• TABLE OF CONTENTS
HIDE
 Front Cover
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Key to symbols
 Abstract
 Introduction
 Electron gun classification, basic...
 Technical discussion
 Experimental evaluation
 Conclusions
 Appendices
 References
 Biographical sketch
 Back Cover














Group Title: investigation of the feasibility of utilizing a negative control grid in a crossed-field election gun
Title: An investigation of the feasibility of utilizing a negative control grid in a crossed-field election gun
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 Material Information
Title: An investigation of the feasibility of utilizing a negative control grid in a crossed-field election gun
Physical Description: xiii, 114 leaves : ill. ; 28 cm.
Language: English
Creator: Bryant, Furnie Smith, 1930
Copyright Date: 1966
 Subjects
Subject: Electron tubes -- Grids   ( lcsh )
Electron gun   ( lcsh )
Magetrons   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis - University of Florida.
Bibliography: Bibliography: leaves 109-111.
Additional Physical Form: Also available on World Wide Web
General Note: Manuscript copy.
General Note: Vita.
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Bibliographic ID: UF00097849
Volume ID: VID00001
Source Institution: University of Florida
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Resource Identifier: alephbibnum - 000559284
oclc - 13454316
notis - ACY4733

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Table of Contents
    Front Cover
        Page i
        Page i-a
        Page i-b
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    List of Tables
        Page v
    List of Figures
        Page vi
        Page vii
        Page viii
        Page ix
    Key to symbols
        Page x
        Page xi
    Abstract
        Page xii
        Page xiii
    Introduction
        Page 1
        Page 2
        Page 3
    Electron gun classification, basic problem and general approach
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Technical discussion
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
    Experimental evaluation
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
    Conclusions
        Page 81
        Page 82
        Page 83
    Appendices
        Page 83a
        Appendix A: Prototype magnetron-injection gun diode design
            Page 84
            Page 85
            Page 86
            Page 87
            Page 88
            Page 89
            Page 90
            Page 91
        Appendix B: Design of experimental grid structures
            Page 92
            Page 93
            Page 94
            Page 95
            Page 96
            Page 97
            Page 98
            Page 99
        Appendix C: Derivation of the electrostatic potential distribution for an array of line charges located inside a cylindrical conducting boundary
            Page 100
            Page 101
            Page 102
            Page 103
            Page 104
            Page 105
            Page 106
            Page 107
            Page 108
    References
        Page 109
        Page 110
        Page 111
    Biographical sketch
        Page 112
        Page 113
        Page 114
    Back Cover
        Page 115
        Page 116
Full Text













AN INVESTIGATION OF THE FEASIBILITY

OF UTILIZING A NEGATIVE CONTROL GRID
IN A CROSSED-FIELD ELECTRON GUN









By

FURNIE SMITH BRYANT, JR.


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY










UNIVERSITY OF FLORIDA
August, 1966

















































UNIVERSITY OF FLORIDA


3 1262 08646 381 6






























Q Furnie Smith Brvant, Jr. 1968


ALL RIGHTS RESERVED














ACKNOWLEDGMENT


The author wishes to acknowledge the assistance

provided by his chairman, Dr. A. D. Sutherland, and the

members of his supervisory committee throughout the entire

program of graduate study, with a very special expression

of gratitude to Dr. Sutherland, without whose faith and

guidance this dissertation would not have been possible.



A special acknowledgment to the Sperry Electronic

Tube Division, Gainesville, Florida, where the author was

employed during the course of graduate study, for spon-

soring the project and granting permission for use of the

material for this dissertation. The author also wishes to

express his gratitude for the generous assistance provided

by Sperry's advanced education program.



The author wishes to thank Mr. Fred Hansen for his

assistance in taking and reproducing the movies and photo-

graphs.














TABLE OF CONTENTS


ACKNOWLEDGMENTS . . . . . . . .


LIST OF TABLES . . . . . . .


LIST OF FIGURES . . . . . . .


KEY TO SYMBOLS . . . . . . .


ABSTRACT . . . . . . . . .


INTRODUCTION . . . . . . .


CHAPTER

I. ELECTRON GUN CLASSIFICATION, BASIC
PROBLEM AND GENERAL APPROACH ... ...


II. TECHNICAL DISCUSSION . . . .


III. EXPERIMENTAL EVALUATION . . . .


IV. CONCLUSIONS . . . . . . .


APPENDICES


A. PROTOTYPE MAGNETRON-INJECTION GUN
DIODE DESIGN . . . . . . ..


B. DESIGN OF EXPERIMENTAL GRID STRUCTURES


iii


Page

ii


v


vi


x


xii


.. 1






4


11


45


81









Table of Contents (Continued)


Page

APPENDICES

C. DERIVATION OF THE ELECTROSTATIC
POTENTIAL DISTRIBUTION FOR AN ARRAY
OF LINE CHARGES LOCATED INSIDE A
CYLINDRICAL CONDUCTING BOUNDARY ...... 100

LIST OF REFERENCES . . . . . . .. 109

BIOGRAPHICAL SKETCH . . . . . . .. 112













LIST OF TABLES


Table Page

la. A Summary of Magnetron-injection
Gun Design Values for the Experi-
mental Prototype Diode . . . ... 49

lb. A Summary of Prototype Diode
Operation . . . . . . . 53

2. A Summary of the 24 Vane Grid
Structure Test Data . . . . . 59

3. A Summary of the 24 Vane Grid
Structure Transfer Characteristic Data 62

4. Calculated Versus Measured Beam Size 65

5, A Summary of the Helical Grid
Structure Test Data . . . . . 68

6. A Summary of the Helical Grid
Structure Transfer Characteristic Data 70

7a. Tube Parameters .. . . . . 78

7b. Typical Beam Parameters . . . .. 78














LIST OF FIGURES


Figure Page

1. Typical Electron Trajectories for a
Cylindrical Diode and Triode . . 9

2. Typical Electron Trajectories for
a Cylindrical Diode and Triode in the
Presence of both Axial Magnetic and
Radial Electric Fields .... . 9

3. Cross-section of a Typical Magnetron-
injection Gun . . . . . . 12

4. Typical Grid Structure . ... 14

5. Typical Electron Trajectories for a
Truncated Magnetron-injection Gun . 16

6. Projection of an Emitting Strip onto
the r 8 Plane . . . ... .19

7. Projection of Non-emitting Strip from
a Conical Cathode onto the r e
Plane . . . . . . . . 19

8. Beam Projection onto r 0 Plane
for an Infinitely Strong Axial
Magnetic Field . . . . . . 22

9. Concentric Ring Grid Structure . . 22

10. Conical Parallel Wire Grid and
Projection . . . . . . 23

11. Typical Electron Movement About the
Cathode of a Crossed-field Gun . . 26








List of Figures (continued)


Figure Page

12a. Planar Model of Parallel Vane Grid .28

12b. Single Cell of Symmetry . ... 28

13. Equipotential Contour Comparison of
Cylindrical Diode and Triode . . 32

14. Comparisons of Cathode Current Den-
sity Distribution (Ref. Fig. 12) . 34

15. Computed Trajectories with Space-
charge in the absence of Magnetic
Field . . . . . . . . 35

16. Equipotential Contours with Space-
charge (% lines refer to anode voltage) 38

17. Equipotential Contours without Space-
charge (% lines refer to anode voltage) 39

18. Cross-sectional view of Beam Tester. .46

19. Photograph of Beam Tester. . . .. .47

20. Plot of Magnetic Field used in Beam
Analysis . . . . . . .. . 51

21. Prototype Diode Microperveance
versus B//Va ratio . . . . 54

22. Beam Profile for the Prototype Diode
with Magnetic Field Parameter B//Va
set at a) 17.1 b) 19.8 c) 22.7
d) 27.7 . . . . . . . 55

23a. Vane Grid Structure . . . . 57

23b. Component Gun Parts . . . .. .57

24. Completely Assembled Vane Grid Gun . 58


vii








List of Figures (continued)


Figure Page

25. Microperveance and Anode Current
versus B/VV- ratio for the Vane
Grid Structure . . .. . 60

26. Grid Transfer Characteristics for
the Vane Grid Structure . . ... 63

27a. Photograph of Helical Grid
Structure . . . . . . . 67

27b.. Photograph of Beam Profile for
Helical Grid Structure. ....... 67

28. Microperveance and Anode Current
versus B/V/ Ratio for the Helical
Grid . . . . . ... ... . 69

29. Transfer Characteristics for the
Helical Grid . . .. . . . . 71

30. Beamlet Pattern Produced by the Vane
Grid Structure ... . . 74

31a. Typical Precession of a Single Beam-
let (Complete Beam Contains 24
Beamlets) .. . . . . . . 75

31b. Plot of Precession versus Axial
Distance (.Vane. Grid Structure) . . 75

32. Photograph of Beam Current, Grid
Voltage and Grid Current ..... . 77

33. Plot of Efficiency versus Frequency
for L-band Tube (Vanxe Grid. S.truc.ture.) 80

A-1. Cross-section of Truncated Magnetron-
injection Gun showing Prototype Diode
Design Values . .... . . . 87


viii








Figures (continued)


Page


List of


Figure


A-2.





