US2916666A - Electron beam gun systems - Google Patents

Description

Dec. s, 1959v Filed June 21, 1954 G. L. HALL ELECTRON BEAM GUN SYSTEMS 3 Sheets-Sheet 1 ATTORNEY Dec. 8, 1959 G. I .HALL 2,916,666

ELECTRON BEAM GUN SYSTEMS Filed June 21,`1954 s sheets-sheet 2 T av,

INVENToR GEORGE L. HALL.

ATTO RN Y Dec. 8, 1959 G. L. HALL 2,916,666

ELECTRON BEAM GUN SYSTEMS Filed June 21, 1954 3 Sheets-Sheet 3 ,l f5 7'3 c E 7'5 Y JL./' 1L JL INVENTOR GEORGE L. HAM

United States Patent ELECTRON BEAM GUN SYSTEMS George L. Hall, Fredericksburg, Va., Vassignor to International Telephone and TelegraphA Corporation, Nutley, NJ., n corporation of Maryland Application JuneZ-l, 1954, Serial No. 437,999 11 claims. (ci. sis- 31) "Electron Optics by V. E. Cosslett and Electrical Optics and the Electron Microscope by V. K. Zworykin, G. A. Morton, E. G. Ramberg, I. Hillier, and A. W. Vance. Briefly, this type of lens is a development of a twocylinder lens system, a third cylinder being introduced v between two identical cylinders, which may be longer or shorter. inlength than the middle cylinder. In its simplest form, the cylinders are reduced to simpleA apertures. The'central element, or aperture', may be at a higher or lower potential than the outer two elements or apertures which are maintained at' the same potential. If this common potential is zero (ground) and the central elementr is connectedv to the cathode of the electron gun system, then only a single negative voltagey need be applied, and the arrangement has come to be known as a univoltage, unipotential, or einzel lens. Iny its 'generic sence, the lens system-of the present invention refers to the einzel or unipotentiallens, but differs therefrom in thephysical' arrangement of the various electrodes incorporated in the lenssystem of this'. invention.

A further configuration of a unipot'entiallens structure is that of the coaxial-cylinder type wherein the inner cylinder may be physically shorter than the outer cylinder with a difference of potential established therebetween for focusing the electron beam. If the potentials applied to the coaxial cylinders are'equal, then we have a region of zerodiiference of potential, commonly referred to as a drift region, said region finding great application in the present development of high velocity electron discharge devices utilizing several of these drift regions with at a lower or higher potential thanithe outer electrodes,y

the total effect is to provide a convergent electron lens. Invthe past, this simple unipotential or einzel lens has found most application in electron microscopes and the usual typel of cathoderay tubewhere a spot of light is swept horizontally across the face of a viewing screen by a. horizontal deflection voltage and vertically by a voltage to be observed to obtaina pictorial representation of the voltage being observed. v y

In certain applications, such as direction finding, it is ice desirable to employ a cathode ray tube having a focused annular ring displayed on the face of the cathode ray tube with radial dellections vbeing produced by signals applied to equally spaced deflection plates around the. circumference of the hollow annular electronbeam. It is possible with such a system to orient the radial dellections in a manner to correspond to signals received. from directional antennassuch that the radial deflections will point in the direction of the antenna transmitting the signal. To produce the desired undeflected focused annular ring, an electron gun system was constructed employing a cathode `capable of producing a hollow cylindrical annular electron beam and an einzel lens structure considered suitable from a ,theoreticalviewpoint to focus the emitted' hollow cylindrical electron beam. upon the screen for production of the desired annular. display ring. The electron gun system utilizing the usual' einzel lens structure, that is a physically symmetrical annular .electrode structure in which the inner Vand outer parts of any one electrode are equally spaced about the mean circumference of the electron beam, was-foundrto produce an annularv electron beam whosemean diametervaried as the yfocusing electrode potential was varied above and below the optimum focusing potential. AThisyvariation yof' means beam diameterr and consequently the trace diameter is an annoying feature andv for successful operation of an annular beam display tube, the mean beam diameter should be-made independent of the focusing potential.

