
Following the analysis of Sec. II, we find the approximate Q of the
structure shown in Fig. 25 from
12.6x 0 + 3.21x 0"-6-6 1 4)
-rand -
-o.6 x lo + 3.99 x 10 -r
-30-
(III. ouri-ANODE ST1RUCrUnE)
(Gc)
3 10 n--- ----- 3490OMc
0) c
0~ ~~~~~ 0. . 2 253)=Ar
0 0.05 01 0.15 02 0.25 3 Y (o)0-05 01 0-1 0.2 .25 Yc(ho
FIG. 21 .- Suiary of experimental results. R/r = 4, r 15, a = 12,A 6, 6 am.
-31-
(III. OLTER-ANOEE STRUCTURE)
Table 5.--Calculated and measured frequencies (in megacycles).
r = 15 mm, R/r - 4, a 12 mm, A - 6 mn, =1 rm, q = 6
n 0 n-i
Calculated Measured Calculated Measured
2120 2091 2780 2763
2120 2078 2780 2769
2110 2041 2800 2785
2100 1922 2830 2813
2075 2890
1930 3030
I,
Vo0(crest)
FIG. 25.--Schematic representation of gap.
Taking R -60mm and - 1.5 mm we have
Q-945 (1 .4)
Q -976 (9 .3)
These Q values are about 50 per cent higher than those of the structures
analyzed in Sec. II. However, for the same resonant frequency and sae
r/R, the Q's in the tvo cases are about the same.
The total losses for this structure are
-32-
I
(III. OUTER-ANOE STRUCTURE)
Relat ivelossdensity
0.5
0.4 Rr
0.3 3
0.2 "
0.1
00 0.2 0.4 0.6 0.8 1.0
p/R
FIG. 26.--Loss-density distribution over plate surface.
FL (21.0 x 1 0 8 r3/2 + 5.32 x l o - )Vo2 ) - )
- (P.3x 1O8 r3/2 + 5.36 x l° 8 V0 2( - 3)
Aiin we take V0 - 5000 v, R = 60 mm, and a 1.5 m:
PL 4 270+1 0 9w (9 -4)
PL - 4 30+126 w (C -3)
Although these losses are smaller than the values of Sec. II, it must be
noted that they would be larger if the frequency was the sme as for
structure of Sec. II.
Figure 26 gives the distribution of losses over the surfaces of the
plates.
-33-
(III. OUTER-ANODE STRUCTURE)
FIG. 27.--Structure used for mode-separation improvement.R/r, C 1 = rl/r , 6<<r.)
F. IDPIEWEr OF MODE SEPARATION
The method of Sec. II has been applied to the structure depicted in
Fig. 27. The equations for determining the resonant frequency for various
values of T, and wq are
Jn '(x) Jn '(Cl x)a - (2(7))p
aJ n Rx)ncx) - n(ElxJ¢("x)
0 n I(f 1x)N n (x) N- N(Ilx)J (gx)
where x - kr.
Table 6 gives the value of x and the mode separation for severalconditions. It is seen that the mode separation is improved by a large q.
This has the disadvantage of a sall r, which may make fabrication of the
structure difficult.
G. COMPARISON OF STRUCTURE OF SECS. II AND III
At a fixed frequency of 1000 Mc, the mode separation and R/r ratio is
given as a function of the interaction space radius B in Fig. 28. We seethat the mode separation is always better for the inverted mgetron structure
Figure 29 gives the mode separation and R/r ratio as a function of the
-34-
(III. OUTER-ANODE STRUCTURE)
R/r and
100 f - f0
70o (i00%)
Mode separation r
50 4
IO R~
R r20
5\\
x\R \
xx
S 3 4 5 7 10 20 30 4o
FIG. 28.-,,@ode separation and R/r ratio at 1000 Mc as a function or RO.-35
(III. OUTER-ANODE STRUCTURE)
R/r and
S10C 1 o 00%)0
70 i° o Mode separation I /
50r
40
30 -
20 R/r• ~II.
Kr
IR
10\ \
7
5 \ •
4
-S \ I N N
2 X
N \N
1 2 3 5 7 10 20
mFIG. 29.--Nod.e separation and R/r ratio as a function of mean radius (r) 1 / 2 .
-36-
(IV. ANODE.CONSIDERATIONS)
Table 6.-- x =2 /A 0 for various C and ', i
Mod=4 =4 2M =2 1 =3 1 1.5,
o 0.666 0.666 1.8o1 0.86o 0.860 1.95
0 o.433 o.418 1.08
1 0.763 o.673 1.350 0.325 0.313 0.7751 0.755 0.608 1.14
1 2.1% 29.1% 8.33%f l f o,1 76.0% 61.0% 25.6%
8 0132.0% 94.3% 46.5%
geometric mean radius R = Rr. We see
that for a fixed effective size the conventional magnetron has a better
mode separation.
IV. ANODE-STRUCTRE CONSIDERATIONS
A. REDUCTION OF OUTER RADIUS
The structure of Fig. 30 is proposed as a means of reducing the size
of the anode.
zo6T__
61
FIG. 30.--Proposed reduced-size anode.