B-1.



B-2.


B-3.



B-4.


C-1.



C-2.


Normalized Potential $ versus z
with Electron Emission Profile Shown
for Prototype Diode . . . .


Single Cell Electrolytic Tank
Equipotential Plot . . . .


Equipotential Profile at Cut-off


Cross-section of a 24 Vane Grid
Structure . . . . . . .


Helical Grid Structure ....


Sequence of Reducing a Line Charge
Located off Axis to Standard Form


Conformal Transformation . . .


. 96


. 99



S. 101


103


* .


. .













KEY TO SYMBOLS


Symbol Description

a Helix radius

b Velocity parameter

B Increasing wave parameter

B Axial magnetic field
z

c Gain parameter

e Electron charge

E Electric field intensity

Co Dielectric constant of free space

Y Radial phase constant

I Beam current

I Anode current
a

Jo Current density at ro

Ae Electronic wave length

K Perveance

m Electron mass

SMagnitude of electron charge-to-mass
ratio







Key to Symbols (continued)


Symbol Description

Q Space-charge parameter

q Line charge

r Radius

rc Cathode radius

ro Spherical radius of conical cathode
magnetron-injection gun

SAngular velocity radians/sec.

Vo Voltage to which electrons are
accelerated

Va Anode voltage

Z Interaction impedance

L J Numbers enclosed denote author
references













Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy



AN INVESTIGATION OF THE
FEASIBILITY OF UTILIZING A NEGATIVE
CONTROL GRID IN A CROSSED-FIELD ELECTRON GUN


By

Furnie Smith Bryant, Jr.

August, 1966



Chairman: Dr. Alan D. Sutherland

Major Department: Electrical Engineering


The purpose of this research program was to investi-

gate the feasibility of utilizing a negative, non-

intercepting, control grid in a crossed-field electron gun.

A further objective was to establish design criteria and

procedures for those grid structures where feasibility was

established.

Theoretical and experimental aspects of the appli-

cation of a negative non-intercepting control grid to a


xii







magnetron-injection gun are discussed. Several grid

structures are analyzed in terms of perveance reduction

factor and grid transfer characteristics.

Several experimental guns were designed and

evaluated. Perveances in excess of 12 x 10-6 amp/volt32,

for a grid Mu in excess of 6 for absolute cut-off, were

observed. Experimental results of beam tester work are

presented in the form of both photographs and data evalu-

ation of beam patterns as observed on a moving carbon

target. An electron gun utilizing this principle was

successfully employed in an L-band traveling wave tube

and tests on that tube are described.


xiii















INTRODUCTION


Present use of microwave amplifier tubes in pulsed

doppler radar has necessitated both a high duty cycle and

high repetition rate capability. A control electrode,

such as a negative grid, offers many advantages to the

user of the amplifier. Beam switching by anode modulation

requires a large voltage swing; and, consequently, ex-

cessive modulator power is dissipated in charging and

discharging the anode electrode capacity. A substantial

modulator power reduction can be achieved by utilizing a

negative control grid. Positive control grids which

intercept current are restricted to medium power tubes--

the limit being dictated by the average grid power dis-

sipation capability and/or the emission of secondary

electrons. This restriction is removed in the negative

grid case because the grid does not intercept current.

Grid designs for both positive and negative grid

operation have been utilized in Pierce-type [1] electron

guns for several years; however, to the author's know-









ledge, these principles have not been extended to the

crossed-field gun--in particular magnetron-injection guns.

Basically, grid control methods are of two types:

intercepting and non-intercepting. Non-intercepting

grids operate on the principle of electron emission

suppression beneath the grid during on-time. This is

accomplished in the positive control grid by either

selective cathode coating or cathode shadowing. Alter-

natively, with negative control grids, the potential of

the control grid never exceeds that of the cathode;

therefore, the force due to electric fields between the

grid and cathode is such as to repel electrons, and

suppression is inherent. Associated with the addition of

a negative control grid is a substantial reduction of

perveance even for medium Mu (15 30) operation. Per-

veances for aperture anode, negative grid, Pierce-type

electron guns are limited to values in the order of

1 x 10- amp/volt3/ for absolute cut-off Mu's of 30 50.1

In addition, even at the lower values of grid Mu and

perveance, there is an undesirable current density

variation across the cathode surface due to electric




IThese limits were reported by Ashley, Sutherland
and Kolb [2].









field suppression by the grid.

The extension of the negative grid concept to the

(linear beam) crossed-field class of electron guns offers

two definite advantages. First, the cathode-to-beam area

convergence for the conventional hollow beam gun is unity.

This places an upper limit on beam current density. In

the crossed-field magnetron-injection gun, this limit is

increased because the area convergence is inversely pro-

portional to the cathode cone semiangle which is typi-

cally very small. Second, the perveance for the basic

diode magnetron-injection gun greatly exceeds that of the

conventional planar design. This increased perveance

capability permits an increase in bandwidth capability

since the two are proportional.

The aim of the research about which this disser-

tation is concerned was to explore the feasibility of

incorporating the negative control grid feature in

magnetron-injection guns, and to determine factors limit-

ing the design of such guns.














CHAPTER I


ELECTRON GUN CLASSIFICATION, BASIC PROBLEM

AND GENERAL APPROACH



Electron Gun Classification



Typically, electron guns are classified in terms of

their perveance--a parameter which remains invariant when

the gun is scaled. Electron gun perveance, K is de-

fined for a diode gun by

K =I/V3/ (1)

where

I = the cathode current in amperes

V = the anode voltage in volts

An electron gun is referred to as having a high perveance

if it is an order of magnitude greater than unity micro-

perveance.1 Similarly, a low perveance electron gun is


iSince typical gun perveances are on the order of
10-6 it is customary to use the term microperveance which
is the perveance defined by Equation (1) multiplied by 106.









one with a microperveance an order of magnitude below

unity. In addition to classification by perveance, guns

are referred to in accordance with their geometric con-

figuration; for example: planar, Pierce-type and crossed-

field. For the first two types, the electrons flow from

the cathode to anode along trajectories that do not

cross magnetic lines of flux; therefore, these guns do

not depend on a magnetic field for proper operation.

However, the third type, the crossed-field gun, does

require a magnetic field. With the latter, there are

two classes or types: (1) guns in which the magnetic

field is perpendicular to both the electric field and

the direction of beam propagation and, (2) those in

which the magnetic field is parallel with the direction

of beam propagation. Magnetron-injection guns fall into

this second category of crossed-field guns.

The design method for the Pierce-type electron

gun differs radically from the crossed-field gun; there-

fore, the negative grid design procedures are similar in

concept, but not the same. Prior to 1960, the only

analytic space-charge flow solutions used in the art of

electron gun design for microwave tubes were those for

rectilinear flow between two planes, two cylinders or

two spheres.








In 1958, Kirstein and Kino [3] published a basic

contribution to the theory of curvilinear space-charge

flow, which led to radical departure from the limitations

imposed by the rectilinear flows which had formed the

basis for electron gun design up to that point. This was

followed by a sequence of papers by Kirstein [4], Waters

[5], [6] and Dryden [7], [8] leading to the synthesis of

space-charge flow pattern suitable for the design of

magnetron-injection guns. Harker [9], [10] in the same

period, published analytic methods for determining the

requisite electrode shapes for setting up and supporting

such flows. In addition, Kino and Taylor [11] have pub-

lished solutions using planar, rather than axially

symmetric geometries. More recently, Okoshi [12] pub-

lished an improvement of the Kino-Taylor theory to

account approximately for centrifugal forces. The com-

puter methods developed by Dryden [7] were used in the

present investigation for the design of the prototype

diode magnetron-injection guns.