It was discovered that a physically symmetrical .annular einzel lens exhibits an inherent static non-symmetrical potential distribution as represented by a ring ofk saddle points of a diameter different from the'mean ,diameter of the hollow cylindrical annular beam. This static electrical dissymmetry wasdiscovered to be one-of the factors thatV produced the undesired variation of mean beam diameter with changing focusing potential.V Fur.- ther investigation of einzel lens structures, particularly those incorporating a drift region area, indicateda second factor which further complicated-'the desired focusing of an annular elect-ron beam'. This second factorrwa's the effect of the space charge" present in the drift 'region' of this type of einzel-lens structures. The first factor predominates in lens systems consisting of electrodes of Various shapes and various potentials. The secondfactor, while its effect may be felt in all einzel lens systems, is

usually found in those lens structures having rdrift'tubev regions.

It is an object of this invention to provide an'improved einzel'lens structurefor focusing hollow curved electron beamswhose mean c'i'rcumfere'ncefis unaffected by the spacey charge withinthe lens elements orvariationsof focusing potential applied'thereto.

Another object of this invention is th'e provision ofv einzel lens structures having electrical symmetry about the horizontalfand vertical mid-'plane thereof for focusing hollow curved electron beams. v

A further object-ofthis inventionv'is the provision'of a physically non-symmetrical einzellens which eliminates the Vstatic electrical dissymmetries and space charge effects. of heretoforeI employedj'physically vsymmetrical, einzel lenses useful in focusing hollow'curved electron beams. v Y j A feature of this invention' 'isanx'einzel leus ystructure including three electrodes positioned in tandemalongl the path of a hollow curved electron'beam, eachof s'aid electrodes includingy inner and outer 'parts with 'respect to the electron beam path for passage' of theI hollow' electron beam therebetween. The inner and outer 'electrode' parts ofA the first and third-4 electrodesf arepositined' to be physically symmetrical with themean circumference of the hollow electron beam and the-electrode,partsy oft the second or central electrode are positioned to be physically 3 t non-symmetrical with respect to the mean circumference of the hollow electron beam.

Another feature of this invention is an einzel lens structureincluding as-thecentral-electrode thereof concentric inner and outercylinders whose circumferences adjacent` a given path including annular electrodes having `inner l and outer parts disposed with respect to the beam path` for passage of the beam therebetween, the electrode parts of certain ones of said electrodes having radii which according to a first order theory are related to the mean radius of the annular beam by the square root of the product of the outerradius of the inner electrode part and inner radius of the outer electrode part.

The above-mentioned and other features and objects of this invention will become more apparent by reference to the following description taken in conjunction with the accompanying drawings, in which:

Fig. 1 is a diagrammatic illustration of an electron gun system employing a physically symmetrical einzel lens structure of the prior art and the non-symmetrical equipotential configuration thereof; l

Fig. 2 is a-diagrammatic.illustration of an electron gun system employing an einzel lens structure of this invention and the resulting symmetrical equipotential configuration thereof;

Fig. 3 is a diagrammatic illustration of a lens structure in accordance with this invention corrected for non-uniform space charge effects of annular drift tube regions; and

Fig. 4 is a diagrammatic illustration of an electron gun system employing an einzel lens structure corrected for both static and spacecharge` eects in accordance with this invention. l

Referring to Fig. 1, there is illustrated therein an electron gun system including an electron lens structure of the unipotential type indicative of the prior art arrangements for focusing curved electron beams. The gun system comprises a cathode 1 suitable for` electron emission to form a hollow curved electron beam, a grid 2 cooperating in projecting the hollow electron beam along a given path and a unipotential lens system 3 disposed physically symmetrical to the mean circumference of the electron beam path.

While numerous curved electron beams may be emitted from cathode structures the most frequently used curved electron beam is a hollow cylindrical one.v The description of the lens structures herein will be related to hollow cylindrical annular electron beams, but it will be obvious as the description continues that the corrections applied to the physically symmetrical lens system for hollow cylindrical annular electron beams may be applied in a similar manner to those lens systems `employed in focusing curved electronbeams other than `hollow cylindrical ones, suchfas a hollow ellipticallens` system and others having similar variations in curvature.

Electron devices suitable forproducing curved electron beams may have electrodes both'internally and externally to the beam. In some instances the internal and external electrodes Willbc at the same potential and in otherinstances will be at a difference of potential. At any rate,` for proper action of-the electrodes incorporated in the lens system, it is necessary to consider the forces acting on the curvedf hollow electron beam both at its outer andinner radii. It is desirable for proper focusing action that the radial electric elds fromthe main radius of the electron beam to its inner and outer extremities be symmetrical( Only when this condition `is satisfied will focusing be possible without deflection,` or will deection be possible Without defocusing.

