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Dec. 3, 1946.
Filed Sept. 21, 1942
FIG. /
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lasrzacr/iva'sLz-cmooe pdrgzvrugosmusmcq- ~
Patented Dec. 3, 1946
John E. Pierce, Millburn, and William 0.
Shepherd, Summit, N.'J., assignors to Bell Telephone Laboratories, Incorporated, New York,
N. 17., a corporation of New York
Application September 21, 1942, Serial No.’ 459,12
11‘ Claims.
(Cl. 250--2"1.5)
2, v.
range of frequency over which the device can be
This invention relates to electron discharge
devices and more particularly to ultra-high fre
quency oscillation generators of the re?ection
tuned electronically. In general, the higher the
transconductance, the greater is this frequency
range and the greater the ratio noted the greater
is this range.
In oscillation'generators of the re?ection type,
such as disclosed, for example, in Patent 2e06,
Realization of a high transconductance ‘in
volves, inter alia, attainment of strong ?elds
effective upon the electrons in' both directions
850, granted September 3, 1946, to John R.
Pierce, an electron beam‘is projected across a gap
in a high frequency circuit element, such as a
of their travel acrossthe gap.
Such ?elds are
cavity resonator, whereby it is velocity varied, 10 obtainable by employing grids across the ends of
the gap. However, grids introduce a heat dissi
and enters a region betweenthe gap and a re
pation problem and the power obtainable from
?eeting electrode wherein the velocity variations
the device is dependent upon the heat dissipat
are converted into density variations and the
ing limitations of the grids. In order to pre
direction of electron travel is reversed. The elec
vent overheating of the grids; a reasonably low
trons are then ‘againprojected into the gap in 15
current density over the grids must be main
the direction opposite to that of their initial
tained. The heat dissipating capacity of the
projection acrossv the gap and deliver energy to
grids is dependent, of course, uponthe size of
the circuit element to sustain oscillations. The
the grids. However, the capacitance between the
operating frequency of such oscillation gener
grids also is dependent upon the size of the grids
ators may be'valried over. a wide range by alter 20
and, therefore, the grids cannot be increased
ing the high frequencyrcircuit ‘element or cavity
unduly in size to increase their heat dissipating
resonator. Also, as pointed out in . the Pierce
capacity because of the attendant increase in the
patent,‘ vdevices of this type are tunable electron
capacitance therebetween.
' '
ically, that is, theloperating- frequency can be .
As noted heretofore, the operating 'frequency
varied through a moderate range by varying the 25 of re?ection type oscillation generators can be
potential of the re?ectinge'lectrode. The ampli
varied over a fairly wide range by varying the
tude of the oscillation changes as the frequency
high frequency circuit element’ associated with
is varied by changing the potential of the re
the gap. Thus changing v the operating fre
quency, however, requires for attainment of op
It has been found that in such devices the 30
timum operation substantial variation in the
amplitude of the oscillations is not a single valued
transit time for the electrons in the region be
tween the gap and the re?ecting ‘electrode, the
function of the potential of the reflecting elec
trode. As this‘potenti'al is varied from small '
transitv time including the time ofv both forward
and reverse motion of the electrons. This transit
time is dependent. upon the potential of there
values through the rangewhere oscillations occur »
and to large values Where ‘oscillation is stopped,
and then decreased, a form of hysteresis occurs
atone or several regions in the potential range.
Hence over certain ranges of potentialof the.
reflecting electrode, once the oscillation has
?ecting electrode and, in known devices, realiza
tion of optimum operation with large changes in
the operating frequency effected by changes in
the high frequency circuit element,.has required
1 reached a high amplitude level it .will. maintain
relatively-large changes in the potential of the
re?ecting electrodes.
One general object of: this invention is- to im
‘itself although over the same ranges mcillations
will'not build up ‘from an. initial non-oscillating
condition. This non-uniform operating. charac
teristic is, of course, undesirabie. For example,
if during the operation-of.thedevice, the volt~, 45
age supply for the device is interrupted, oscilla-v
tions may not build up even after the supply is
again connected and the voltages are restored
to the values extant-before‘ the interrupticnof
the Voltage supply.
' Desiderata for. reflectiontype osciilation ‘gener-_
. ators 'are a“ hightransconductance‘ and‘ a‘ high
ration of “transconductance to'the capacitance‘
prove the operating characteristics of electronic
oscillation generators of the re?ection type.