The term prototype diode is defined as the diode
electron gun, consisting of cathode, focus electrode, and
anode, which would result if the negative grid were
physically removed from the triode.









Basic Problem



By definition, the path of an electron will be

referred to as "normal" if its trajectory is that of the

prototype diode to which a grid is added. The placement

of a grid in the cathode-anode region will cause beam

interception and/or deflection. To illustrate this,

consider the cylindrical diode. Figure la shows the

paths of electron flight from the cathode to anode in the

absence of magnetic field. These trajectories are

radial as the only electric field component present is

radial. Figure lb shows the effect of adding a negative

grid. The grid is seen to cause a focusing action which

1
destroys the laminar diode flow. The grid apertures

act as convergent electrostatic lenses, imparting lateral

motion to all electrons except those emitted at a plane

of symmetry between two wires.

When an axially symmetric field is placed parallel

to the cathode axis, the problem of beam perturbation

caused by the grid takes on additional complexity. In





Laminar flow means that the electron velocity
function is a single valued function of position, and
that the beam can be divided by imaginary surfaces into
isolated non-penetrating sections.









the absence of the grid, for the cylindrical diode case

just discussed, the trajectories are bent as depicted in

Figure 2a. The addition of the grid causes transverse

deflections of the electron paths to be superimposed upon

this basic flow pattern. The resultant non-laminar curvi-

linear flow becomes so complex as to make an analysis,

which includes the all important effects of space-charge,

well nigh impossible. This is illustrated in Figure 2b.

While the cylindrical diode, and triode, have

been utilized in the above to illustrate this point, the

flow in the magnetron-injection gun is even more complex.

In such guns, an axial electric field component is

purposely introduced, for example, by forming the anode

and cathode as portions of concentric conic sections.

This is done so as to provide an axial acceleration com-

ponent which causes the electrons to turn and eject from

the gun without striking the anode, when the magnetic

field is present. This non-laminar three dimensional

motion makes analytical methods of predicting the space-

charge flow patterns hopelessly complicated.



General Approach

For the reasons just outlined, the procedure used

in this investigation is largely experimental. The












bNODE



- CATHODE






TRAJECTORY


la. Diode


lb. Triode


Figure 1. Typical Electron Trajectories for a
Cylindrical Diode and Triode


e Bz FIELD


6 Bz FIELD
--TRAJECTORY


CATHODE


TRAJECTORY


2a. Diode


Figure 2.


2b. Triode


Typical Electron Trajectories for
a Cylindrical Diode and Triode in
the Presence of both Axial Magnetic
and Radial Electric Fields


CATHODE





10


prototype diode version of the magnetron-injection gun

utilized was designed using the analytic methods of

Dryden and Harker referred to above. Various grid

structures were then added, and the resultant performance

was then experimentally determined. Where feasible,

approximate analytic methods were then developed to

explain the observed experimental performance.















CHAPTER II


TECHNICAL DISCUSSION



Introduction



A cross-sectional view of a magnetron-injection gun

is shown in Figure 3. The component parts are as labeled.

The theory of operation is best described by considering

a single electron emitted from any point on the cathode.

In the cathode anode region the electric field will have

components both parallel and perpendicular to the cathode

surface. Therefore, as the electron leaves the cathode,

it will experience both radial and axial accelerations.

The radial acceleration vector is perpendicular to the

axial magnetic field. The resultant Lorentz force will

cause the electron trajectory to bend around the cathode.

A condition of balanced flow will occur when the centri-

fugal force, electric field force and magnetic field force

are equal. The presence of the axial component of elec-

tric field causes electron ejection from the gun. When




















........ UNIFORM
-" MAGNETIC
FIELD



CATHODE





FOCUS ELECTRODE






















Figure 3. Cross-section of a Typical
Magnetron-injection Gun









properly designed, in the presence of space-charge, all

other electron trajectories will be magnifications of

this one. The anode of the magnetron-injection gun, un-

like the cylindrical diode, is non-intercepting. The

beam is ejected from the gun into a drift region. If the

cathode is truncated, the beam will be hollow; thus, the

often used term hollow beam magnetron-injection gun.

The object is to select an appropriate grid con-

figuration that offers a minimum perturbance to the nor-

mal electron flow pattern.



Factors Effecting the Selection of a
Grid Configuration



Beam Dynamics

The first decision required is the establishment

of a grid configuration which least affects the electron

dynamics of the prototype electron beam. Figure 4 shows

three grid configurations aften used in cylindrical

triodes. For the Pierce and planar triode guns, the mesh

grid is usually selected. The supported parallel grid

ring and helical grid are more appropriate for the conical

triode gun.

Some insight into the grid selection for a crossed-

field negative grid gun can be gained from examining


























4a. Mesh Wire Grid


4b. Supported Parallel
Grid Ring













4c. Helical Grid


Typical Grid Structure


Figure 4.










Equation (2). This equation is known as Busch's theorem

and shows that the angular velocity of a charged particle

moving in a static, axially symmetric, magnetic field is

a function of position only.


S= (1 c ) (2)
2 r2

In this equation rc refers to the radial coordinate of

the point of electron emission from the cathode and r

is the radius anytime later. A typical plot of the tra-

jectory in the r z plane for an electron emitted from

the center section of the cathode would be as shown by

the solid line in Figure 5. Dryden [7] shows that all

other trajectories are simply magnifications of these.

Therefore, electrons originating from the ends of the

cathode would appear as illustrated by the dotted tra-

jectories. The grid selection must permit electron

passage over several grid sections in the gun region as

radial expansion, inherent in the gun operation, produces

an angular velocity in accordance with Busch's theorem.

If electrons from a thin strip along the cathode

are tagged and identified with respect to the particular

area location from which they were emitted (independent of

the time of emission), their projection onto the r 9






16


















R











/ "'~ ~ ~~ ~ -- -- -----------





z

B6


























Figure 5. Typical Electron Trajectories for
a Truncated Magnetron-injection Gun









plane, first located at the cathode apex and continuously

moved along the +z axis.

The forces acting on the beam in the gun region in

the absence of a grid are:

1. An outward force due to the radial com-
ponent of electric field.

2. An axial force due to the axial component
of electric field.

3. A 9 directed force due to interacting
of the radial velocity component with
the axial magnetic field.

4. An outward centrifugal force due to ro-
tation about the axis.

5. An inward force due to the interaction
of the 9 velocity component with the
axial magnetic field.

6. Outward force due to space-charge.

After the beam is injected into the drift tube, the elec-

tric field force is due only to space-charge. Using

Gauss' theorem, the field at the edge of the beam due to

space-charge can be calculated.



eS E da = -2nTr p = Q (Charge inclosed in
dr the beam per per (3)
unit length)

And for a total beam current I and voltage Vo the'

radial field is given by


dcp -I(r) (4)
dr 2rer V2TV









where

r = radial coordinate in the beam

Q = -I
ie

e = axial electron velocity = 2IV



S = lel have been used.
m

From (4) above, it is noted that the electric field and

force on the outer electron shell is greater than the

force on the inner shell; therefore, for a balanced flow

condition, the outer shell must rotate such that 6

(outer shell) > 6 (inner shell). This difference in

angular velocity will produce a shear in the beam; con-

sequently, the conclusion is drawn that any grid system

so located as to partition the beam azimuthally could

cause beam break-up in the drift region. A single cath-

ode strip arrangement and its projection on the r @

plane is shown in Figure 6.