Turning again to Fig. 1, the lens system 3 is illustrated as `being a physically symmetrical annular electrode structure including accelerating electrodes 4 and 5 and a focusing electrode 6 disposed symmetrically between electrodes 4 and 5. Each of the electrodes 4 and 5 include therein an annular aperture 7 for passage of the annular electron beam therethrough.` Aperture 7 of electrode 4 is defined by an outer annulus 8 and an inner disc 9, each having a proper diameter to position aperture 7 symmetrically with respect to the mean circumference of the l annular electron beam. The aperture` 7 of electrode 5 is defined in a like manner and it will be obvious from the illustration that electrodes 4 and 5 are identical in all respects and disposed symmetrically from electrode 6. In the physically symmetrical electron lens, focusing elecy trode 6 likewise provides therein an aperture V10f0r passage of the electron beam symmetrically therethrough with the confining walls of aperture 10 being defined by annulus 11 and` disc 12. It will `be recognized that in such a physically symmetrical lens structure the mean t. radius of the electron beam which passes symmetrically through apertures 7 and 10 is related tothe radius of disc 12 and the inner radius of annulus 11. The relationship deducible from the geometry of the structure'utilized iny the prior art is i (employing the notationsv of Fig. l) `Where r1 equals the radins of annulus 12, r2 equals the `mean radius of the electron beam and r3 equals the inner radius of annulus in the prior art have inherent static dissymmetries such that the` electric fields from the mean radius ofthe electron beamto` its inner and Youter extremities are not symmetrical. `This condition produces a radial detlectionof the electron beam in addition to a` focusing thereof. This radial' deflection is illustrated by the equipotential plots shown in Fig. 1. 'Itwill be recognized that the greatest dissymmetry exists `in the region of the saddle points 13. Infact, the saddle points 13 are displaced radially from the mean radius 14 of the electron beam. It has been further discovered that if the inner and outer electrode parts 11 and 12 were extended longitudinallyI to form concentric cylinders that the dissymmetries of the electric field are further complicated by an appreciablespace charge built up between the cylinders. l l

Referring noW to Fig.` 2 and employing the same reference characters therein with respect to identical structure, an embodiment of the unipotential lens system of this invention is illustrated which overcomes the electrical dissymmetn'es of the prior art lens structure of Fig. 1.1

j A lens system in accordance with this invention may include electrodes v4 and `5 identical with the electrodes 4 and 5 of Fig'` 1 with apertures 7 being disposed symmetrically about the mean circumference or radius 14 of the electron beam. The correction applied to the lens structure of this invention is concerned with the modification of the focusing electrode `6a in a manner to position the aperture 10a to be physically non-symmetrical withl respect to the mean radius 14 of the electron beam path. Ithas been discovered that this non-symmetrical positioning of aperture 10d shifts the saddle points 13 of `the equipotential distribution for coincidence with the mean radius ofthe electron beampath. Tests performed on the lenssystem modified to have a physically non-symmetrical focusingelectrode illustrated that good focusing of an annular electron beam was accomplished without radial deflection thereof. t p p t The physically non-symmetrical characteristic of electrode 6a, as established by thel inner radius of outer part 11a and the outer'radius of inner part 12a, may be accomplished in either one of twov ways. The lirst way would be to increase the diameter of disc 12 such that the radius r1' of disc 12a is greater than the radius r1 of disc 12 of Fig. 1. 'Ihis would require a remachining of the inner electrode part of focusingelectrode' and probably would be the most undesirable means of accomplishing the modification of a normal physically symmetrical unipotential lens structure. The preferredmeans of accomplishing the desired modication' of electrode 6 would be to remove a predetermined amount of material by a machining process from the annulus 11, thereby making the radius r3 of annulus 11a larger than the radius r3 of annulus 11 of Fig. 1.

The modification of a physically symmetrical lens here in set forth is not restricted to the correction of static dissymmetries of physically symmetrical three-apertured lenses but may be employed to correct similar electrical dissymmetries in single-apertured or double-apertured lenses as well as other curved einzel lens systems.

While the lens systems of Figs. l 'and 2 are illustrated diagrammatically, attention is directed to the copending application of J. H. Bryant and A.' G. Peifer, Serial No. 301,590, now Patent No. 2,753,484, entitled Signal Indicating Device for an example of the proposed structure and supporting means of the present lensstructure to provide a cooperating mechanicalassembly. Briefly the electrodes are held in a parallel relationship by an arrangement of ceramic tie rods, certain ones of which support the outer electrode parts and others of which support the inner electrode parts with the tie rods looped and secured together to form a rigid mechanical structure.

