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Патент USA US3061730

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Oct. 30, 1962
3,061,720.
H. EWALD
SPECTROGRAPH
Filed Feb. 29, 1960
5 Sheets-Sheet 1_
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INVENTOR
-HE/NZ E WALD
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ATTORNEYS
Oct. 30, 1962
H. EWALD‘
SPECTROGRAPH
Filed Feb. 29, 1960
3,061,720
3 Sheets-Sheet 2
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INVENTOR
HE/NZ EWALD
“W W
ATTORNEYS
Oct. 30, ‘1962
H. EWALD
3,061,720
SPECTROGRAPH
Filed Feb. 29, 1960
3 Sheets-Sheet 3
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INVENTOR
Fig. 7
HE/NZ EWALD
BY
ATTORNEY$
United States Patent O??ce
3,051,720
Patented Oct. 30, 1962
1
2
3,061,720
FIGURES 1 and 2 are schematic views of toroidal
condensers for use in a spectrograph constructed accord
SPECTROGRAPH
Heinz Ewald, 36 Clemenssu-asse, Munich, Germany
Filed Feb. 29, 1960, Ser. No. 11,604
5 Claims. (Cl. 250--41.9)
ing to my invention;
FIGURE 3 is a sectional view of a mass spectrograph
according to my invention, with direction and velocity
focusing which does not have intermediate radial images
in and between the ?elds and for which the aberration
The present invention relates to spectrographs. More
in particular, the present invention relates to mass spec
coe?icients are equal to zero;
FIGURE 4 is a sectional view of a mass spectrograph
trographs and energy spectrographs having condensers
which are corrected for image errors.
The term “spectrograph” as used in the present speci
?cation and claims is intended to comprehend spec
10 according to my invention, with a homogeneous ?eld
and a toroidal condenser having plane entrance and exit
front surfaces and for which the aberration coe?icient
A33 is equal to Zero;
FIGURE 5 is a schematic view of a spherical condenser
trometers.
It is known that spectrographs comprise condensers
which are mostly of the toroidal-shaped type which is 15 for use in a spectrograph constructed according to my
to be understood as comprising the spherical-type con
densers, but which can also be cylinder-shaped.
These condensers are electron- and ion-optical focusing
invention;
possible to provide condensers with a satisfactory correc
tion of image errors. Although it has become known to
provide condensers in spectrographs corrected to some
extent for image errors with respect to the image error
coefficient (hereinbelow designated as A33) of the half
effective axial angle of divergence of the rays of par
The electrodes of a toroidal condenser as shown in
FIGURES 1 and 2 for example, have a common rota
tional axis, e.g. in FIGURE 1 the z-axis of an r, 95,
FIGURE 6 illustrates a single condenser plate used in
the spectrograph shown in FIGURE 4, and
systems with the help of which rays of charged particles,
FIGURES 7, 8 and 9 illustrate sectional views of the
such as electrons, elementary particles, or ions may be 20 condenser plate of FIGURE 6 and respectively taken at
separated into an energy spectrum. Spherical and cylin
lines 7, 8, and 9 therein.
drical condensers are special cases of the more common
The following considerations, with reference to FIG
toroidal condensers.
'
URES 1 and 2, will more fully explain the novel feature
The known spectrographs are unsatisfactory because of
of my invention and the considerable advance over the
considerable image errors. Heretofo-re it has been im
art.
z-system of cylinder coordinates, and a common plane
of symmetry, as in FIGURE 1 the plane z=0. Their
radial and axial main radii of curvature in the points
ticles passing through the spectrograph to the place of
image, it has hitherto not been possible to provide special
kinds of spectrographs with condensers wherein all image
of the circle of intersection with the plane of symmetry
=0 may be r,,, rb and R,,, Rb, respectively. The radial
error coe?icients are corrected so as to become zero.
plane of symmetry and vertical to it in planes going
through the z-axis, respectively. The centers of these
curvatures coincide with the origin of the‘coordinate
and axial main circles of curvature are ‘falling in the
Furthermore, the partial image correction of just one
image error coe?icient according to the known art re
quires a complicated and particular con?guration of the
system or they are located in the plane z=0 on the circles
front surfaces on the entrance ‘or the exit side or on
both sides of the condensers. The front surfaces must 40
have curvatures calculated in a determined manner.