More speci?cally, objects of this invention are to
substantially eliminate hysteresis e?ects in elec
tronic oscillation generators‘ of the re?ection
type, to increase the operating frequency range
50 thereof and to increase the electronic tuning
, range thereof, to obtain a high transconductance
and a high ratio of transconductance to ‘capaci
' tance for such generators, and to reduce the
of varia ion in re?ecting electrode
between the gap de?ning electrodes. Boththe 55 Imagnitude
optimum operation with
transconductance and‘ the ratio‘noted a?ect the
changes in the operating frequency of such
In one illustrative embodiment of this inven
tion, an electron discharge device comprises a
pair of grids de?ning a velocity variation gap,
an electron gun opposite one of the grids and
a. re?ecting electrode opposite the other of the
g In accordance with one feature of this inven
tion, the electron gun is constructed and ar
ranged to produce a hollow cylindrical beam
which is projected across the gap substantially
parallel to the axis thereof. More speci?cally,
in accordance with one feature of this invention,
the electron gun comprises a cathode having a
I8, of greater diameter than the grid I8 and in
juxtaposition thereto to define a gap 22.
The two grids I8 and 2| together with the sup
ports therefor and the portions of the enclosing
vessel between the annular members It and 20
bound a resonant cavity 23 into which a coupling
loop or pick-up 24 projects, the loop being con
nected to one of the conductors I4 and to a metal
lic sleeve 48 coaxial with this conductor.
10 resonant cavity may be tuned in various ways
to change the operating frequency of the device.
For example, it may be tuned by flexing the wall
member 60, as disclosed in the application Serial
No. 439,375, ?led April 17, 1942, of Robert L.‘
laterally continuous electron emissive surface, for
Mounted within the cylindrical portion E1 is a
example circular and provided with a central for
cylindrical beam forming electrode 25 having a
wardly projecting portion, facing the grid oppo
?aring end 26 and supported upon a platform
site the gun and a beam forming electrode adja
21 which is in turn supported from the header
cent the cathode which in cooperation with the 20 I2 by a plurality of insulating strips 28, only one
grid structure concentrates the electrons emanat
of which is shown. The‘ beam forming electrode
ing from the emissive surface into a hollow elec
25 encompasses a cathode which comprises a
tron beam wherein, adjacent the grid, substanu
heater ?lament 2s and a cylindrical cathode
tially parallel electron flow obtains. In a par
member 36 only the end surface SI of which
ticularly advantageous construction, the for 25. toward the grid I8 is coated with electron emis
wardly projecting portion is in the form of a cusp.
sive material. This emissive surface which, in
However, it may be of other forms, for example
the construction shown, is circular, is provided
conoidal or cylindrical.
with a central forwardly projecting portion which
In accordance with another feature of this
may be in the form of a cusp, as shown, or of
invention, the re?ecting electrode and the grid 30' other form, for example conoidal or cylindrical.
to which it is opposite have opposed surfaces of
Because of the form of the emissive surface 3!,
predetermined con?gurations such that the elec
32, the ?aring end portion 26 of the beam form
tron stream projected across the gap is formed
ing electrode 25 and the curved end wall I9 of
into a hollow beam of greater diameter which
the grid structure, the electrons emanating from
is reflected across the gap and is substantially 3.5 the surface 3i, 32 are concentrated into a hollow
focussed upon an annular imperforate region of
cylindrical beam coaxial with the electrode sys
the grid structure opposite the gun, beyond the
tem and in which in the region adjacent the grid
boundaries of the grid in this structure.
58 the electron motion is substantially parallel.
The invention and the above-noted and other
Inasmuch as the emissive surface 3i, 32 is lat
features thereof will be understood more clearly
erally continuous, it will be appreciated that all
and fully from the following detailed description ’ elemental areas thereof contribute to the space
with reference to the accompanying drawing in
current so that a high current beam with a rela
tively small diameter cathode is obtained and,
Fig. 1 is an elevational view mainly in section
further, substantially uniform space charge
of an electron discharge device illustrative of one
effects in front of the cathode are obtained. It
embodiment of this invention;
" Will be noted, further, that as illustrated in Fig. 2,
Fig. 2 is a diagram showing the con?guration
the electrons are concentrated into a hollow beam
of the electrodes in the device illustrated in Fig. l
of an outer diameter slightly less than the diam
and illustrating the equipotential lines in the
eter of the grid I8 and which traverses a region
region between the re?ecting electrode and the 50. of the grid 18 near the periphery thereof. The
grid to which it is opposite and also the. electron
current density in the beam at this region is rela
trajectories in the device; and
tively low so that local heating of the grid is
Fig. 3 is a graph showing typical output power
small. Such heating as occurs is in a region of
reflecting electrode potential relations in devices
the grid adjacent the support member I7 and,
wherein hysteresis effects occur.