Suppose now that a non-emitting ring is located

concentric with and in the center of the cathode as

illustrated in Figure 7a (such a non-emitting ring would

be created by a negative grid ring located above the

cathode surface). A projection of this ring onto the

r e plane produces a pair of concentric hollow beams












ONICAL CATHODE


EMITTING STRIP











r 9 plane



Figure 6. Projection of an Emitting Strip
onto the r 9 Plane


CONICAL CATHODE


OUTER BEAM EDGE


NON-EMITTING
STRIP


SHADOW OF
NON-EMITTING
STRIP





DINNER BEAM
EDGE


Figure 7. Projection of Non-emitting Strip
from a Conical Cathode onto the
r 6 Plane










as illustrated in Figure 7b. This projection pattern.

appears to have the proper symmetry for a well-defined

beam in that shear produced by slight angular velocity

differences does not distort the pattern. However, to

build and support a grid system which so shadows the

cathode in only an axially periodic manner presents a

complex engineering task. The problem is one of mechani-

cally supporting each grid ring while electrically oper-

ating all rings at the same potential yet electrically

isolated from the cathode. Any interconnecting wire

would partition the beam in an azimuthal direction in the

projected view. Grid construction and experimental

evaluation of two systems similar to the above are dis-

cussed in Chapter III and Appendix B.



Cathode Mask Ratio

A very important triode parameter to consider be-

fore analyzing any one specific grid configuration is the

grid-to-cathode mask ratio. Consider the case of an

electron emitted from a conical cathode magnetron-

injection gun immersed in an infinitely strong, axially




'The definition used in this dissertation for grid-
to-cathode mask ratio is the ratio of the ray projection
of the grid area to the cathode area in the r 8 plane.









symmetric, magnetic field, Bz Movement is restricted

to a direction parallel to Bz at the radius of origin

since 9 of Equation (2) is reduced to zero. To an

observer looking at the cathode from a distant point

along the positive z-axis, the truncated cathode cone

area would appear as a ring with an area of approximately

1/sin eo times the cone area as illustrated in Figure 8.

The addition of a grid consisting of concentric rings,

located as illustrated in Figure 9, would completely

mask the cathode when the grid wire diameter projections

overlap on the r 9 plane. This arrangement would be

quite sensitive to magnetic field variations in a practi-

cal device and does not seem feasible from the viewpoint

of a projected grid mask ratio.

Next, consider the conical grid wire configuration

of Figure 10a. For the same set of conditions as above,

the grid mask ratio is the ratio of the cross-section

area of one grid wire times the total number of wires

divided by the cathode area. Its projection onto the

r 9 plane is illustrated in Figure 10b. This arrange-

ment appears feasible from a grid mask ratio point of

view since the projected mask ratio is the same as the











BEAM PROJECTION

- .- ,-z


-BEAM
CROSS
SECTION


CATHODE


Figure 8. Beam Projection onto r 9 Plane
for an Infinitely Strong Axial
Magnetic Field






ANODE



RING GRIDS






CATHODE


Figure 9. Concentric Ring Grid Structure


r

%*Z












Anode


lOa


















10b









Figure 10. Conical Parallel Wire Grid
and Projection









screening fraction.

Closely associated with grid mask ratio are two

other important gun parameters: the gun perveance and

cut-off MU.0 Although the exact cut-off Mu is not a

function of magnetic field, the ability to design a

"sharp cut-off" triode in the strict sense is possible

only to the degree that the current density of emission

at the cathode is not a function of magnetic field.


Grid Cut-off Mu

The effectiveness of a grid in controlling cathode

current is a function of several parameters. These in-

clude the height of the grid above the cathode, grid

pitch and shape. When electron perturbations are not a

design factor, the range of grid Mu is from zero to

infinity. However, trajectory perturbations in the

crossed-field gun impose severe limitations on the grid

design from the standpoint of the magnetic field require-

ments if anode interception is to be prevented. As





1Screening fraction is the ratio of the grid cross-
sectional area to the cathode area.

2The cut-off Mu of a triode is by definition the
magnitude of the ratio of anode voltage to grid voltage
required to reduce the cathode current to zero.








stated earlier, a normal electron path involves both

radial expansion and angular acceleration about the axis

of symmetry. A typical electron trajectory is illus-

trated in Figure 11. Since a negative grid is a non-

intercepting grid, the electron must.rise above the grid

to escape. If this is to occur, the grid cannot be

placed excessively above the cathode. Thus, the magnetic

field imposes limitations on the cut-off Mu.

Consider now a parallel plane approximation for

both the concentric grid ring and conical grid structures

shown in Figures 9 and 10. Both structures can be

represented by the same model; however, the orientation

of magnetic field with respect to the grid is different.

Examining Laplace's equation in cylindrical coordinates


Va = L (r ) + 1 b2Cp + a (5)
r 57 Sr r2 0-2 bz2


we see that if r is large compared to Ar in the

region of interest, then the Laplacian becomes


V3^ = 2CP + 2cp (6)


where y has replaced r for the planar approximation.

Using this approximation and replacing the round grid

wire with rectangular vanes, the model assumes the




























































Figure 11. Typical Electron Movement About
the Cathode of a Crossed-field
Gun









geometry given in Figure 12a. Substitution of rectan-

gular vanes is required for both structural reasons and

the desire to minimize lens aberrations by suppression of

cathode emission beneath the grid. The model has several

planes of symmetry. A single symmetry cell is illus-

trated in Figure 12b. Since the cut-off Mu is indepen-

dent of magnetic field, it can be determined by solving

Laplace's equation for the particular value of negative

grid voltage which just reduces the off-cathode potential

gradient along the symmetry axis depicted in that figure.

For a sharp cut-off grid transfer characteristics,

each cell or segment of a cell must cut-off simultan-

eously. Examining the electrical contours established in

Appendix A for the prototype diode magnetron-injection

gun, it is observed that the cathode anode separation is

not uniform along the cathode. The separation decreases

as the exit end of the cathode is approached; therefore,

the grid height and/or pitch must be altered to keep the

cut-off constant. The magnitude of this effect became

apparent during experimental evaluation. This evalu-

ation showed that as the grid was biased to cut-off




1The measurement techniques are presented in
Chapter III.














z z z z


ANODE
, ,


Z


GRID


I o I


CATHODE

( o)


>..

ac
U-


>.

0
bO






( b)


Figure 12.


a) Planar Model of Parallel
Vane Grid

b) Single Cell of Symmetry


/ / /


DLI


w
I
I



I <(
LL.
or

w
Z
I-j

I,


iw -










electron emission from the front (small end) of the

cathode decreased more rapidly than from the center and

rear sections. A constant Mu design based on a tapered

grid vane is discussed in Appendix B.



Perveance Reduction Factor

To the author's knowledge, no analytical expres-

sion has been published for the determination of cathode

current density distribution for the model of Figure 12,

even in the absence of magnetic field. Erickson and

Sutherland [13] have published a digital computer analy-

sis of non-laminar space-charge flow which establishes

self-consistent solutions of Poisson's equation, the

equation of electron motion, and the equation of current

continuity when the conditions on the boundary are fully

specified. It was through an improved version of their

program that the form of the current density distribu-

tion along the cathode in the absence of magnetic field

was established.

Computer Program. The computer program is formu-

lated to handle the problem of analysis rather than





The program actually used is a program presently
being developed by Dr. A. D. Sutherland for the Sperry
Electronic Tube Division, Gainesville, Florida.










synthesis. A synthesis program would, in general, deal

with problems of generating suitable boundary shapes and

potentials to produce a given flow pattern. Analysis

seeks self-consistent solutions of Poisson's equation of

current continuity, when the conditions on the boundary

are fully specified.

The boundary conditions for the planar model of

Figure 12 are simple. A complete solution involves only

the region between a plane of symmetry and an axis of

symmetry.

The values of current density and current density

distribution along the cathode surface are first esti-

mated. The peak current can never be greater than that

for the prototype diode. The computer starts with this

assumed current density distribution and then solves

Laplace's equation for y(r,z) subject to the specified

boundary potentials. Knowing c and the electron

entrance conditions, the equations of motion are solved

for the position coordinates of each electron. Space-

charge density is then computed based on these position

coordinates and the whole procedure is repeated, using

Poisson's equation, until a convergence criterion is

satisfied.









