Kobe University Repository : Kernel
Title
φ-SELECTION IN A DOUBLE THIN LENS BETA-RAY
SPECTROMETER (I) : S-FOCUS(Double Thin Lens型βRay Spectrometerに於けるφ-Selection (I))
Author(s)
Higuchi, Motoaki / Oohira, Kyouzou / Matsui, Hiroshi /
Takazawa, Kazunori
Citation
兵庫農科大学研究報告. 自然科学編,3(2):23-31
Issue date
1958
Resource Type
Departmental Bulletin Paper / 紀要論文
Resource Version
publisher
DOI
URL
http://www.lib.kobe-u.ac.jp/handle_kernel/81006067
Create Date: 2017-06-19
¥'-SELECTION IN A DOUBLE THIN LENS BETA-RAY
SPECTROMETER
I
s- FOCUS
M. HIGUCHI, K.
OHIRA,
H. MATSUI and K. TAKAZAWA
Some difficulties that occur in the application of the <;o-selection proposed by Jungerman
and Beard to a double thin lens beta-ray spectrometer are described. One of the most
important difficulties is that in a 5-focus, in which the electrons emitted from the source
points at various radius 5 of a large source are focused, available source radial width, LIS, turns
out to be smaller than the expected. Thus, in order to get the best fccus mode based upon the
<;o-selection, the quantitative comparison between the 5-focus including the first order a-focus
and the complete a-focus including somewhat the S-focus should be made.
5)
Introduction
the: most promising fin baffle for the <;o-selection, to
our double thin lens spectrometer.
One of the defects in helical spectrometers is
that the point source must be used at high precision work. Though they have greater gathering
power than that of flat spectrometers, luminosity
turns out to be smaller on account of the small
source area.
Theoretical Con3ideration
It is assumed that the radial position of an
electron, emitted from a source point located off
the axis at radius 5, is given approximately by
1)
Hubert has improved the line profile for a point
source by originating the slit system that cut sharply higher momentum side. Adding, near the source,
Y-p+m (S, a) Scos.y*
2)
(1)
from the analogy to the case of homogeneous
a cone shaped baffle that cut the undesired ray
(different momentum ray), we have successfully
made the line profile for a finite source to be
similar figures to that owing to Hubert slit system.
Moreover, in order to increase the intensity, we
have intended to use a ring source consisting of
axial symmetric source points.
5)
magnetic field spectrometers. p is th3 radial position
of the electron emitted from a point source and
.y* = <;0 + .y, .y is the proj3ctecl angular position
(Fig. 1). m is the characteristic of non-homogeneous
magnetic field spectrometers and is determined
empirically from the calculated trajxtories of 5=
0.225 cm, <;0=0 ray and 5=0.350 cm, <;0=0 ray as
follows
3).4) 5)
Recently Jungerman and Beard proposed an
interesting idea about the improvement of the
optimum condition in helical spectrometers. They
introduced a new freedom <;0, the angle made by
the projection of the electron velocity vecter on a
plane perpendicular to the instrument axis at the
source with the radius of the source point, into
the electron motion in the homogeneous magnetic
field beta-ray spectrometers. It is shown that, by
proper selection of the angle <;0, an inverse 3/2
power dependence on the resolution is made possible
by removing all dependence of the resolution on
the source dimensions, thus enabling extremely
large sources.
m=acosa+ bS+ c
a : emission angle
a, b, c: constants.
(2 )
Though it is not a good approximation, Eq. ( 1 ) is
adopted to carry out ord~r estimation, since it is
required to calculate numerically a number of
angular momentum rays to proceed further approximation.
The change fro~ a point source ray at the ring
focus for a point source is given by
Both effects of a cone baffle and those of a ring
source are comprehensible from this unified view
point, <;o-selection. Therefore we investigate theoretically and practically, how much inprovement is
obtainable by the application of the 5-focus, using
5cos.y*)LIa 2 + m5cos.y*,
23
(3)
Sci. Rep. Hyogo Univ. Agric.