hence, relatively rapid heat ?ow from this grid
' occurs.
Referring now to the drawing, the electron dis
Consequently, excessive heating of the
grid I 8 is prevented and a relatively small grid
charge device shown in Fig. 1 comprises a cylin
in relation to the total beam current may be
drical metallic enclosing vessel It having an end
employed. The capacitance between the grids
portion ii of reduced diameter, and closed by a
metallic header I2 provided with eyelets I3 to 60 I8 and 2| will be correspondingly small.
Mounted opposite the grid 2| as by a leading
which leading-in conductors I 4 are sealed her
conductor 33 sealed to an eyelet 34 on the end
metically by vitreous beads I5. Mounted within
portion II by a vitreous bead 35, is a re?ecting
the vessel I0 is a metallic grid structure including ,
electrode, which is coaxial with the cathode and
a laterally extending, annular, metallic member
structures. The re?ecting electrode includes
I6 secured to the inner wall of the vessel, a cylin
an outer cylindrical portion 36, an intermediate
drical portion H which may be integral with the
dished or inclined portion 31, the convex surface
member I6, and a mesh grid l8 extending across
of which faces the grid 2|, and a central cylindri
one end of the cylindrical portion I1, the portion
cal portion 38 projecting toward the grid 2|.
I’! being imperforate and having a rounded end 70
During operation of the device, the beam form
wall I9.
ing electrode 25 is maintained at cathode poten
A second metallic grid structure is mounted
tial or at a small negative potential with respect
within the vessel and comprises an annular sup
to the cathode, the grids I8 and 2| are biased at
port 28 af?xed to the wall of the vessel I0 and
a positive potential with respect to the cathode
a vcentral mesh grid 2| convex toward the grid
and thare?ecting. electrode is maintained. ate
negative potential with 3respect; to ,the cathode,__
flectingielectrode, and to subsequent bunching; of
theielectrons-in the space between the.__grid_ 2|;
and the reflecting, electrode.- The other is that
The " electrons emanating fromq the ,1 cathode _; are"
concentrateddntoearhollowrrdrlmdrical been? as
not'édih“ ‘ étdfbrél; and projected.acrossthe- can I 2.2.’
wherein they’. are...’ velocity, varied. ‘ The . velocity.v
due‘to' the, density and velocity varied stream,
which crosses thegap 22 in thereverse direction.
'variedstrca'm isgconvertedhin? the space between
If thegbunched and velocity variedistream of
the, gridv 2| .andl'the. reflecting.,electrode, into va
electrons ., passes, through the grid l8v into the
region between this grid and the cathode, be?
d¢n§ity<variedstream-Whichis-pmiectéd through’,
thejgrid 2] ,.in._ the , reversoldirectiflnt, The reverse,
electron .str'eamdelivers. energy. to. thefield with
' the“ forward1
direction, , that 1 is, , toward; the-re
cause ofacombination ofspace charge in?uences,
in the resonant. cavity23, wherebyzoscillation itsv
re?ection, and . grouping and interception by the‘
sustained- .
inthe stream being projected toward the grid l8.‘
Thisdensityvariation:v corresponds to a second
cathodefthis stream produces acvdensity variation
'Thenopposred ‘surfaces: of,‘ the. , grid 2 l l . and the i
re?ecting. electrode. are, of. suchv con?guration
that the, eljectronsprojectedinto the region be
tween, the grid" 2] and the, reflecting. electrode,
the'electrons in the. space between the grid 2|
and the reflecting electrode. For small ampli
tudes of oscillation, thertwoconduction factors,
havemtheir, direction of motion reversed and are.