It is therefore an object of the present invention to
provide a spectrograph with condensers which are more
perfectly corrected for image errors than any of the
r=r,,—-Ra and r=rb--Rb, respectively.
The section of a circle r=ae(ra<ae<rb), z=0 located
in the plane of symmetry between the electrodes together
with its straight prolongations outside of the sector ?eld
may be designated as mean orbit.
Orbits of charged
particles progressing in the neighborhood of this mean
known spectrographs.
orbit can be calculated with formulas generally known
in the art.
The potential surface between the two electrodes ex
It is another object of the present invention to provide
a spectrograph with condensers which are more perfectly
corrected for image errors than any of the known spec
trographs, which correction obtains even where double
tending through the mean orbit has the radial radius
focusing mass spectrographs having condensers with plane
radius of curvature in these points is indicated by Re
(see FIGURE 2). A neighboring surface of equipoten
tial may have the axial radius of curvature R in the points
of its circle of intersection with the symmetry plane 1:0.
For points of the symmetry plane the derivative
of curvature ae in the points of the mean orbit; its axial
entrance and exit surfaces are used.
It is still another object of the present invention to
provide a spectrograph with condenser-s which are more
perfectly corrected for image errors than any of the
known spectrographs, and which do not have any inter
mediate radial images in and ‘between the ?elds besides
the ?nal images.
Other objects and advantages of the present invention
will become apparent as the description and explanation
thereof proceeds.
60
indicates the amount of the change of the axial radius
of curvature R of the surfaces of equipotential when
proceeding from a point of the mean orbit in radial
r-direction to a neighboring point Re and R’e can be
calculated as functions of ra, ae, rb, Ra, Rb, and vice
versa RE and Rh can be calculated as functions of r,,, ae,
The objects are achieved by the invention which is
based on my discovery that in the known spectrographs
condensers, and particularly double curved toroidal con
densers are characterized by the fact that the value R'e,
rb, Re, R'e
to be presently de?ned, is equal to one (R',,=1). Accord 65
This formula is given by Formulas 4, 2 and 3 in my
ing to my invention the de?ciencies of the known art
paper in “Zeitschrift fiir Naturforschung” (ZfN), vol.
are overcome by providing condensers characterized by
14a, page 198, referred to below
the fact that the value R’e is unequal to one, and may
also become negative.
The invention is illustrated in the accompanying draw
ings, wherein:
3,061,720
4
wherein r may be either ra or rb for the calculation of
either Ra or Rb.
It will be understood from the ‘formulas given in the
various papers referred to below, which formulas have
been made part of this speci?cation, that this R’e is one
of the variables to be selected in order to verify the
equations for the error coefficients A11, A12, A22 and A33.
As stated above this R’e is to be unequal to unity which
is a condition found by me to render at least one of these
coe?icients substantially zero in the types of apparatus
discussed ‘below. This is independent of the particular
meaning of R’,,. For explanatory reasons, however, it
is believed to be readily apparent, that R'e=l has also
the following geometrical meaning: As it can be seen
from FIG. 1, the radial radii 11a and rb have a common
in the ?elds and also of the values of R’e of the con
densers.
According to the present invention, the condensers are
so constructed, that the values R’e are unequal to 1 and
may also be negative. It is thus possible to construct
mass spectrographs corrected for image errors with
which do not have any intermediate radial images in and
between the ?elds besides the ?nal images. It is further
more possible to construct so-called double focusing mass
spectrographs which are corrected for the radial angular
aberration of axial origin (A33=O) and have plane en
:- trance and exit surfaces of the condensers, while the
coe?‘icients A11, A12, A22 may be unequal to zero. And
it is also possible to construct energy spectrographs which
are corrected for angular aberration with A11=A33=0.
in this'case the R of an eqnipotential surface would vary
It is, of course, also possible to bring the coefficient
as does r taken in the direction of r; thus dR/dr=\1
would necessarily follow therefrom. Accordingly, the 20 A33 to zero in a known manner, speci?cally by providing
origin.