Vol. 3, No.2
than a standard one, 12°41'.
culation shows that
Straightforward cal-
o2p
-]
op
4a=2(acosao5cos'l-*- ~2)·{2(3kJk+
o2p
m5cos'l-*) (acosao5cos'l-* - ;;2,) + (asiJla:o
va
2 ~
5cos'l-*)} .
( 7)
Now let 51 and 52 be the inner and outer source
radius and let Xm be the maximum value of X =
Fig. 1.
1<1'* -
-}!, the angular variation from the optimum val-
ue of
'1-*=-;-, permitted by the fin
baffle. Therefore
Projection of electron trajectory on a
plane perpendicular to the axis of the
instrument.
1t
('I-*=2±X),
where k=P/i, P is the electron momentum in Hp
units and i is the magnetizing current in amp.
(8)
According to the reference 5), the fraction of
monoergic electrons emitted isotropically from
the source which are counted is given as follows.
The choice of <p = ; - tJ; yields very small source
effect, m5costJ;*. Thus one obtains 5-focus in
addition to the first order focus of the emission
angle.
The spread in 4a permitted by the Hubert slit
system is given by
op
1
For example, if m (52)52Xm> i3fi4k> 2 4yp:
5 max
I
(4 )
=
21t
4~S 21t5d5
S
4asina:od'l-*
0
Smln
Al
S
Xm
A2
S
-Xm
Al
-Xl
=si~"'O{f 5d5 4a(I-~~ )dX+ f 5d5
51
5COStJ;*)4a22 + m5costJ;*.
.Ja(l- iJ}.)dX+
(6)
Jal and 4a2 are respectively the portion with larger
emission angle and that with smaller emission angle
Sl
(cm)
Xm
(rad.)
0.5
0
0
0
0
0
0.2
0.5
0.2
0.052
0.052
0.052
0.052
0.052
0.052
0.052
0.314
Az
-Xl
1
op
I
Sl + S2
.JYP
(cm) m - 2- Xm/4Yp
------------ --- --- ----_.- --- - -
1.0
0.7
0.5
0.2
1.0
1.0
1.0
X2
f 5d5f 4a(I-~)dX},
Ai = m(A 1 )X:;;'(.Jy p - ak 4k )
Table
52
(cm)
52
1/
(%')
0.07
0.07
0.07
0.07
0.55
0.37
0.26
0.10
0.32
0.27
0.26
0.24
0.04
0.97
0.24
0.07
0.07
0.30
0.68
0.34
0.37
1.27
0.89
0.51
I
(x 104cm2)
-------
-----
1.17
0.69
0.38
0.08
0.62
1.10
0.79
3.56
;=1/1/1
(x 10)
--------.
6.40
4.88
2.88
0.63
4.87
5.62
3.48
2.50
. __.. _ - - - - - - - -
24
X,n
(9)
Saries:
XII, 1958
Natural Science
•
5
4
•
3
2
i
o~~~~~~~~~~--=-~--~-
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9J..O
m.xm (51 + 52)/2
4yp
Fig. 3. "I vs mean source effect curve. "I shows
maximum at 0.55-0.6. (Xm =0.052 radians)
4)
Fig. 2.
The relative half-maximum width
the formula
is given by
(S2 )
Integration map (shaded area) for the
source with q>-selecting fin baffle.
_
( 52_ ~2
'1/-0.00038
4ypl +0.00042 4Y~ +0.239 %
(5 1 =0, Xm=0.052).
1
op
Az m(A2)Xm ak 4k
Xl =
'1/
(11)
From the comparison between the change of the
radial position corresponding to the variation of
1/1*. 41/1*=0.052 radians, estimated from m5cos1/l"i'approximation and the same one calculated by
1
op
m(5)5(4yp- ak4k)
1
op
X2 = m(5)5 ak 4k.
Keller's numerical method,B) it becomes clear that
the former is about two times larger than the latter.