projectednthrough the grid 2|,inv the, form of a
hollow, cylindrical beam of a diameter greater
than thatofthe forwardly projected beam, which
are in opposition so that the tendency for osoilla-_
tion is weak. However, as the amplitude of oscil
is substantially focussed upon thewall IS. The.
requisite: con?guration _ of these surfaces ,in any
lation. is‘ increased, the second opposing. con
ductance factor decreases and the device tends
particular device can be determined in known
ways, for example, by determination, in an elec-'
trolytio tank, of the equipotential lines in the
tof- oscillate increasingly strongly until an
equilibrium... is reachedat a high amplitude of
region _,be._tween these surfaces and calculation
of ‘the electron trajectories. ,In the particular
construction illustrated in Fig. 2, the lines E
represent 'the'equipotentials, the numeral on each
of;these vlines indicating its potential as a frac
conductance factor, in addition to that due,to
the, initial velocity, variation and the grouping of '
In, devices‘ constructedin accordance with this
invention, the reverse electrons are intercepted
tionof-the total‘direct'current potential differ
ence between thegrid 2] and there?ecting elec-,
trode. "' Thein'ner diameter of the electron beam
by the imperforate wall 19 end, ‘therefore, sub
stantially noneof thereverserelectrons enters
the-region between the. cathode and the grid I8.
Hence,v the second opposing conductan‘ce'factor
notedabove is eliminated, the hysteresis effect is.
in; this construction is approximately 100 mils
likewise eliminated and, av uniform operating,
and the outer diameter thereof is approximately
characteristicis obtained.
. 200 mils; The ‘other dimensions in ,Fige2fare to
It: will benotedgthat the, opposed surfaces of
‘the grid_2l_‘ and they intermediate portion 31 of}
It may. bev notedfurtherthat prevention-of flow
of . the reversed. electrons into the cathode region
eliminates the possibility- of - bombardment of the -
cathodegby such electrons ~. and thus prevents
the/re?ecting electrode are convex withrespect 40 overheating. or variation of the cathode heating
to thecathode andthat the surfacesof the re
?eeting electrode toward the, grid 2'. ,bOund an
annular recess; toward which the electronv ‘beam.
iswinitially projected, Because of‘ the con?gura
tion of-thesurfaces involved, the electrons,,typ1
cal trajectories of which are illustrated by the
linesrL in'Fig, 2,jprojected_linto the region be-v
tween-the grid 21 and re?ecting electrode are, as
noted heretofore, “reversed in direction, concen
trated intoahollow cylindricalbeam of greater
diameter than the grid 18, and projected through
the-"gridZI to the annular wall portionl9,‘ the
reverse beam being substantially focussed upon.
the lwalliportion» l9.
' ‘
Wherebvtheoperating life.v of , the cathode is in
‘creased._,and uniformity of cathode emission is,
assured. :
_ As has been pointed out heretofore,theoper
» ating; frequencyrof, .thegdevice, can beer-altered by
varying the resonant- cavity.- When the frequency:
is thus variedthegtransit time of the electrons in
the regionbetweenvthe- grid 2| and the re?ecting
electrode, both, the, forward and . reverse vmove
mentyo?the electrons beingconsidered, must be
varied .a1s0to obtain optimum operation, This
involvesqvarying the potential of the re?ecting
electrode inasmuch ,as/it is this potential which
is_,.1arg,ely.determinative of the transit time, It
As has been noted heretofore, in_ known oscillaT ; . will»v hie-‘noted; from Fig. 2 that .the equipotential
tion generators'of the-re?ection-type a hysteresis
lines of the ?eld betweenthe grid 2| and the
effect occurs and a non-uniform operatingwchar
reflecting, electrodes» are not uniformly r spaced,;
' acteristic'results.v Typical plots of power?output
thisibeinggdueito the shielding effect of the cen
tral portion Stand the outer cylindrical portion
versus potential of ‘the re?ecting electrodes for
such devices'are shown in Fig. 3 wherein plot a, (if) 36 of the re?ecting electrode. As shown in Fig.