Having now illustrated the means of correcting an annular electrode structure for non-uniform static eects, it is necessaryV to consider the changes or dissymmetries produced by the'presence of an electron beam in the structure. A general analysis is diflicult but a few of the elects of space charge in an electrode structure may be resolved in an approximate manner. Any electron beam which is appreciably dense, if allowed to drift, will acquire in timel a non-,uniform cross-sectional charge and potential distribution due to the natural repulsion of the electrons in the electron beam. Therefore, within a drifting electron beam, there is some line or surface which is at a lower potential than the surrounding drift vtube or region. Hence, anelectrostaticy field will exist between the potential minimum Vand the walls of the drift tube.

` Fig. 3 illustrates a lens structure in accordance to this invention including therein as thev central element, concentric cylinders operated at the same potential which deline adrift region for the electron beam being focused by a lens structure of this type.,v The inner cylinder 15 may be considered to be a longitudinal extension of disc 12 of the focusing electrode 6 of Fig. 1, while the outer cylinder 16 may be considered a'longitudinal extension of annulus 11 of focusing electrode 6." Electrodes 4 and 5 as before are appropriately positioned symmetrically with Arespect to electrode 6c. The electronV beam passing through electrode 6c in the passage provided between theouterv surface of cylinder 1S and the -inner surface of cylinder 16 exhibits a certain radial electric field, E(J and El." For a first approximation; the potential minimum surface in the electron beam may be assumed to be an equipotential cylinder of radius r2. If we let r1 and r3" represent the radii of the inner and outer drift tube f walls, respectively, and assuming infinitely longer cylinders, itcan be shown that r2=\/r1" r3 inorder to have lequal forces between the electron 'beam potential minimum and the respective drift tube walls; f

This relationship may be deduced as follows. Starting with the fundamental electric lieldA relationship Within concentric cylinder arrangement, it may be showntha't VB- V T I l y rylmT-;

and

which results in r2=\/ r1 r3. Upon examining the above equations, it can be concluded that the diameter of either the inner or the outer cylinder may be adjusted to make E=E,. Naturally, it would be best to decrease the large lield, Eo, by decreasing r3". In certain applications where the enclosure for the electron lens system is restricted in diameter, the increasing of r3" Would be impracticall and therefore, the radius of r1 should be increased.

Since proper focusing in a lens structurehaving a drift region requires equal forces between the electron beam potential minimum and the respective drift tube walls and 4the relationship rg'-a/rl" r3" must be satisfied, it is obvious that the physically symmetrical system will not satisfy these conditions since in a physically symmetrical system By modifying a drift tubeportion of such a unipotential lens structure in accordance with the formula there has resulted an equal current interception by the inner and outer walls and a much improved focusing'of annular electron beams. A successful reduction to practice of a lens structure for a navigational aid application incorporating the modification herein described resulted in a lens where r3=1.00 inch, r2"=0.750 inch, an r,"=0.5625inch.

Comparing the modification of electrode 6a of Fig. 2 with the necessary modification of the drift tube electrode 6b of Fig. 3, it will be recognized that both modifications are in the same direction. That is to say, r3 and r3' must be both increased or r1" and r1 must be both increased to remove the undesired electrical dissymmetries occurring in physically symmetrical lens systems. Recognizing this fact and the fact that the same relationship of radius changes holds for the removal of both static and space charge non-uniformities of electrical properties, lens Structures of the unipotential type may be modied in accordance with the square root relationship set forth herein to provide `electrical symmetry for these lenses having both `static and sneeeeharse nonuniforrnites- .With reference to Fig. 4, an annular`unipotential lens structure is illustrated which has been corrected for both static dissymmetry and nonuniform space charge effects.

Annular lens structure 3b is shown diagrammatically to comprise a first set of concentric electrodes 17 and 1S operated at one potential V1 and a second set of concentric electrodes 19 and 20 operated at a second potential V2. The outer radius rl" of electrode 17 and the inner radius r3'" of electrode 18 are related to r2", the mean radius `of the electron beam, by the square root of the product of r3" and rl" which will correct for the space charge effects present in the drift region between electrodes 17 `and 18. The outer radius 1'1" of electrode 19 and the inner radius r3" .of electrode 2t) are related to 1'2" also by the square root of the product of 1'3" and r1" which will correct Ifor the space charge effects present in the drift regionbetween electrodes 19 and 20. It will be recognized, however, that r1','` is less than r1" and that r3 is greater than r3" by an amount suicient for a given application to assure that static dissyrnmetries do not exist between the rst and second set of electrodes forming the lens structure 3b. This relationship of radii will remove space charge effects in each of the drift regions and will assure an equipotential plot of the electric eld between the sets of electrodes which is electrically symmetrical about the mean radius r2" of the electron beam path.