This means that the slit width on the integration
map is underestimated by the factor-l/2. As the
results of the correction for this error with the
help of Eq. QO) and (11), the intensity I and the relative
half-maximum width '1/, shown in Table I. must be
multiplied respectively by -4/3 and -3/4. Choosing
52 = 1. 0 cm, 51 = 0 cm, Xm = 0.052 radians and
4Yp=0.07 cm, the improvement over the optimized
Hubert system that is roughly estimated becomes
-12. As the realizable cases, for the case of 52=
1.0 cm, 51=0.5 cm, X m =0.052 radians and 4yp=
0.07 cm. the improvement over the 0.1 cm <p disc
source with Hubert system is -4. Thus it is
expected theoretically that the considerable improvement is made possible by the application of
the 5-focus with the use of the q>-selecting fin
baffle to our double thin lens beta-ray spectorometer.
The integration limits are shown in Fig. 2.
The results of the numerical surface integral
are summarized in Table I and in Fig. 3.
For
example, a line profile for the case of 52=1.0 cm,
51=0.5 em, X m =0.052 radians and 4Yp=0.07 cm is
shown in Fig. 4.
From these results the followings are observed;
1) The ratio "I of the peak intensity to the threehalves power of the relative half-maximum
width '1/ shows maximum at (mean source
effect) =0.55-0.6 x (slit width) for 51 =0 cm
and X m =0.052 radians. This fact should be
compared with the case of the optimized Hubert
system, (source effect)=0.5x (slit width.)
2) It seems likely that "I decreases with decreasing
52/51.
3) The peak intensity is given by the formulae
52
-6
1={1.104yp - 4.02} x 10 cm 2
Baffie Design
(52=0.5 ..... 1.0, 5 1 =0)
1={6.42(;;)2 +7.91(~t~)} x
It is assumed that the electron of certain mo-
10-~m2
(52=0.--0.5.51 =0).
mentum ko, emitted from any point on the source
with the emission angle ao, moves near the source on
the surface of the cone of angle 2ao. whose axis is
(10)
25
Sci. Rep. Hyogo Univ. Agric.
I
Vol. 3, No.2
source were used, the available source area should
become to be infinitesimal smalL Therefore, it is
necessary to find the other baffle surface permitting
the rays from some finite source area. For this
purpose, we used the surface 0"1 and another curved
surface 0"3, involvig the ray originating from a
certain point C with <Po and having the edge
parallel to OA at any axial distance. The point C
is chosen so that the projected position of the
electron at Zo originating from this point C with
<Po may be C1'
When this curved surface "3 and the above
mentioned 0"1 are used for baffles, these baffles
permit the <po-rays with emission angle ao, originating from any point on the source area OAB. And
X,n is defined by the edges of these baffles at Zo.
If we adopt the smaller value of Zo (::;::2 cm), it is
difficult to work the baffle because the slit width
becomes so small, and if the larger value (> 12cm),
the above assumptions for the trajectory on the
cone surface seem to be invalid.
-5
S X!O
7
6
4
When Zo = 12.1 cm, - ao = 12°41' andSo = 1 cm, the
angle e is obtained as 2°5'35/1. The section of our
baffle perpendicular to the instrumental axis has
86 slots, as shown in Fig. 6. In this case, a half
of the source area is not available owing to the
finite width of baffle walls. If the small source
radius is utilized, the work of the baffle becomes
difficult, so that the minimum source radius Smi"
is chosen as 0.5 cm. The outer radius rout and
inner radius rinn of <p-selecting slits, indicated in
Fig. 6, are determined so as to permit the a,Jtax
(= 14°35') and txmin (= 10°47') ray respectively.
In our actual design, piling 34 aluminum plates
of 3 mm thickness with such 86 slots worked by
cutter, a <p-baffle block is constructed.
2
1
1420
Hp/amp.
Experhnent
Fig. 4. Line profile for the case of S2 = 1. 0 cm,
S1=O.5cm, X m =O.052 radians and 4Y1,=O.07cm.