- 37 -
I(IV. ANODE CONSIDERATIONS)
This structure is analyzed for the n = 0 mode with the assumption ofR > > 8 and of the boundary conditions of continuous voltage and current atz = O, p R. The resonant frequency is determined by
2 tan = 0 (Ar)N0 (0R) "N0'(%r)J(P 0 R) (28)
1 tan o 0 = NO '(,r)JO'(POR) "o' (POr )NO '( oR(
where Po = w N . Table 7 gives the results for both the n = 0 and
n 1 1 modes.
Table 7.--2itr/ 0 (= 3r) for R/r = 2
n2 Ir 2 1 2
1 1.20 0.875 0.575
0 2 0.965 0.696 0.470
3 0.835 o.605 o.405
1 1.4 "1.1 O 0.76
1 2 ol.2 " 0.9 0.67
3 "'1.06 "'0.78 "'0.55
An experimental structure with r = 26 mm, R/r = 2, 7jr - 1, 82 = mm,
and 8 1 1.5 =" was used to test the calculated results. The measured fre-
quencies were 1305 Mc (n = O) and 1752 Mc (n = 1). The calculated values
were 1286 Mc (n = 0) and 1645 Mc (n = 1).
B. MA4GMiRON STRUCTURE WflTH LARGE MODE SEPARATION
The conventional-magnetron structure shown in Fig. 31a has good mode
separation. The structure shown in Fig. 31b is one half of a simplified
version of the structure, suitable for calculation of frequencies.
The lower resonances are given by
tan -i = cot9)2 T (29)
and
38-
(IV. ANODE CONSIDEAIONS)
yx
I6 z( - 2bo x
(a) (b)
FIG. 31.--Structure with improved mode separation: (a) proposedmodel (length z0 along axis); (b) simplified model (open-endedat z -+ zd2).
n21-P2 .(24 24z0
The lowest frequency is given by Ax = A . The results from these equations
are given in Table 8 and as can be seen the mode separation is the better
the shorter z;0. Values of 100 per cent or more are easily obtained. However,
this structure is not satisfactory for high-power operation.
Table 8.--Resonarrt frequencies in terms of Oa.
Y b 2 p 2 + /, 2 Mode separation
a- [ -First ode Next mode Z/a - 2 - 2 "/ 1 o/ " "
1 0.725 1.75 1.73 1.07 139% 47.6%
1 o.826 1.70 1.78 1.13 106% 36.8%
1 0.528 1.2,4 1.66 o.946 13% 79.2%2 2 o.6.1 1.16 1.68 o.994 90.1% 62.6%
-39-
(Iv. ANODE CONSIDERATIONS)
C. OUTER-CATHODE ANODE STRUCTURE W1TH SHORT-CIRCUITING BARS AIDNG OUTER EDGE
Inside the cavity of Fig. 32, the fields are given by the following
expressions: z
c~b
rBars ; diam. 2a)
Bars G (ap length
2d D(Iiam. 2a
i Diamn. 2b
FIG. 32.--Anode structure with outer short-circuiting bars.
Ez = EoJ0 (kp ) cos n0 (30)
where k = 2X/ X and Xn is the wavelength in free space for the nth mode.
ThenH, = j :.L nEEO
0 nEj(kp) sin no j B f0 Jn( ) sin noP O U Jn 0 nn ikp ni
S Jn'() Cos n -- J '(p) cos n
The capacitance between two adjacent bars and the inductance for each
bar are assumed to be given by
\ og(d + d2 " 4a 2)
CO~ iog(h) tan. k4
Since the boundary condition is taken asHod 1
A "J + JC+L (32)
4o -
(IV. ANODE CONSIDMIAIONS)
we obtain, from Eqs. (28) through (30), NS
Jn' (kR)" 2 r b 12 kR. - og - tan Rjj - (33)
J () d a alog[(d +dy- 4a )/2a].
Some numerical results derived from Eqs. (31) are shown in Table 9.
Table 9.--Results for Fig. 32.
I b d d R f " f 0Y a g koR klR tR a a 0 1
1.56 2 2.5 12 2.28 3.58 0.57
2 2 4 20 2.14 3.30 o.
1_ 2 2 1 10 2.4o 3.83 0.6010
D. CYLINRCAL CAVITY
Some experiments in this Laboratory have made use of the TE-mode
structure depicted schematically in Fig. 33. The resonant frequencies
of this structure are given by
J '(nR) - 0 (34)
For the n - 0 mode the frequency separation is 20.3% assuming no variation
of the fields along the axis. To realize this situation in practice, end
cavities such as shown in Fig. 34 must be used. The dimensions of the end
cavity are obtained by solving Maxwell's equations subject to the boundary
condition of 0 -\JI701 H0o '(kp) for 0 <p R, and E.0 for
Rp< :5 R at the plane z a O. The expression forl 0 at z 0 is
E0" 0 AJl(kp)
- 41 -
(IV. ANODE CONSIDERATIONS)
Anode bars
I,I, I - - h ° _III i Cathode .JI I.i End cavity
lR_
IIIMain cavit
S -1 -- -
2R
FIG. 33.--TE-mode structure. FIG. 34.--End cavities forTE-mode structure.