If the axial radii R9, and Rh had also common
origin, then dR/dr would necessarily be ‘unity, because
the front surfaces on the entrance or the exit side or
discovery is that dR/dr%l as a condition to render the
error coe?icients zero, is equivalent to the condition that
on both sides of the condensers with curvatures which
are symmetrical to the plane z=O the needed radii of
the origin of Ra be unequal to the origin of Rb in case
ra and rb have a common origin.
curvature q of which can be calculated in a manner known
.
in the art.
The first order focusing properties (radial and axial
focus lengths and image distances of the usually astig
matic focusing) of an energy spectrograph consisting of
On the basis of the foregoing explanation the invention
will next be described with reference to two examples of
spectrographs with condensers according to the invention
illustrated in FIGURES 3 and 4 of the accompanying
one or several toroidal condensers, as well as such prop
erties of combinations of such condensers with magnetic
?elds to mass spectrographs are mainly dependent of the 30 drawings.
The ?rst example illustrated in FIGURE 3 relates to
values of a6 and Re and of the mean angle or angles of
a mass spectrograph with direction and velocity focusing
deflection ¢e in the condenser or in the condensers, re
which does not have intermediate radial images in and
spectively. They are not dependent of the value or the
between the ?elds and for which the aberration coeffi
values, respectively, of R'e; but the second order focusing
cients A11, A12, A22, A33 are equal to zero. FIGS. 6 to
35
properties, especially the image errors at the points of
9 illustrate a toroidal condenser plate used for this ex
the images are also dependent of the value or the values,
ample de?ning a straight entrance but a curved (curvature
respectively, of R’,,.
q)-exit.
When imaging an object point located on the mean
A schematic section through the apparatus within the
orbit on the object side, e.-g. a point of the entrance slit 40 symmetry plane 1:0 is shown in FIGURE 3. In this
of the spectrograph, into a radial focusing line located
?gure the values ¢m=90° and ae/Re=1.36 are given
on the mean orbit on the image side (or, in the case of
arbitrarily and vertical entrance of the mean orbit into
the so-called stigmatic ‘focusing into an image point lo
cated on the mean orbit) by using particle rays progressing
in the neighborhood of the mean orbit, the radial image
the magnetic ?eld (e'=[)) and the attainment of stigmatic
focusing (equal radial and axial image distances of the
?eld combination) are assumed. The distance l’e of the
errors are determined by the general formula
entrance slit from the entrance limit of the electrical
?eld shall be equal to the focal distance
In this formula on and a, are the half effective radial and
axial angles of divergence of the rays passing through
the spectrograph to the place of the image; 17 represents
H.
the half maximum relative difference of the kinetic en
of the electrical ?eld.
From the knowledge of gbm,
ergies of the rays passing through the spectrograph to
the place of the image.
a, dz, 1; are small compared to
1. There is another way of writing the image coe?i
cients, which is given in ZfN, vol. 12a, page 538, par
as
K
ticularly on page 539, lFormula 8, thereof
l'.e‘=ge and from the Well-known ?rst order double focus
wherein a’, and a'z are the same as a and 0:2 given above
but wherein B is half the maximum relative difference of
the velocities ‘of rays passing through the spectrograph
at the place of the image (see L.c., page 538 supra). It
is apparent, that ,8 and 17 are interrelated by constant
factors. It is further apparent, the 111:0 then, of course,
is also A11=0 etc. and vice versa. The coe?icients A11
to A33 are ‘functions of the geometrical data of the ?elds
and their combinations, i.e. of the radii of curvature of
the mean orbits, of the surfaces of the electrodes, of
the ?eld boundaries, of the directions of the ?eld bound
(35
ing condition follow the values ¢e=29.5°, ge=2.86ae.
By making zero simultaneously the expressions for A11,
A12, A22 given in “Zeitschrift fiir Naturforschung” 12a,
539 (1957) (H. Liebl and H. Ewald, The Image Errors
of Double Focusing Mass Spectrographs, Equations 9,
10, 11), the values ae=2.S6am, d=5.37am, k’=O.745am,
R’e=-2.43 "are obtained.
The three equations ‘for A11, A12 and A22 are:
O
aries, the relative arrangements and distances of the ?elds
and the entrance slits, of the mean angles of de?ection 75
3,061,720
aside of the known, i.e. arbitrarily selected ¢m and
c=ae/Re, the equations include the ‘following abbrevia
tions:
calculated
value of R’e will be explained in the follow
ing
example.