2, theaequipotentials nearest the’ ‘re?ecting elec
indicatesvthe characteristic as the reflecting elec
trode potential is made progressivelycmore nega- ,
trodetarespacedz-a greater distance'apart than
tiveywith respectto the cathode, and plot b in
dicates. the-characteristic as the reflecting elece
those ,nearest the.:grid,.2l.. Hence, a ‘relatively
large-,variation of path length and transittime-i
trodegpotential is made progressively less negative
with respect to the cathoderthe range of potential
for ’ the, electrons in, the region ‘between the grid
being the same for both plots. Hysteresis, it‘will'
re?ectingyelectrode potential results.- 'Conse
one? when the operating frequency of ~_ the de-._.
viceasa teredby varyingthe resonant ,cavity only .
be noted, may occur‘at either‘ofvthe regions
or :cL-y' .or- at both.
Although this~invention is not to- be-limited
thereby, the following theory ‘is believedto be ex-."
planatoryofthe hysteresiseffect. There are two
sources of conductance vacross theugapw?; one.
OI swhighia?hat' due?ethe .gvelocity.variatioapi .
»- and re?ecting electrode,- with'variation; .in the;
arelativelypsmall change in there?ecti-ng eleci,
' tredepgétéhtial isnecessary'to maintain optimum
operation so. thatthe operating frequency may.
bevaried vover azwide range and optimum Zopera-V .
tionmadntainedby. smallchangesin theqre?octg. .
a? SignLegit’.ieereiestedaemss reggae "he. .75 mesa-creamer.. f
a ‘re?ecting-electrode having a convex surface‘
' Furthermore, because‘ of the relatively wide
spacing of the equipotentials as compared with
the spacing in a uniform ?eld of the same extent
and potential, the electron transit time in ‘the re—
gion between the grid 2! and the re?ecting elec
facing said one grid,
4. An electron discharge device comprising a_
high frequency circuit element including‘, a pair
of grids mounted in juxtaposition anddefining a
trode is affected to a'relatively large extent by
gap, means for projecting a hollow substantially
parallel ray electron beam across said gap in
the velocity variation the electrons receive in
crossing the gap 22 ‘in the ‘forward direction, that
cluding a cathode opposite one of said grids, and,
is, toward the reflecting electrode. This, in effect,
enhances the transconductance. As has been
a re?ecting electrode‘ opposite the other of said
grids, said re?ecting electrode having therein an,
noted heretofore, the transconductance is en-'
hanced also due to the fact that the grids l8 and
annular recess facing said other grid.
5. An electron discharge device comprising-a:
21 assure subjection of the electrons to strong
high frequency circuit element including a pair
?elds in both directions of their traversal of the
of grids mounted in juxtaposition and de?ning a
gap 22. Hence, and because of the relatively 15 gap, means including a cathode opposite one of
small size of the grids, with consequent small in
I said grids for projecting an electron stream across
tergrid capacitance, it will be appreciated that in
said gap, the surface of the other of said grids,
devices constructed in accordance with this in
facing away from said cathode being dished, and
vention a high ratio of transconductance to ca
a re?ecting electrode opposite the dished surface
pacitance is obtained whereby a wide range of 20 of said other grid, said re?ecting electrode in
electronic tuning is realized,
cluding an annular intermediate portion and
Although a speci?c embodiment of this inven- '
central and outer cylindrical portions projecting
tion has been shown and described, it will be
from said intermediate portion toward said other
understood, of course, that it is but illustrative
and that various modi?cations may be made 25
6. An electron discharge device comprising a
therein without departing from the scope and
highv frequency circuit element constituted - in
spirit of this invention as de?ned in the append
part by a pair of grids mounted in juxtaposition
and de?ning a gap, means including a cathode
‘ What is claimed is:
opposite one of said grids for projecting a hollow
>1.'An electronic oscillation generator compris
cylindrical beam across said gap substantially
ing a high frequency circuit element constituted
in part by a pair of reticulated members mounted
in juxtaposition and de?ning a gap, means oppo
site one of said members for projecting across
said gap anelectron beam in which, adjacent said ‘
one member, the motion of the electrons consti
tuting said beam is substantially parallel, and
means for reversing said beam after it has crossed
said gap "and projecting it across the gap in the
reverse direction in the form of a stream directed
upon an area laterally beyond the periphery of
said one member, said last-mentioned means in
cave surface.
cluding a reflecting electrode opposite the other
of said members.