A _ OH 0 2 R l* J1 (ksp)p (35
f,0i12 J 2 2(k s RI) 1~ rn (35
where ksRI are the roots of Jl(x) = 0.
Matching only the first term, the approximate cavity dimensions are
(i .6t3;H/)2 (36)(R (RJIR)2 _ 1
The matching condition for the s-th mode
() 2 1(1 + m)2 (yR)2(ksn) 2 (7R)2 - i)
where m is an integer.
- 42-
V. CONCLUSIONS
Resonant frequencies and mode separation have been determined for
a conventional and for an inverted magnetron structure. These structures
were chosen for their desirability as high-power magnetron circuits from
the point of view of having the largest possible interaction volume.
It is shown that the circuits proposed here have a better mode
separation than conventional structures such as the "rising sun."4
The structures proposed are easier to fabricate than conventional
circuits.
REFERENCES
1. C. W. Hartman, "Production and interactions of electron beams incrossed fields," Series 60, Issue 325, University of California (ElectronicsResearch laboratory), 31 October 1960.
2. S. P. Yu and P. N. Hess, "Slow-wave structures for M-type devices,"IRE Trans. ED-9: 51-57, 1962.
3. J. R. Pierce, "Traveling-Wave Tubes," Bell Syst. Tech. J. 29:390-460,1950.
4. G. B. Collins, "Microwave Magnetrons" (vol. 6, M.I.T. Bad. Lab. Series),McGraw-Hill Book Co., New York, 1948; pP. 739-796.
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LIST OF SCIENTIFIC REPORTS PUBLISHED UNDERCONTRACT AF 19(628)-324
SR-No. 1: D. H. Sloan, C. Sfiaskind, and Staff, "Production and control of electron beams,"Series No. 60, Issue No. 203, 15 June 1958.
SR-No. 2: V. Bevc, "Injection of space-charge-balanced electron beams for microwave tubes,"Series No. 60, Issue No. 204,15 June 1958.
SR-No. 3: A. J. Lichtenberg, D. H. Sloan, C. Sisaskind, J. R. Woodyard, and Staff, "Electronand plasma beam dynamics," Series No. 60, Issue No. 238, 15 June 1959.
SR-No. 4: E. D. Hoag, "Glow cathodes in pulsed magnetic fields," Series No. 60, Issue No.239, 15 June 1959.
SR-No. 5: J. N. Dukes, "A gaseous-conduction linear amplifier with magnetic focusing,"Series No. 60, Issue No. 240, 30 June 1959.
SR-No. 6: B. N. Edwards, "A study of the Hall effect in gaseous conductors," Series No. 60,Issue No. 253, 30 September 1959.
SR-No. 7: J. W. Hansen, "Scheme for improving beam-tube performance by depressingcollector potential," Series No. 60, Issue No. 260, 15 December 1959.
SR-No. 8: D. H. Sloan, C. Susskind, A. W. Trivelpiece, J. R. Woodyard, and Staff, "Electronand plasma beams," Series No. 60, Issue No. 284, 15 June 1960.
SR-No. 9: R. E. Lundgren, "Extraction and modulation of electron beam from Philips iongage," Series No. 60, Issue No. 306, 31 August 1960.
SR-No. 10: C. W. Hartman, "Production and interactions of electron beams in crossed fields,"Series No. 60, Issue No. 325, 31 October 1960.
SR-No. 11: D. R. Noel, "Special deflection systems for cathode-ray tubes," Series No. 60, IssueNo. 329,2 December 1960.
SR-No. 12: B. E. Dobratz, "A study of circuit'independent oscillations in a gaseous conduc-tor," Series No. 60, Issue No. 344, 15 February 1961.
SR-No. 13: J. F. Fry, "The effects of rf energy on the pumping speed of a titanium sputterpump," Series No. 60, Issue No. 355, 18 April 1961.
SR-No. 14: B. Maxum and A. W. Trivelpiece, "Cyclotron-wave nonconvective instability,"Series No. 60, Issue No. 379, 1 July 1961.
SR-No. 15: G. August, "Coulomb collisions in strong rf electric fields," Series No. 60, IssueNo. 397, 24 August 1961.
SR-No. 16: G. August, "Plasma confinement of electromagnetic waves," Series No. 60, IssueNo. 398, 24 August 1961.
SR-No. 17: Y. Ikeda, "Behavior of the space charge in a plasma magnetron," Series No. 60,Issue No. 433, 15 June 1962.
SR-No. 18: M. Chamran, "Electron beam in the cold-cathode magnetron," Series No. 60, IssueNo. 453, 15 June 1962.
SR-No. 19: B. E. Dobratz, "Positive-column striations in gaseous conductors," Series No. 60,Issue No. 454, 19 June 1962.
SR-No. 20: Y. Ikeda, "Anode structures for cold-cathode high-power magnetson," Series No.60, Issue No. 455, 30 June 1962.
SR-No. 21: L. Spinazze, "Dc electroluminescence in manganese-activated aluminum-ozidefilms," Series No. 60, Issue No. 482, 11 September 1962.