Practically all electrode systems which have apertures therein to cooperate in focusing curved electron beams display non-uniform static equipotential distributions which result in non-uniform radial effects on electrons placed in geometrical planes of symmetry.` In addition, space-charge effects result in unequal attraction of electrons to the inner and outer walls of an appreciably long drift region. The modifications or correction disclosed hereinabove have been related to hollow cylindrical type lens structure, but it must be kept in mind that these modifications can be effectively applied to electron lens structures other than cylindrical to remove the inherent electrical dissyrnmetries present therein in a manner similar to that disclosed herein for cylindrical type structures.

While I have described above the principles of my invention in connection with specific apparatus, it is to be clearly understood that this `description is made only by way of example and not as a -limitation to the scope of my invention as set forth in the objects thereof and in the accompanying claims. l i

I claim:

1. An electron gun structure using an electron lens of the einzel type to maintain the dimensions of a hollow cnn-.ved electron beam substantially constant comprising means to project a hollow `curved electron beam having a predetermined mean circumference along a given path, a plurality of electrodes disposed along said given beam path, means to couple a first potential t certain of said electrodes and a second potential to others of said electrodes to establish an electrostatic eld 4between adjacent ones of said electrodes, each ofsaid `electrodes having unipotential inner and ,outer parts with respect to said -llollow beam for passage of said hollow beam along said given path between said parts, said electrode parts of at leastone of said electrodes being positioned in an asymmetrical relationship with respect to said predetermined mean circumference to establish a symmetrical electrostatic field about said mean circumference.

2. electron gun structure using an electron lens of the einzel type to maintain the dimensonsof a lhollow curved electron beam substantially constantcomprising means to project a hollow curved electron beam `having a predetermined mean circumference along a given path, a plurality of electrodes disposed along said given beam path, means to couple a rst potential to certain o f said eleotrodes and e second Potential to others of said electrodes to establish elo etrostatle` eld between adjacent ones `of said electrodes, l each `ofsaid electrodes having inner and outei'` parts with respect to said hollow beam for Passage of said l'lolltwvhewn` along said given path he-` tween said parts, saidelectrode parts of at least one of said electrodes being positioned in an asymmetrical relationship with respect to said predetermined mean circumference to `establish a symmetrical electrostatic field about saidmean circumference, said inner part of `said one of said electrodes having a i given .outer circumference and said outer part of said one of said given electrodes having a given inner circumference, the product of said inner and outer circumferences being related to the square of the mean 'circumference of said beam path.

3. An electron gun strncture using `an electron lens `of the einzel type to` maintain the dimensions of a hollow curved electron `beam snbstantially constant comprising means to project `a hollow curved `electroil beam having a predetermined mean circumference along a given path, a plurality of electrodes `disposed along said given `beam path, means to couplea rst potential to certain of said electrodes and a second `potential `to others of said electrodes to establish an electrostatic field between adjacent ones of said electrodes,leach of said eletrodes having inner and outer parts with respect to said hollow beam for passage of saidh'ollow beam `along said given path between Ysaid parts, saidelectrode `parts of at least one of said electrodes being vpositioned in an asymmetrical relationship with respect tosaid predetennined mean oircumference to establish a symmetrical electrostatic field about said mean circumference, said electrodes being three in number and Said one 'ofsaid electrodes being disposed symmetrically between the other two of said electrodes, said one of said `electrodes, including said inner part havinga given outer circumference and said outer part having a given inner circumference, the product of said given inner and outer circumferences being related to the square of the mean circumference of said given beam path.