Fig. 7 shows the baffle geometry of our spectorometer near the ring slit for the point source, and
the baffle R travels along the field axis to the
position of H.-I, R-2,.··, etc.. Using a Cs137 ring
source, of which inner radius 0.5 cm and outer
radius 1 cm, the line profile of the 661 kev. Kinternal coversion is obtained at the R-l slit
position, as represented by curve (1) of Fig. 8. This
line profile have two large maxima owing to the use
of the large ring source.
When the <p-baffle of 34 plates was set at the
regular position in front of this ring source, the
intensity of the experimental line profile was much
weaker than expected. As shown by the curve (2)
of Fig. 8, the maximum peak is found at 2.335
amp. and the resolution O. 5~·b. Removing ten and
twenty source side plates from the <p-baffle block,
the intensity of the line profile becomes larger step
by step but these peak currents are almost the
parallel to the field axis. And the rotating angle is
assumed to be the same as that of the point source'
For the present, an attempt of designing the <Pselecting baffle will be made on these assumptions.
"'0.
Fig. 5 shows the electron position projected on
the source plane perpendicular to the field axis.
The points A1 and C1 represent the projected
positions of the electrons at the axial distance zo,
originating from the source point A of radius So
with the emission angle ao, in the directions of
projected angles of <Po and <Po + X 711" respectively.
The value of <Po is chosen so as to make cos
(<Po + "'rO) vanish. The lines A1A2 and C 1C2 parallel
to OA represent the edges of the curved surfaces
"1 and "2 involving the rays of <Po and <Po + X ,It ,
originating from the source line ~A.
If the curved surfaces "1 and 0"2 from Zo to
26
XII, 1958
Series: Natural Science
o
,
....
... ...
",1II1i
'" '"
Fig. 6. Section of the baffle perpendicular to
the instrument axis.
Fig. 5.
of this difference will be obtained when the inner
baffle R is at the position of R·4 and the outer
baffle R' displaced to the R'-(l). The N line profile
has the maximum peak at the expected spectrometer current i o, and it is implied that the selected
rays have the trajectories running through between
R'-(I) and R-(4), at the current i o. Actually, the
numerical calculation shows that the trajectory of
the 1420 gauss cm/amp.-ray with <)?o = - 40°59'15"
and emission angle eto = 12°41' from the source
radius 1 cm, has the lower radial distance by 4.5
mm than that of the point source, at the axial
distance of the ring slit. The difference of the
rotating angles of these is found to be 17°, and it
is hardly negligible.
Thus, it is not unreasonable that the small line
profile with 0.5% resolution was obtained, when
we used the <)? (= - 40°59'15") selecting baffle.
Projection of curved surfaces used
as baffle surfaces.
same as the curve (1). These line profiles are represented by the curves (3) and (4) of Fig. 8. From
these experiments, it seems that the line profile
may be obtained from electrons passing through
the <)?-baffle slits but not from scattered electrons.
Let us consider the maximum peak current of
the line profile (I) of Fig. 8. As represented by
the curve A, the profile obtained with the cone
baffle 2) for 1.2 mm dia. Cs137 source at the slit
position of R-l, indicates the maximum peak
current of 2.379 amp., as expected, and the resolution 0.37%. Considering the signification of the
fact that the peak current of the line profile is
lower by 0.044 amp, than the expected value, the
rays selected by the baffle have probably the source
effect corresponding to this current deviation.
When the spectrometer current is set at 2.379
amp., the rays passing through the <)?-baffle will be
at the lower radial position than that of the ring
slit, corresponding to 0.044 amp. in average. If the
spectorometer current is set at the lower value to
fall on the ring slit, the rays may be stopped by the
Hubert baffle and the available .Jet may decrease,
so that the peak intensity becomes probably extremely small.
To confirm experimentally above considerations,
we obtained the line profiles for several R-slit
positions with the <)?-baffle of 14 plates. For the
slit positions of R-2, R-3, R-4, and R-5 the line
profiles (5), (6), (7), and (8) are obtained, respectively,
as shown in Fig. 8. The difference of curves (7)
and (6) yields the line profile N. The line profile
Further Investigation
By the experimental analysis, we know now the
--------··...-----.'l
I
iI
!