“2. 'An electronic oscillation generator compris- _
ing a high frequency circuit element including a
pair of grids mounted in juxtaposition and de?n
ing a gap, means for projecting a substantially
cylindrical, hollow electron beam across said gap
in one direction, said means comprising a cathode '
opposite one of said grids, a beam forming elec
trode adjacent said cathode and an electrode
member having an imperforate portion encom
passing and extending outwardly from the pe
riphery of said one grid, and means for re?ecting
said beam after it has crossed said gap, in the
form of a stream substantially focussed upon said
' imperforateportion, said re?ecting means includ
ing a re?ecting electrode opposite the other-of
3. An electronic oscillation generator compris
ing a high frequency circuit element constituted,
in part by a pair of circular grids mounted‘ in jux
tapos'ition and de?ning a gap, one of said grids
being dished away from and of greater diameter
than the other of said grids, an imperforate mem
ber extending outwardly from the periphery of
said other grid, means'for projecting an electron
stream across saidgapthroughregions of said
other grid removed from the central portion
thereof, said means including a cathode opposite
said other grid, and means for reversing said.
parallel to the axis thereof, the other of ‘said
grids being concavo-convex and having its con
vex surface toward said cathode, and a' re?ecting
electrode opposite the concave surface of said
other grid, said re?ecting electrode including an
annular intermediate portion having a convex
surface facing said concave surface and including
also inner and outer cylindrical portions project
ing from said annular portion toward said con
'7. An electronic oscillation generator of the re
?ection type comprising a resonator bounded in
part byv a pair of juxtaposed grids de?ning a gap,
means for projecting a hollow cylindrical electron
beam across said ‘gap in one direction, said means
including a cathode opposite one of said-grids
and beam forming electrode means in cooperative
relation with said cathode, and means for re
?ecting saidbeam after it has traversed said gap
in said one direction and projecting it into said
gap in the opposite direction in the form ‘of a
hollow stream, said second means including a re-v
?ecting electrode opposite the other of said grids,
the facing surfaces of said electrode and said
other grid having portions dished and convex
with respect to said cathode.
8. -An electron discharge device comprising
means for producing a hollow cylindrical elec
tron beam comprising a cathode having a sur-'
GU face including a central forwardly projecting por
tion and a laterally extending portion surround
ing said projecting portion, both "of the project
ing and laterally extending portions being highly
electron emissive, a cylindrical beam_ forming
electrode encompassing said cathode and having;
a portion extending forwardly from adjacent the:
periphery of said surface, and an electrode mem
bér adjacent said beam forming electrode and
having an annular portion overl?ngjsaidj-for
wardly extending portion.
9. An electron discharge device comprising
‘means for producing a hollow cylindrical electron
beam after ithas crossed said gap and projecting
beam comprising a cathode having a circular
it‘in‘the reverse direction to impinge .upon ‘said
. , electron emissive surface provided with a central
imperforate member, said lastnreansincluding .75. cusp; a beam "formirigelectrode encompassing"
9 ,
said cathode and having a cylindrical outwardly
?aringportion extending from adjacent the pe¢
riphery of said emissive surface, and a cylindrical
electrode member encompassing said beam form
ing electrode and having an annular'concave sur
face adjacent said ?aring portion.
10. An electronic oscillation generator of the
reflection type comprising a high frequency cir
cuit element constituted in part by a pair of elec
trode members having juxtaposed apertured por
11. An electronic oscillation generator of the
re?ection type comprising a high frequency cir
cuit element constituted in part by‘ a pair of
juxtaposed apertured members de?ning a gap, an
an electron gun opposite one of said members for
projecting a hollow cylindrical electron beam in
one direction across said gap, electrode means op
posite‘the other of said members and cooperating‘
therewith for forming said beam after its pro
10 jection across said gap into a hollow reversed
electron stream of greater diameter than said
tions de?ning a gap, means opposite one of said
beam and projecting said hollow stream across
portions for projecting an electron stream across
said gap in the reverse direction, and means for
said gap, and means opposite the other of said
intercepting said hollow stream after it has been
portions for producing in the region adjacent said
projected into said gap, said electrode means in
other portion a reflecting ?eld non-uniform in
cluding an annular reflecting surface opposite
potential distribution in the direction of projec
tion of said stream thereinto, said re?ecting ?eld ' said other member and shielding means extend
ing from the inner and outer edges of said sur
producing means including a re?ecting electrode
face toward said gap.
surface in alignment with said other portion and
shielding means electrically integral with said ~
electrode surface and extending from the pe
riphery thereof toward said other portion.
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