4. An electron gun structure using an electron lens of the einzel type tomaintain the dimensions of a hollow curved electron beam substantially constant comprising means to project a hollow curvedfelectron beam `having a predetermined mean circumference along a given path, a plurality of electrodes disposed `along said givenbeam path, means to couple a first potential to certain o f said electrodes and e second potential to othersof said eleotrodes t0 establish an electrostatic |field betweenadjacent ones of said `electrodes, each ofsaid eleletrodeshsvng inner and outer parts with respect to said hollow beam for passage of said hollowheamelons .said given `Path between said parts, said eleetroderart's of atleast one of said electrodes being positioned an asymmetrical relationship with respect` to said predetermined' mean circumference to establish a symmetrical electrostatic iield about said mean circumference, said inner part including a disc and said outer part including an Avanriulus disposed concentric vto saiddisc.`

5. A structure according to claim 4, wherein said disc and said annulus of said one of said electrodes have given outer and inner` radii, respectively, and the mean radius of said beam `path `is related to the` square root of the product of said given outer and inner radii.

6- An electron son struotnretusins electron lens of the einzel type to maintain the dimensions of e hollow curved` electron beam substantially `constant comprising means to Aproject a hollow curved electron beam `haft/ing a predetermined mean circumference along a given path, a plurality of electrodes disposed `allonge said given beam path, means to couple a first potential to certain of said electrodes and a second potential to others of said electrodes to establish an electrostatic field between adjacent ones of said electrodes, each of said electrodes having inner and outer parts with respect to saidhollow beam for passage of `Said hollow beam `along said given path between said parts, said electrode parts of at least one of said electrodes being positioned in an asymmetrical relationship with respect t-o said predetermined mean circumference to establish a symmetrical electrostatic field about said mean circumference, said electrodes numbering three and being disposed transversely of said given beam path, each of said electrodes including a disc disposed within said given beam path and an annulus disposed to surround said given beam path, the product of the inner radius of said annulus and the outer radius of said disc of said one of said electrodes being related to the square of the mean radius of said given beam path.

7. A structure according to claim 6, wherein said one of said electrodes is disposed symmetrically between the other two of said electrodes.

8. An electron gun structure using an electron lens of the einzel type to maintain thedimensions of a hollow curved electron beam substantially constant comprising means to project a hollow curved electron beam having a predetermined mean circumference along a given path, a plurality of electrodes disposed along said given beam path, means to couple a rst potential to certain of said electrodes and a second potential to others of said electrodes to establish an electrostatic field between adjacent ones of said electrodes, each of said electrodes having inner .and outer parts with respect to said hollow beam for passage of said hollow beam along said given path between said parts, said electrode parts of at least one of said electrodes being positioned in an asymmetrical relationship with respect to said predetermined mean circumference to establish a symmetrical electrostatic field about said mean circumference, said one of said electrodes comprising a first cylinder disposed within said given beam path and a second cylinder disposed to surround said beam path, the inner radius of said second cylinder and the outer radius of said first cylinder being non-symmetrically related to the mean radius of said given beam path.

9. A structure according to claim 8, wherein the product of said inner and outer radii is equal to the square of the mean radius of said given beam path.

10 10.v An electron gun structure using an electron lens of the einzel type to maintain the dimensions ofa hollow curved electron beam substantially constant comprising means to project a hollow curved electron beam'having a predetermined mean circumference along a given path, la plurality of electrodes disposed along said given beam. y path, means to couple a first potential to certain of said electrodes and a second potential .to others -of said electrodes to establish an electrostatic field between adja-"' cent ones of said electrodes, each of said electrodes -having inner and outer parts with respect to said hollow beam for passage of said hollow beam along said given path between said parts, said electrode parts of at least one of said electrodes being positioned in an asymmetrical relationship with respect to said predetermined mean circumference to establish a symmetrical electrostatic eld about said mean circumference, said electrodes numbering at least two, each of said electrodes including a rst `cylinder disposed within said given beam path and a second cylinder disposed to surround said given beam path, said rst cylinder having a given outer radius and said second cylinder having a giveninner radius, the product of said given inner and outer radii being equal to the square of the mean radius of said given beam path.

1l. A structure according to claim l0, wherein the outer radius of said rst cylinder of one electrode is greater than the outer radius of said first cylinder of the other electrode by a given amount and the inner radius of said second cylinder of said one electrode is less than the inner radius of said second cylinder of said other electrode by a given amount to provide a symmetrical electrostatic field between said electrodes for focusing v said beam without deection thereof.

References Cited in the tile of this patent UNITED STATES PATENTS 2,124,270 Broadway July 19, 1938 2,409,693 Okress Oct. 22, 1946 2,466,064 Wathen et al. Apr. 5, 1949 2,791,711 Harris May 7, 1957

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