28
38
Axial Distance (cm)
Fig. 7.
27
Ring baffle geometry showing
various settings.
Sci. Rep. Hyogo Univ. Agric.
f
m[
~
where pr' is the projected distance from the source
point to the electron position at the ring slit·
According to the numerical calculations, the rotating
angle for the finite source radius (5=1 cm) is
different from that for the point source. And the
value of p' is found to be appreciably apart at the
ring slit from that for the point source. For
finding any approximately good functional forms
for .1Yr, therefore, it is necessary to calculate the
trajectaries of a large number of rays with various
initial conditions.
Giving up to find analytically our desired values
of <P from Eqs. (3), (4) and (5), we obtained directly
these values of angle <P from numerical calculations.
To obtain the desired values of angle <p, the next
procedure seems to be useful. The source radius,
the emisson angle, and the electron momentum
being held constant, pr' and fr in rq. (3) are the
functions of <po Substituting the values for the
<Po = - 40°59'15" ray into pr' and 1fr, the equation
".
66
)000
Vol. 3, No.2
1000
1
involves <p explicitly in cos (<p + 1fr) only.
Then
Yr as a function of <p is represented by the dotted
curve of Fig. 9. If the value of <p is - 70° 17'5" ,
Yr estimated from this dotted curve is equal to p.
By the numerical calculation of the trajectory with
this angle, dYr is found to be - 0.01 cm. When
the values for <Po = - 55° ray are substituted into
pr' and 1fr, a similar curve is obtained and, surprisingly, the desired value of <p obtained from this
curve is about - 70°. Thus, when the values of pr'
and 1fr of a ray with any value of angle <p in this region
are calculated, one may obtain the desired value of
<p approximately. Furthermore, it is interesting to
see that the three Yr points corresponding to the
<p= -40°59'15", -55°, and -70°17'5", are lying on
the straight line to a good approximation as shown
in Fig. 9. As represented by the line 5-0.5 of
Fig. 9, three points for rays originating from the
source radius 0.5 cm tend also to lie on the straight
line. Thus if the Yr values of any two rays with
different angles <p are obtained, we may find the
desired values of angle <p to a better approximation.
2.50
Spectrometer Current (amp.)
Fig. 8.
Exrerimental line profiles.
fact that the ray with the angle <p, which make
cos (<p + <Pro) vanish, shows some appreciable source
effect at the ring slit for the point source. Therefore the question is how we obtain the desired angle.
At the ring slit for the point source Yr is the
radial distance of the ray originating from a source
point of radius 5, and p the radial distance of the
point source ray. The difference of Yr and p, 4y,.,
satisfies the next equation;
.1Yr =
=
y
pr'2 + S2';2p~.' 5cos~;::¥ - I'
(fr* = <P + fr)
52
5
(12)
•
pr'Cl + { ----'2
+ 2,cos1fr*}) - p
1'1'
1',.
Fig. 10 represents the a-focusing property of the
rays with the angle <p = -70°17'5". These three
rays originate from a source point located off the
axis at radius 1 cm with emission angle a: = 12°41',
14°35' and 10°47'. The position of the aAocusing
is not the same for the point source but it deviates
by 0.7 cm in axial distance and is somewhat lower
in radial distance. However, the spherical aberration
coming from the .1a is smaller than that for the
point source. Then, the position of the ring slit
may be chosen at this position. ~uch values of
angle <p that these <p-rays emitted from the source
,
1 52
1 54
= (Pr - p) + 5cOSfr* + 2- - , - -8---------a
Pr
Pr
1 53
1 52
2
- -2 ~cosfr
-2- ----'(COS1fr*) + ...