'w'
r‘ l
neghblbly
smal
L2=I% sin H¢e+-2_2%(c0s (¢e.H) _1)
H f
__l’e
“
l
Z’e
Mass spectrographs with A11=A12=A22=0 and
30 l'e=ge in which intermediate radial images in or between
.
the ?elds are allowed would require much larger angles of
I€1_Zl; 00:’ H¢e+H <1_T) Sm H4)“
de?ection in one or in both of the ?elds.
2
K2=E(1——cos H(be)
A further example illustrated in FIGURE 4 relates
to a mass spectrograph with direction and velocity focus~
a
A:
36
_3_£ 1
35 ing having a homogeneous magnetic ?eld and a toroidal
1e
condenser having plane entrance and exit front surfaces,
2( +R )
and for which A33=O.
A schematic section through this apparatus located
within the symmetry plane is given in FIGURE 4. In
40 this case the values
6 =91
e=29.7"
m:875"
Re
ae=12 cm. Re=9.6 cm. am=15 cm.
These are given by the paper referred to in the last
are given arbitrarily and vertical entrance of the mean
mentioned Paper (Ewald and Liebl Z. Naturforsch, vol. 45 orblt into the magnetlc ?eld 15* assumed (6'=0)- More‘
12a, page 128, et seq., 1957).
Over,
Furthermore, it appears that these equations for An,
1, :0 :
A12 and A22 include: the angle 6' which is the angle
between the straight mean orbit of the particles entering
8
°°
ac
ct Wat
Vm
g
Re 6
is assumed As follows from “Zeitschri? fur Natup
the magnetic ?eldaand the normal to theentrance bound- 50 forschung” 12a’ 539 (1957) (H. Li?bl and H_ Ewald, The
my of the magmfuc ?eld m the entranfe pomt' (See Page
Image Errors of Double Focusing Mass Spectrographs),
538 1-°-)’ 31‘? Iatlos ‘Te/“m, d/“w, (‘m/k , and R e‘
The Waning of d’ as’ am and k_ can be taken from FIG'
and 12a, 32 (1957) (H. Ewald and H. Liebl, The Image
Errors of the Toroidal Condenser), there is for each ?eld
3' d 1_S the d1S_tance of the, exlt ,Of the condenser,and 5 combination of this kind a linear dependence between R’e
magnet‘? de?ectlqn System’ m_ which ‘the Fnean 0T1?“ of 5 and fag, which for the special values given above has the
the particles therein have a radius am. k’ 18 the radius of
the curved entrance boundary of the magnetic de?ection
form
0 2841
system.
If one selects a’ arbitrarily, the three equations for
R'e=_ '
2
'
amaz I
_
a
A11’ A12 and A33 are linear in R'e_ If one also Selects 60 In my example R e=—0.229l 1s chosen for WhlCh value
one of the four yet unknowns arbitrarily, the other three
7633 and also A33 are equal to Zero
can be calculated in simply solving these three equations
In the ?rst one of these Papers referred to abmfe
now having three unknowns. The above mentioned ?gures for as, a’, k’, and R’e have thus been obtained. By
(_ZfN’ VOL 12a, Page 539 (1957)’ the formula ‘for A33 15
gwen by
making zero the expression of A33 given in “Zeitschrift 65
?ir Naturforschung” 12a, p. 544, Equation 17 (1957)
A33=i(L33_|_1/2L2p2)
.
,
.
.
.
.
(H. Liebl and H. Ewald, Stigmatically Focusing Mass
usmg me abbrevlatlons glven m the other paper‘
Spectrographs With Double Focusing Practically of SecL __ E B (30-2) _& _l
B
. H
ond Order), the value q=—0.642ae was obtained, q be- 70 33- ae2 2H(5c——2) H
H+H“*(5c_2> sin ¢,,
ing the radius of a cylindrical curvature of the exit surB I,
face of the condenser the axis of which is located within
the symmetry plane and is vertical to the direction of
the mean orbit between the two ?elds.