Formulation of Initial Cathode Current Density

Distribution. The cathode current density specification

can be approximately determined by solving Laplace's

equation for both the prototype diode and triode. This

solution is obtained through analogue techniques such as

an electrolytic tank. Equipotential plots of each model

are compared at a particular equipotential on the triode

plot where the variation in potential from the plane of

symmetry to the axis of symmetry is about 5%.1 This

particular equipotential is then designated as a false

anode. The ratio of triode to diode false anode poten-

tial raised to the three-halves power permits the calcu-

l.ation of a cathode current density correction term.

For example, Figure 13 shows an electrolytic tank plot

of the cylindrical negative grid model'examined in this

study. The solid lines are the diode equipotentials,

and.the dotted lines show the distortion of these lines

produced by the grid. Based on the 5% criteria, the

false anode is located between the 20% and 25% con-

tours. From Child's law, the current density reduction

factor becomes


1The choice of .5% is based on computer results.


















-50%





40%


Figure 13. Equipotential Contour Comparison
of Cylindrical Diode and Triode









t CPt (-) 3/(7)
Jd (Pd

where cpt and CPd are the % potential values at the

false anode location of the triode and diode respectively.

This establishes the peak triode current at the axis of

symmetry. A current density distribution is then assumed

for estimating the current density at all points along

the cathode. Since the grid pitch is uniform, the

assumed current density distribution function must be a

periodic function in z which goes to zero at each plane

of symmetry. Based on these criteria, a cos2e distri-

bution was selected.

Computer Results. Data presented in this section

were calculated for the case of zero magnetic field in

the gun region. The deviation of the actual computed

cathode current density distribution from the assumed

cos28 function is shown in Figure 14. Curve 4 is based

on the diode peak current. Curve 3 is a corrected esti-

mation for this problem based on a 40% equipotential.

Curve 2 is the computed curve and curve 1 is the cosae

approximation. Electron numbers along the absissa

indicate test electron positions along the cathode.

Figure 15 shows the non-laminar nature of the electron

trajectories in the presence of a grid with space-charge












28


26


24 -

(4)
22

DIODE- PEAK
20




o 2 (3)
16


14

(2)
x 12 I
1" (-) \)
<0 |8 --- -- S- -- \ -- J- -- -- -- ----%












4 6 -14.3 Cos e \
I-













0
8, --- --____^-- \ -- -- -- -- --

















2 3 4 5 6 8 9 10 11 12
ELECTRON NUMBER


Figure 14. Comparisons of Cathode Current
Density Distribution (Ref. Fig. 12)



















30

Numbered curves refer to
test electron number



0





20 0
0


0






15
0



















9 8 7 6 5 4 3 2 1
*o


















0








8 7 6 5 4 3 2 1 0

normalized distance along the cathode



Figure 15. Computed Trajectories with
Spa'ce-oharge in the absence
of Magnetic Field
e 7 6 5 4 3 2 I
norulize ditanc alog te cahod

Figue 15 Copute Traectrieswit
Spacechare in he asenc
of ManeticFiel









effects included. Reflections at the axis of symmetry

indicate actual axis cross-over. The true trajectory is

simply a reflection of these trajectories at the inter-

cept points along the axis of symmetry.

Analysis of these data immediately showed that the

perveance reduction factor computed in the absence of

magnetic field was not appropriate for estimating the

perveance reduction factor with magnetic field included.

Experimental results showed that the grid configuration

analyzed had an average perveance reduction factor of

approximately 35%. This is contrasted with a peak com-

puted value of 51% at the axis of symmetry. The average

reduction is greater than this. This lack of correlation

prevented further utilization of the computer program in

this analysis because the present program will not treat

the case where the cathode and magnetic field intersect

at a small angle. However, some very useful information

resulted from the data obtained and is discussed below.

The following discussion is a heuristic argument

which explains the reason for the difference in measured

versus computed perveance reduction data. Referring back'

to Figure 14, it is noted that even in the presence of

space-charge, electrons cross the axis of symmetry. This









means that directly above the section of the cathode

least shadowed by the grid is a concentration of space-

charge. Associated with this space-charge is a substan-

tial potential depression. Figure 16 is an equipotential

plot with space-charge included. Figure 17 is the

Laplacian solution. A comparison of the two exemplifies

the potential depression produced by the space-charge.

However, had a magnetic field been included in the pro-

gram, the electron trajectories.would not have converged

nearly as much. Because electrons tend to follow mag-

netic lines of flux, the Lorentz forces would have caused

a more linear trajectory path from anode to cathode.

Further, in the actual magnetron injection gun, the

electron focal plane may well be outside the gun region

since there the electrons are accelerated axially.

The fact that a reduced perveance reduction factor

results from the inclusion of magnetic field, suggests

that the perveance of the negative grid Pierce-type guns

can be increased by permitting flux to thread the cathode

along normal trajectory lines.






I-V

of i' ff- /p y


^lr~~~~ IjJ~ I '' :} ^


I


\ f L~ ~-I: i ": d V~ l~i~~


i is "s




























































Figure 16. Equipotential Contours with Space-
charge (% lines refer to anode voltage)






















































Figure 17. Equipotential Contours without Space-charge
(% lines refer to anode voltage)









Beam Precession



Focusing arguments require that the electrons of

an electron beam collimated by a magnetic field all

process about the axis of symmetry or that they rotate

about flux lines and have a processing motion about the

axis. Brewer [14] presents a complete discussion of this

motion for hollow and solid beams. However, the detec-

tion and measurement of this motion has presented quite

a challenge. In fact, it has been reported by the Litton

Electron Tube Corporation [15] that although calculations

indicate beam rotation must be present, it had not been

measured. Their conclusions were that perhaps the type

of focusing applicable to the magnetron-injection gun

was not known This is a paradox because, when the cath-

ode is completely immersed in the axial magnetic field,

one can only conclude that the space-charge forces must

cause precession about the axis.

The beam produced experimentally by the radial

vane grid is discussed in Chapter III. There it is shown

that the beam is broken up into an array of finite

diameter line charges. The potential distribution for

this situation can be approximated by determining the-

solution of Laplace's equation for a symmetric array of









line charges of infinitesimal diameter inside of a

conducting cylinder. Such an analysis is presented in

Appendix B. The resultant potential expression is


qtl l
cq(r,8) =tn

r 2n r n
(-)2 + 1 2( -) cos n e
F r (8)
( ) 2n (2n 2( ) cos n
ro ri r

An examination of Equation (8) reveals that when

the radius r corresponds to the radial position ri

of the line charges, and when the azimuthal position 9

also coincides with that of any one of the line charges

(6 = ) then the potential expression exhibits a pole.

These poles exist as a consequence of the approximate

representation of a finite diameter line charge with one

with infinitesimal diameter. Stated differently, the

poles are the consequence of the "self potential" of the

line charges themselves. That this'is the case can be

revealed by an examination of Equation (8) for a region

in the immediate vicinity of one of the line charges

(say, 8 = 0 r = r, )

Let r = r1 + 6

where 6 is a very small number compared to r .

Then, in expression (8), terms involving r can be









approximated to second order through the binomial expan-

sion as

r 2n 0 2n
--) =(1 + -)
r, ri


6 (2n)(2n 1) 6 2
1 + 2n- + --) (10)
rI 21 r2


r n 6 n n6 n(n 1) 6 2
(-) ( + -- + (--) (11)
r. rI r, 21 rl

The expression for the numerator of the logarithmic term

becomes:

Numerator n (6)2 (12)
r1

Equation (8) can now be written as
6 2
q(r) n --q n (13)





p(r) tn (6) -tn n
2nTeo 2rTEo


t r n ro n qt
+ n (--) (-) + -nn(rl) (14)
2neo L ro r J 2o

The first term of Equation (14) will be recognized

as the potential of the line charge itself, centered at

6 = 0 and accounts for the pole. The remaining terms

are due to the presence of the other line charges in the

array.

Our interest centers upon the motion of any one of









the line charges caused by the presence of all others.

This can be evaluated by subtracting from Equation (8)

the "self potential" due to the line charge of interest,

which is the cause of the pole. Taking the gradient of

the resultant expression will yield the electric field

due to all other line charges.

Letting cp'(r) be the potential resulting from

the above operation, we find:

Sq [ r n ro n
Cp'(r) -Ln n + tn (--) (-) ] (15)
2TTo ro r

r n ro n

E' -Vc'(r) v 1 (16)
r 2 r re rn ro n
(- ) _F
ro r

It should be emphasized that these two equations are valid

2n
approximations only when r r1 and e6 -- .