1'1' "
or
*-
pr
= (pr' - p) + 5cos1fr* + .1,
(13)
1 52 1 54
.1Yr= ((1'/ - p) + -2-- -,- -8 ~-'3 + ... ) +
Pr
Pr
1 52
1 5
,
(1-:2 p/'.!- 2 p/coSfr*+",)SCOSfr*
=d' + m'5cosfr*'
(14)
28
XII, 1958
2.1
.....
Series: Natural Science
~--------------------------------------------------~
1.9
~
llO
Q
~
.....
'" loS
....'"
'"
III
<)
Q
15
';;j
~
'" 1.7
~
1.6
-600
Angle <p
Fig. 9. Calculated Yr-values vs <p curves. The desired <p-values are estimated
from these to a considerably good approximation.
ted by this slit have the undesired value of <po To
pass through selectively all the rays with the
emission angle between 14°35' and 10°47', we must
have such a slit ABCD for S = 1 cm and A'B'C'Dt
for S=0,5 cm. When we want to utilize all over
the source radius from 1 cm to 0.5 cm, we must
have a large slit area from ABCD to A'B'C'D"
Such a large slit permits the rays of undesired values
of <p and the spread of the rays at the ring slit
becomes large. For the possible design of the
baffle permitting the rays of the desired values of
<p, the baffle slits for the various source radius
must lie upon one another.
Therefore, let us consider the focusing of the
rays from various source radius at the lower radial
distance than the ring slit for the point source. From
points at various source radius focus at this position,
can be found to a good approximation by the graph
smilar to Fig. 9. For source radius 0.5 cm, this
angle is found to be _75°. If the rays with these
angles could be selected, the expected improvement
would be obtained.
However, one must face to the difficulties as
below in the actual design of this baffle. The slot
EFGH, shown in Fig. 11, is a similar one to the
slot A1A2C2Cl in Fig. 5. The rays of the desired
values of <p and emitted from the source points
located from radius 'I cm to 0.5 cm with the emission angle 12°41', pass through this slit. However,
the almost rays with the smaller emission angle
than 12°41' could not pass through it and all the
rays with lager emission angle than 12°41' permit-
29
Vol. 3, No.2
Sci. Rep. Hyogo Univ. Agric.
than that for the point source (-2.0536 cm), the
rays origirating from the larger source radius must
have the smaller v31ues of cp to focus at the same
radial position, in the region of these values of rp.
ThuB, the slots of the baffle for various source
radius tend to 'lpproach each other. The better
condition of overlapping of these slots may be
found for other values of cp, but if the values of
cp shown in TabJe 1I are adopted it does not seem
to deviate appreciably from optimum value. To
examine the system of the baffle slit permitting the
rays of the ,mgle rp in Table 1I, the slots for source
radius 1 lOrn, 0,9 lOrn, and 0.8 cm are shown in
Fig, 12. These slots, at the axial distance 12 cm
from the source, have the large common part of
an;,). Therefore, it is likely to decrease largely the
Etr2Y pass3ge of undecired rayE. When the baffle
ic set from wch position to the neighbourhood of
the source, the expected spread of the line profile
may be obtained, However, in the neighbourhood
of the source, these slots for various source radius
become to be apart from each other. To keep the
avail;:ble source area a half, the next neighbouring
slits must have the shaded area indicated in Fig.
12, From the configuration of these slits, it is
evident that the setting of the baffle at the axial
distance 4 lOrn is difficult, if the source radius from
1 cm to 0.8 lOrn is utilized. When the source radius
is utilized from 1 cm to 0.8 lOrn, the baffle can not
be sct within the axial distance 6 cm. If there is
no baffle near the source, it is necessary to set the
baffle at the position far from the source, so as to
hold X",=3°. However, at a too far distance from
the source, the slit width becomes large, so that
the neighbouring slits overlap each other.