The computation of the needed values of the axial
radii of curvature RE and Rh of the electrodes ‘from the 75
+5___2 1- (cos 11458-0052 ?qbe)
c
a“
v-
,2
sin 2‘I/FQSa
2(5c——2) at,2
B=c+c2(1+R'e)
c
3,081,720
8
curves of intersection of the electrode surfaces with
V meridian planes extending through the rotational z-axis
are symmetrical to the plane z=0.
Mass and energy spectrometers and spectrographs cor
rected for image errors according to my invention enable
the realization of higher intensities and accuracies in
measuring ion abundances, masses and energies. They
will be used with great advantage for physical, chemical,
medical, geological, and other problems.
It will be understood that this invention is susceptible
1O
This equation for A33 can be made zero, for example,
with the set of values given in column 6, lines 42 and 43.
to modi?cation in order to adapt it to different usages
This equation is linear in R’e as it can be seen from
hend such modifications within this invention as may fall
and conditions, and, accordingly, it is desired to compre
within the scope of the appended claims.
the appearance of R’e as factor in B, appearing as factor
in L33.
15
The manner of determining the needed axial radii of
curvature of the condenser electrodes, with R’e and with
the radial radii of curvature ra and rb of the electrodes
What I claim is:
1. A mass spectrograph having direction and velocity
focusing means, comprising; a toroidal condenser defining
a mean angle of deflection ¢e, a magnetic de?ection sys
tem disposed in the path of particles leaving said con
schung" 11a, 156 (1956) (R. Albrecht, The Potential in 20 denser, said condenser and said de?ection system causing
an image error de?ned by the sum of
Doubly Curved Condensers), and'is described more ex
being given, is described in “Zeitschrift fiir Naturfor
plicitly in “Zeitschrift fiir Naturforschung” 14a, 198
(1959) (H. Ewald, Concerning the Image Error Correc
tion of Doubly Focusing Mass Spectrographs). This
formula has been given above in column 2. From r,,: 11.6 25 with a’, and 0/2 being radial and axial angles, respec
tively, of a particle path with respect to said mean orbit
cm. and rb=l2.4 cm. and the values given above follows
and said 19 being half the maximum relative difference of
the velocities of rays passing through said spectrograph
at the place of the image thereof, wherein A11, A12, and
trograph, A11=A33=0. The spectrograph has a toroidal
condenser with the values ¢e=30°, ae=Re, ra=0.95ae, 30 A22 are determined by the following variable dimensions:
¢m, being the mean angle of de?ection in said magnetic
rb=1.05ae, l’e=l",,=3.73»ae (object distance=image dis
de?ection system; c’, being the angle between the straight
tance), R’e=—1.046, Ra=1.()62ae, Rb=0.9S5ae, which
for this example Ra=9.70 cm. and Rb=9.52 cm.
According to still a further example of an energy spec
mean orbit behind said condenser and the normal to the
entrance boundary; am, being the radius of the mean orbit
has a plane entrance front surface and a cylindrically
curved exit front surface of the radius of curvature
q=—1.67aB (outwardly convex-shaped). Due to the 35 of particles in said magnetic de?ection system; ae, being
the radial radius of the mean orbit of particles in said
equality of tie and Re the mean surface of equipotential
condenser; Re, being the axial radius of equipotential sur
between the electrodes is a spherical surface but the elec
face through said mean orbit in said condenser; a’, being
trodes have toroidal surfaces each having unequal main
the distance between said condenser and said magnetic
axial and radial radii of curvature. R’e and from this
Re, and Rb and also q may be calculated from the rela 40 de?ection system; l'e, being equal to the focal distance
of said condenser; It’, being the radius of the entrance
tions Au=0 and A33=0. The formulas for All and A33
boundary of the magnetic field of said magnetic system;
are described in “Zeitschrift fiir Naturforschung” 12a, 33
R’e, being the derivative of axial radius of the equipoten~
(1957) (H. Ewald and H. Liebl, The Image Errors of
tial planes by radial direction in the plane of the mean
the Toroidal Condenser), where, however, instead of A11
orbit in said condenser; said variables being selected under
and A33 the designations F11/a2 and F33/OlZ2, respectively,
simultaneous condition of A11, A12, A22 being substan
are employed.
tially zero, with R’e being unequal to unity, and wherein
There is stated that
the axial radii Ra, Rb for said condenser are determined
F11=(aeK11-l-l"e'L11) 'd'rz
thus, in this case
by the equation
50
Re2
A11=aeK11+l"e‘L11=0
_ We use l"e instead of l"re for the sake of clarity, but
1t is understood that l"e in this speci?cation is identical
with l"re in the paper just referred to. This l"re=l”e
wherein r may be any of the r,,, rb, for determination of
can be calculated. Formula 36 in ZfN, vol. 12a, page 33. 55 RB and Rb, respectively.