Observe that the radial field along radii which

pass through each line charge is negative and finite,

resulting in a net outward radial force due to space-

charge effects. If the array is restrained by an

axially symmetric magnetic field, the line charges will

process about the symmetry axis. In addition to this,

motion, the electrons in each line charge of finite

diameter experience forces associated with the line

charge itself.









During the experiments to be described in Chapter

III, this particular beamlet pattern, in contrast with a

truly hollow beam, permitted observation of beam shear

as well as beamlet rotation. Beam precession was

detected in accordance with the above theory only after

the pulse width of the grid pulse was reduced below 8

microseconds. With a 4.5 microsecond pulse width, beam

precession was easily noticeable. It is concluded that

ion neutralization, even at vacuums of 5 x 10-8 torr,1

is sufficient to prevent detection of beam rotation.


1The beam tester was continuously pumped with an
8 liter ion pump. The indicated vacuum was as stated.















CHAPTER III


,EXPERIMENTAL EVALUATION



General



The prototype diode magnetron injection gun was

designed from Dryden's [7] theory. A complete design is

given in Appendix A. A cross-section of the experimental

beam tester used for evaluating the beam formation is

shown in Figure 18. Figure 19 shows a photograph of the

complete tester unit including solenoid, target drive

motor, and mounting rack. Basically, the beam is col-

limated by the axial magnetic field of the solenoid and

impinges on a thin carbonized target located in the tele-

scoping tunnel. The carbonized target used was approxi-

mately .003 inches thick and was made by reducing a piece

of chemical filter paper in a hydrogen atmosphere. The

bellows serve as an axial expansion joint which allows

continuous target movement from a plane directly in front

of the anode aperature up to 25 centimeters from the anode.












AXIAL EXPANSION
JOINT (Bellows) I


CARBON


-ADJUSTABLE
JACK


- BASE PLATE

-POLE PLATE











SUPPORT
SHELL


-GUN STRUCTURE


Figure 18. Cross-sectional view of Beam Tester


















































































Figure 19. Photograph of Beam Tester


rma~----- I
~









The system is motorized such that the target can be

moved very slowly with respect to the gun anode; thereby

permitting motion picture photography of the electron

impingement (through target luminescence) as well as

still photographs to be taken.

The required beam power for observable target

luminescence was approximately 5 watts. In order to

operate at the design values, summarized in Table la, a

negative grid modulator was utilized. The grid was

pulsed from a condition of grid cut-off up to cathode

potential. The target was isolated electrically from

all other elements and maintained at a potential positive

with respect to the anode potential to prevent secondary

electron emission. Measurement accuracy of such an

arrangement is somewhat questionable from the standpoint

of an exact evaluation of beam size and characteristics.

There are two basic sources of error. First, the target

imposes an equipotential surface in the tunnel that is

not present in an actual microwave device, which alters

the electric field in the region of the target. Second,

the power required to produce target luminescence is a

function of heat transfer by radiation and conduction

from the disk target. The rate of decrease in intensity



















Table la. A Summary of Magnetron-injection
Gun Design Values for the Experi-
mental Prototype Diode







8o = 40

Jo 204 ma/sq. cm

I .92 amperes

B 600 gauss

G =10

# = .07

N 1.275

V = 1220 volts

Kd = 21.5 x 10-6 amp/volt3s









of radiation was recently analyzed by Vaidya and Gandhi

[16]. Their diagram of relative emission intensity showed

that the emission intensity decreases very rapidly outside

the beam-illuminated area. However, since a comparison

of beam size and shape at various target locations is the

primary objective, the errors introduced by the above

will cancel and can be neglected.

In each experiment the beam tester was evacuated

into a 60 liter/second oil diffusion pump through a

liquid nitrogen cold trap. Metal out-gassing was

accelerated by baking the tester at an elevated tempera-

ture for several hours. An 8 liter ion appendage pump

was attached to the tester before bakeout and operated

continuously after cathode conversion and removal of the

tester from the oil pump. The appendage pump permitted

continuous monitoring of pressure as well as pumping.

The axially symmetric uniform magnetic field used

in the evaluation of all the experimental guns was

established with a long solenoid-- a plot of which is

given in Figure 20. The rear of the cathode was located

at the point marked K on the graph. On that graph

Z1 and Z2 depict the range of target movement.
















1000


S600



500



400



300
0 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17
INCHES














Figure 20. Plot of Magnetic Field used
in Beam Analysis









Experiment #1



The first experiment was to construct and evaluate

the prototype diode in the beam analyzer without the grid.

A summary of operation is given in Table lb and Figure 21.

A photograph of the beam profile taken at Z 5.9 inches

from the anode exit plane, is shown in Figure 22a. The
B
ratio ~ for this photograph1 was the design value of
a
17.1 The slight eccentricity of the beam reflects a

misalignment of the cathode to magnetic field axis. The

performance of this prototype diode was so close to the

predicted values that the misalignment appears negligible.

B
Photographs were also taken at -- values of 19.8, 23.7
rVa
and 27.7 shown in Figure 22b, 22c, and 22d, respec-

tively. It was observed that vorticity and beam breakup

resulted from this increase. The instabilities produced

are very similar to those observed by Kyhl and Webster

[17]. All photographs were taken with a beam power of

approximately 5 watts utilizing 20 microsecond cath-

ode pulses.


1
The significance of this ratio is discussed in
Appendix A.

















Table lb. A Summary of Prototype Diode Operation


Micro-
perveance

26.10

24.58

24.10

21.95

20.83

20.45

20.20

19.90

19.79


Anode
Voltage
(Volts)

100

100

100

100

100

100

100

100

100


Anode
Current
(ma)

2.0

1.5

0.4

0.2

0

0


0

0

0


Cathode
Current
(ma)

26.10

24.58

24.10

21.95

20.83

20.45

20.20

19.90

19.79


B
v -


13.30

14.00

14.83

16.92

18.83

20.75

22.70

24.78

26.70



















24




22

S^3DESIGN MICROPERVEANCE
DESIGN

20
MICROPERVEANCE




18
18----------------------------------------------------




16 -----------
SANODE CURRENT




13 15 17 19 21 23 25 27


E

z
w


2w
0
0
z


NORMALIZED MAGNETIC FIELD,B/VV'
















Figure 21. Prototype Diode
Microperveance vs B/v-a ratio













vA.. .
I . ~ ir,. gj r, 4'jj~


22a 22b


22c 22d


Figure 22. Beam Profile for the Prototype Diode with
Magnetic Field Parameter B//V- set at
a) 17.1 b) 19.8 c) 22.7 d) 27.7









Experiment #2



A photograph of the grid structure used in this

experiment is shown in Figure 23a. This structure

corresponds to the parallel vane grid model described

in Chapter II. The grid vanes are rectangular in cross-

section and are supported from the focus electrode. The

detailed parts are shown in Figure 23b, where the grid is

shown assembled with the cathode. The completed gun

assembly, showing support rods and mounting rings, is

shown in Figure 24. Details of the grid design procedure

are given in Appendix B.

A summary of the experimental data is given in

Table 2. These data are also shown plotted in Figure 25.

B l/
At the design value of = 17.1 gauss/volt1 the

anode current is approximately 22 ma corresponding to

only 62% beam transmission. The required magnetic field

B
for 100% beam transmission corresponded to a ratio
va7
of 22.8 gauss/volt The perveance at this value was

14.1 x 10-6 amp/volt2 which represented a perveance

reduction factor of 34.4%. At the diode prototype design

value of 17.1, the perveance reduction factor was 8.5%.

The required increase in magnetic field for 100% beam

transmission represents the degree to which the grid




































Figure 23a. Vane Grid Structure


Figure 23b. Component Gun Parts






58
























rJ~J- -~ -*;"
Y gt~7:~~~r;inf~




0 -. 4.. -










































fr-....',
-v-
Figure24. CompletelyAssem d VN


































: .' ./ .- .. ...-....
0,,

0- -`; 9ML, J.



