2.5
"s
U
'.J
"u
2.0
(3) /'
~
...,"
UJ
~
til
;a
'I
i
1.5
"
P:<
33
.36
35
Axial Dist<:r:cc (cm)
Fig. 10.
a-fccming property of t11e rclYS
of ip = - 70° 17' 5"-
the curves ~-1 and E<J.5 in Fig. 9, the values of <p
are found to be - 54' for S= 1 em and - 41 '40' for
5 = O. 5cm, if Yo' is 1. 8 lOrn. :'imibr!", for the other
source radius, it can be ;:ffumecl that the cp-c1cperdence of the r<ldial distance Yo' will be repre,'cn tcd hy
the straight lire in theEe cp-region,
The values of Yr at ip= - 40° and the tangenti;)1
values are interpobtec1 by these of three str;:ight
lires, S-O, E-1 and E-0,5 in Fig. 9. Then, the straight
line for any arbitr;)ry source radius are obtained
approximately. The str;)ight line" denoted by S0.6,5-0.7,5-0.8 and 8-0.9 arc dr<lwn hy this arproximate method for source radius 0,6, 0,7, 0,8
and 0.9 lOrn, respectively, By the graph in Fig. 9,
the values of cp at Y,' = 1.8 cm ;l[C found, The2e
values are shown in T,'ble n,
Table 1l
5
k
y.
cm
gauss cm/amp.
C1TI
As a result, the available source width is found
to be only 0.2 lOrn at S = 1.0 lOrn, for 5-focus suggested by Bearc1,5) Thus, in actual design, we could
not obtain the available source radial width so large
as expected.
----------
1.0
0.9
0.8
0.7
0.6
0.5
1420
12'41'
-54')
1/
/I
- 53')
fI
'/
fI
'/
'/
"
1/
'/
- 51'30'
- 49'20'
-46°20'
- 41 °40'
1,798 8462
(1.8)
1,800 9645
(1.8)
(1.8)
(1. 8)
Conclusion
The S-focus, that could be expected theoretically
to be capable of the considerable improvement,
conta.ins come difficulties as described. Although
the elaborate calculaticn to find the optimum cp,
str2Y pass8.ge of the ur·clE:,ir8d cp-rays and difficult
fabrica tion arc not so imrcr12nt, y8t it is important
that 2vailable source \\ icah mcst be small to diminish the loss factor. TnuL it is concluded that the
~-------
The numerical calculations show that the radial
distances of the rays with these values of cp, are
1. 8 cm to a good approximation at Zr. The ray
originating from each Eource radius with a certain
emission angb other than 12°41' m3Y have the
maximum radid distance at Zr, but this emiffion
angle 3nd its maximum radial distance may be not
EO far from those of the ray with the emission
angle 12°41'. For the source radius 1 lOrn, the ray
with the emission angle -12'46' has the maximum
radial distance -1. 7990 lOrn at z,.. As seen in Table
1I, if the radial distance of the focusing is lower
5-focus, including fin:t orckr ,,-focus, must be compared quantitatively \'.ith the complete a-focus,
ineluding somewhat S-fccus, to find the best focus
mode depending on the .;c-ckction.
(Laboratory of Physics, Received Aug. 30, 1958)
30
Series: Natural Science
XII, 1958
Fig. 11. Slot geometry for the rays focusing
at the radial distance of-2.05cm.
References
1)
P. HUBERT, Ann. de Phys. 8, 662
(1953)
2)
K. TAKAZAWA, M. HIGUCHI, K. OHIRA
and H. MATSUI, Sci. Rep. Hyogo Univ.
Agric. Vol. 3, No.1, Ser: Natur.
Sci., p. 9 (1957)
J. A. JUNGERMAN and D. B. BEARD,
Rev. Sci. Instr. 27, 56 (1956)
J. A. JUNGERMAN and D. B. BEARD
Rev. Sci. Instr. 27, 650 (1956)
D. B. BEARD, Rev. Sci. Instr. 28, 19
(1957)
J. M. KELLER, E. KOENIGSBERG and
A. PASKIN, Rev. Sci. Instr. 21, 713
(1950)
3)
4)
5)
6)
B A
o
Fig. 12. Slot geometry for the rays focusing
at the radial distance of-1.8cm.
31