The abbreviations are given in the same paper
A
2. Energy spectrograph comprising; a particle entrance
L11, c, H, and A are the same abbreviations as given
slit; a toroidal condenser having an entrance front sur
explicitly above. Using ae=Re and l'ezl",a we obtain
for R’,, the relation
face and an exit, said entrance front surface being dis
65 posed at a distance l’e from said particle entrance slit;
and from this with ¢e=30‘°, R’e=—1.046.
However, in the expression for F33 We have to insert
Lari-I33 from “Zeitschrift fiir Naturforschung" 12a, 544
(1957) (H. Liebl. and H. Ewald, Mass Spectrographs
Practically With Second Order Double Focusing). Using
R'e=——l.046, q is calculated from the condition F33=0.
It will be noted that instead of toroidal condensers
toms-like condensers may be used provided that the axial 75
said condenser focusing said particles at a distance 1",,
from said exit; said condenser having a radial angle of
(p, of de?ection, radial radii of the condenser plates ra
and rb, axial radii thereof, Ra and Rb, and de?ning a
mean particle orbit of radial radius (18 along the equi
potential surface having axial radius Re, the ratio ae/Re
being designated 0, said condenser being defined by the
equations:
3,061,720
9
10
_
a6
H=’\/ ___£%a=‘/2_c
H-V2—c_ —Re
20 under conditions of R’e unequal to unity.
with R',, being unequal to unity.
‘n’
4. In a spectrograph, a toroidal condenser including
3. Mass spectrograph comprising; a particle entrance
slit; a magnetic de?ection system de?ning a mean angle
two toroidally shaped condenser plates in which ra and rb
are respectively predetermined radial radii of the said
plates,
ae and Re are the radial radius and the axial radius,
boundary of radius k’ whereby an angle 6' is de?ned be- 25
respectively, of the mean particle orbit along an equipo
tween the mean particle orbit and the normal to said en
tential surface between said plates, axial radii RI, and Rb of
trance boundary at the place of entrance; a de?ecting
said
plates being determined by the equations:
condenser having planar entrance and exit surfaces and
being interposed between said particle entrance slit at a
distance l'e therefrom and said magnetic de?ection sys- 30
tern at a distance d therefrom; l’,a and d being taken from
said entrance and said exit surface, respectively, said de
of de?ection pm of radius am, having a curved entrance
R, +(1_R/
R,2 )2
Rb=§1 Tb—ae+1_R,
?eeting condenser having a radial angle <1),, of de?ection,
radial radii of the condenser plates ra and rb, axial radii
thereof, Ra and Rb, and de?ning a mean particle orbit 35
of radial radius 06 along the equipotential surface having
axial radius Re, the ratio a,,/Re being designated c, said
condenser being de?ned by the equations:
A33: _L33 _1L2P»=0
2
1': i
l—2R’,,R
rb_ae+-_-1_
52,
e
5. In a spectrograph, a toroidal condenser including
two toroidally shaped condenser plates in which ra and rb
are respectively predetermined radial radii of the said
40 plates, ae and Re are the radial radius and the axial radius,
respectively, of the mean particle orbit along an equipo
tential surface between said plates, axial radii Ra and Rh
of said plates being determined by the equations:
wherein R',, is unequal to +1.
_ 2 ‘r
+2(5c—2) 531)“ “be
B=c+c2(1+ R18)
‘’
wherein R’e is smaller than +1.
+%2 %(cos H¢,—— nos2 42%)
BM?
‘’
References Cited in the ?le of this patent
55
Ewald, Liebl and Sauermann article in pages 129-137
of Zeitschrift fiir Naturforschung, vol. 14A, 1959.
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