Figure 24. Completely Assembled Vane Grid Gun











Table 2. A Summary of the 24 Vane
Grid Structure Test Data


Anode


Anode


Voltage Current
(Volts) (ma)

200 112

200 109

,200 99

200 91

200 40

200 8.0

200 1.3

200 0.0

200 0.0

200 0.0

200 0.0

200 0.0

200 0.0

200 0.0


Magnetic
Cathode Field


Current


B


(ma) (Gauss)

112 0

109 112.5

104 135.0

100 157.0

93 180

81 205

65 225

48 270

40 315

38 323

37 334

32 360

28 404

26 448


Grid
/V Voltage
(Volts)
(Volts)


0 -2

7.82 -2

9.5 -2

11.1 -2

12.7 -2

14.3 -2

15.6 -2

19.1 -2

22.2 -2

22.8 -2

23.5 -2

25.4 -2

28.6 -2

31.7 -2


Micro-
per-
veance

42.5

38.6

36.8

35.4

32.9

28.7

23

17

14.2

13.5

13.1

11.3

9.9

9.17


























M ICROPERVEANCE


120


100
-- -- --- ^ -- ^---- -- - ioc




ANODE CURRENT DESIGN
VALUE 60

40
100% BEAM
TRANSMISSION
THROUGH
THE ANODE 20



S5 10 15 20 25 30

NORMALIZED MAGNETIC FIELD,B//V


















Figure 25. Microperveance and Anode
Current versus B//Va ratio
for the Vane Grid Structure


30


z




0
w

z
4


r


,zu









perturbs the beam in the gun.

Table 3 gives a summary of the grid transfer

characteristic data for this structure. These data are

shown plotted in Figure 26. The anode voltage was held

B
fixed at the value indicated corresponding to a -

ratio of 22.8. The Mu (95) average was 9.75.

Photographs of the impingement of the beam on the

carbonized target were taken at various distances from

the target. A typical beamlet pattern for this structure

will be illustrated in later discussion of Experiment #4.

These photographs were taken in anticipation of detecting

beam precession about the tunnel axis. Later analysis

of these photographs showed no net beam precession around

this axis; however, it was observed that each beamlet had

a characteristic rotation about its own axis. Since this

mode of rotation does not provide an inward force to

balance the known space-charge forces discussed in Chap-

ter II, an error was apparent or the rotation was too

small to detect within the range of the axial target

movement. Ion focusing was not suspected at this time as





1Mu (95) is the ratio of anode voltage to grid volt-
age required to reduce the current to 95% of its maximum
value at V = 0 volts.
g










Table 3. A Summary of the 24 Vane Grid
Structure Transfer Character-
istic Data





Grid Voltage
(Volts) Cathode Current (ma)
-V Ik; Va=600 Ik Va=800 Ik Va1000 Ik Va=1200


0 180.0 277.0 384.0 560.0

10 145.0 251.0 350.0 500.0

20 111.0 211.0 310.0 475.0

30 79.5 158.0 262.0 395.0

40 46.2 120.0 212.0 350.0

50 25.2 79.0 178.0 275.0

60 9.9 52.9 137.0 237.0

70 1.6 29.0 92.0 183.0

80 0 14.5 65.0 120.0

90 6.6 40.0 86.0

100 1.3 22.4 66.0

110 0 13.2 43.5

120 6.6 30.0

130 2.64 19.0

140 0 10.0

150 2.7

160 0





















ANODE VOLTS CURVE NO. Mp 95

600 ----- ---.- 9.35
800----- 2o ---$ 10.0
1000 ----- 9.-.79
1200----- ----- 9.76


B/IV-t = 22.8

Mji Averge = 9.81
Design Objective= 10.0







4




2
-- --------- /


-150


-100


600






500






400




E

300

I-
Z




200
w
0
0
r
I-



100






0


- 50


GRID VOLTAGE,Vg (VOLTS)






Figure 26. Grid Transfer Characteristics
for the Vane Grid Structure


-200









the indicated pressure on the ion gauge of the appendage

-8
pump was 8.5 x 10 torr. Furthermore, the pulse width

of the negative grid pulse had been reduced to approxi-

mately 12 microseconds--a pulse duration usually con-

sidered too short for ion buildup.

Further beam analysis was accomplished by observing

the beam through a telescope with a graduated reticle.

The beam size was measured and found to be smaller than

the corresponding diode prototype. An average of 10

readings for each diameter is given in Table 4. The

smaller size and beam thickness of the measured data is

attributed to the stronger magnetic field required to

reduce the anode interception to zero in the grided case.

B
The above data were taken at 22.8. Another source

of error in beam thickness is probably due to a shadowing

effect of the grid support ring into which the 24 grid

vanes are terminated. This ring was designed to function

as a front focus electrode. However, the exact location

of the ring with respect to the cathode front edge was

at best an approximation of a normal focus electrode for

a truncated cathode and could easily have suppressed

electron emission from a small portion of the cathode

front edge, thereby producing both a thinner beam and

reduced perveance.




















Table 4. Calculated Versus Measured Beam Size


Beam Outside
Diameter

Beam Inside
Diameter



Beam Thickness


Calculated



0.495 inch



0.392 inch



0.0515 inch


Measured



0.475



0.382



0.0415


% Error



10.4



10.2



1.2.4









Experiment #3



A photograph of the grid structure used in this

experiment is shown in Figure 27a. This structure

utilized rectangular .004 x .007 inch tape wound

helically such that the wide dimensions was facing the

cathode. This undesirable orientation was necessitated

by mechanical difficulties encountered in attempting to

wind the tape in the form of a helix with the narrow

dimension facing the cathode.

A summary of the experimental data is given in

Table 5. These data are also shown plotted in Figure 28.

The degree to which this grid orientation reduced the

perveance was surprising. It was somewhat anticipated

as discussed in Chapter II, but the amount required

experimental verification.

The beam generated by this structure definitely

showed breakup. A photograph of the beam breakup only

a few centimeters from the anode is shown in Figure 27b.

Measurements of beam size were not performed due to the

poor beam shape produced.

Table 6 gives a summary of the grid transfer

characteristic data for this structure. These data are

shown plotted in Figure 29. The anode voltage was held








































Figure 27a. Photograph of Helical Grid Structure


Figure 27b. Photograph of Beam Profile for
Helical Grid Structure











Table 5. A Summary of the Helical
Grid Structure Test Data


Magnetic
Anode Anode Cathode Field Grid
Voltage Current Current B Voltage
(Volts) (ma) (ma) 7a (Volts)

200 0 3.0 42.3 -2

300 0 7.5 34.6 -2

400 0 17.0 30.0 -2

500 0 30.0 26.8 -2

600 0 45.0 24.4 -2

700 0 67.0 22.6 -2

800 0 95.0 21.2 -2

900 0.25 130.0 20.0 -2

1000 1.0 185.0 19.0 -2

1100 1.3 250.0 18.1 -2

1200 2.3 330.0 17.3 -2

1300 4.3 420.0 16.6 -2

1400 10.0 580.0 16.0 -2


Micro-
perveance

1.06

1.44

2.13

2.68

3.06

3.62

4.20

4.80

5.85

6.85

7.94

8.95

11.10














































20 24


32 36


NORMALIZED MAGNETIC FIELD, B/v/V












Figure 28. Microperveance and Anode Current
versus B//Va Ratio for the
Helical Grid


0
O --- - - -- - -- -- -




8 :DESIGN VALUE






100 % BEAM TRANS-
MISSION THROUGH
THE ANODE




MICROPERVEANCE

ANODE CURRENT

C-- 11 ,


IU -

8
Z'
w
6 a:
a:

4
o
2 z











Table 6. A Summary of the Helical Grid Struc-
ture Transfer Characteristic Data


Grid
Voltage
(Volts)
-V


0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190


IkVa = 600


101.1

81.2

62.0

50.5

38.7

32.6

21.7

15.5

10.1

3.8

1.6

0


Cathode Current (ma)
Ik Va =800

155.0

140.0

116.0

101.0

85.0

73.5

58.0

50.4

38.7

31.0

21.7

15.5

10.1

3.86

1.55

0


Ik Va = 1000


233.0

202.0

183.0

155.0

144.0

128.0

113.0

96.6

83.5

70.0

58.1

46.5

38.7

31.0

20.1

14.0

7.75

4.5

1.5

0



















































-150 -100 -50

GRID VOLTAGE, Vg (VOLTS)


Figure 29.


Transfer Characteristics for
the Helical Grid


250






200





E
150


z

a:

100 O
UJ
0
I-
o


-200.








B
fixed at the values indicated corresponding to a
"a

ratio of 18.5 gauss/volt3/. The Mu (95) average was

6.5.

The perveance reduction factor at the design value

of 17.1 amp/volt3/2 was approximately 71%. The perveance

reduction for zero anode interception was approximately

80%1 This gun structure proved clearly impractical.


Experiment #4



This experiment was designed to repeat Experiment

#2 with an appropriate grid vane taper for constant cut-

off Mu as discussed in Chapter III. A further objective

was to re-examine the doubtful data on beam rotation.

The grid modulator was modified to produce pulse

widths down to 1 microsecond. The grid structure of

Experiment #1 was modified through a potting and grinding

operation such that the rectangular grid vanes had a 33%

taper. This taper was based on electrolytic tank work

representing cross-sections at the small and large ends

of the cathode, rather than the average cathode position

used in the first experiment. Details of this work are

summarized in Appendix B.

The grid transfer characteristics were very









similar to those in Experiment #2 and are not repeated.

The anticipated increase in cut-off sharpness and in-

creased perveance reduction factor was partially success-

ful. The perveance attained was 14.7 amp/volt The

grinding and reshaping of the grid structure produced

vane pitch variations that prevented the sharp cut-off

characteristics expected. The extent to which the vanes

are non-uniformly spaced are illustrated in the beam

photograph of Figure 30. Although the electron beamlet

produced by this structure was irregular in size, the

beam profile did not show signs of beam breakup as the

target was moved along the axis to a position 5.9 inches

in front of the anode. This photograph was made at a

beamlet focal point approximately 10 centimeters from

the anode.

The beam voltage during measurement was 825 volts.

The pulse duration was 4.5 microseconds. The peak tar-

get current was 120 milliamperes.

Beam precession was detected at a pulse width

under 10 microseconds. Data of beam precession were

taken in the form of 35 mm slides every half centimeter

for a total distance away from the anode of 16 centimeters.

Figure 31b shows a plot of this precession. The rate of
































































Figure 30. Beamlet Pattern Produced by
the Vane Grid Structure








































Figure 31a. Typical Precession of a Single
Beamlet (Complete Beam Contains
24 Beamlets)


0 10 20 30 40 50 60 70 80 90

Beam precession in degrees



Figure 31b. Plot of Precession versus Axial
Distance (Vane Grid Structure)


0




"4
-H
M
0
a
4J


-4)
0
k









"4-
H
r-4

to









precession was approximately 180/cm. The manner in which

the beamlets moved on the carbon screen is illustrated in"

Figure 31a. A photograph of the grid current, beam

current and grid voltage pulse is shown in Figure 32.

The droop in the cathode current at the leading edge of

the grid pulse is due to a magnification of the grid

pulse by the Mu of the structure.






The purpose of this experiment was to verify that

the beam analysis performed and the negative grid design

developed can be utilized in an actual microwave ampli-

fier. The traveling wave tube selected was an L-band

amplifier with a reputable record of performance. The

design change simply entailed the removal of a planar

gun and substituting a negative grid magnetron injection

gun (radial vane grid type). Pertinent traveling wave

tube design parameters are summarized in Table 7.

Symbols used in this table conform to those of Pierce [18].

The electronic efficiency for this tube type


IThis tube type is presently in production at the
Sperry Electronic Tube Division, Gainesville, Florida.





















Grid Current
Pulse, Vertical
Scale, 1 ma/cm




Cathode Current
Pulse, Vertical
Scale, 20 ma/cm





Grid Voltage
Pulse,
Vertical Scale,
40 volts/cm




Time Scale
1 Microsecond per Division











Figure 32. Photograph of Beam Current,
Grid Voltage and Grid Current










Table 7a. Tube Parameters


Frequency (MHz) 500 750

ya 1.55 2.32

yro 1.15 1.72

Z 260 112

c .25 .20

b 1 3.31

4(QC) 2.12 2.76

B 41.5 39

Xe (Inches) 1.77 1.18

Bc/Xe Gain/Inch (db) 5.9 6.3








Table 7b. Typical Beam Parameters


Beam OD

Beam ID

Beam Current

Beam Voltage

Efficiency Peak


Planar Gun

0.602 inches

0.438 inches

.862 amperes

1900 volts

22%


MIG

0.475 inches

0.382 inches

0.5 amperes

2100 volts

18%


1000

3.1

2.3

54.5

1.4

1.67

3.44

35.5

.885

6.0









utilizing a planar gun is typically 20 22% Rf

evaluation of the negative grid design showed a peak

efficiency between 17 18% A graph of saturated

power output and efficiency versus frequency is given in

Figure 33. The beam size of the negative-grid magnetron-

injection gun was 20% smaller than the original design

value for this circuit, which partially accounts (through

potential depression) for the reduced efficiency and the

increased beam voltage requirement as noted in Table 7b.

Additional differences are associated with the higher

beam rotational energy in the magnetron-injection gun

case.

















80






70

-EFFICIENCY











_50 POWER OUTPUT






A0


500


600


700


FREQUENCY


800


900


1000


(MHz)


Figure 33. Plot of Efficiency versus
Frequency for L-band Tube


(Vane Grid Structure)


-0 2(
0,

2
LU
C-)
ILI

S-)
z
0
cr

w
-1 10
w


E




0~
c-


0

0.
a-


f A















CHAPTER IV


CONCLUSIONS



The experimental data reveal that the cathode grid

mask ratio, defined and discussed in Chapter II, is the

dominant factor influencing the reduction of perveance.

In the case of the helical grid, this mask ratio was large,

and the perveance reduction was excessive. With the

radial vane grid, the cathode mask ratio approached the

screening fraction itself (which is clearly the limiting

minimum value), and the resultant perveance reduction was

considerably less. Another factor entering into the

reduction of perveance is the manner in which the presence

of the grid perturbs the longitudinal electric field com-

ponent above the cathode surface. In the case of the

helical grid, these perturbations are gross, while with

the radial vane grid configuration they are minimized.

In the latter case, the longitudinal field component is

reduced only in magnitude, but not in direction.










Although the grids evaluated were not perfect from

the standpoint of construction and final alignment,

experimental evaluation indicates that the negative grid

concept can be successfully incorporated in the magnetron-

injection gun.



It should be noted that the practical matter of

gun alignment in the crossed field gun is a serious and

difficult one to accomplish. Variations in the grid plane

perpendicular to the cathode are magnified by the area

convergence ratio of the gun.

The conclusion with respect to beam precession is

that for long pulse or continuous duty operation, the

beam is nearly neutralized by positive ions even at an
_Q
indicated vacuum of 5 x 108 torr. This neutralization

would suggest that after the beam has been operating

long enough for complete ion buildup, the magnetic field

could be removed. This is not the case, though as the

electron gun is an excellent ion pump and would be free

of ions, thus for proper operation, the magnetic field

is still required.

It has been demonstrated that satisfactorily well-

defined beams can be obtained from a negative grid crossed

field gun. The present understanding of such guns is





83



largely empirical. Further work is necessary for an exact

analysis of beam trajectories in the presence of an axial

magnetic field with components both parallel and perpen-

dicular to the cathode.






































APPENDICES














APPENDIX A


PROTOTYPE MAGNETRON-INJECTION GUN DIODE DESIGN


The prototype diode design used in the experiments

discussed in Chapter III is based on Dryden's theory [7].

As previously stated, Dryden solved the case of an axially

symmetric flow from a cone cathode in the presence of an

axially symmetric magnetic field. The magnetic field in

this analysis is restricted to the uniform field case.

Following Kino, Dryden derives the following relation-

ships between the physical quantities and radial variation:

Velocity ~ rn (A-l)

Potential V r2n (A-2)

Electric Field E r r2n (A-3)

Magnetic Field Intensity B m rn-1 (A-4)
2n-2
Volume Charge Density p r 2 (A-5)

Cathode Surface Current 3
3n-2
Density J f r (A-6)

where n is an arbitrary constant.,




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