- Email: [email protected]
Circular hole iron septum magnet
Nuclear Instruments and Methods 184 (1981) 587-589 North-Holland Publishing Company
CIRCULAR
HOLE
IRON
SEPTUM
587
MAGNET
Hiroshi N O M A , T e t u h i r o S H I O D A and Yasukazu Y O S H I Z A W A
Department of Physics, HiroshirnaUniversity,Hiroshima,Japan Received 10 March 1980 and in revised form 25 November 1980
An iron septum magnet was designed for the charged-particle beam splitting system. Magnetic field measurements of the septum model magnet with a circular hole were performed for several conditions. The hole field is B 0 = 60-250 G for a hole radius of 12 mm and the gap field is Bg = 5--6 kG for a gap distance of 8 mm with a septum thickness of 1 mm. The multipole field strength in the circular hole is obtained from the field distribution.
An iron s e p t u m magnet has been used for the splitring system o f the high energy p r o t o n beam. This magnet has a hole in the pole tip and some part of the beam passes through the hole where the magnetic field is weak. The magnetic field in the wedge shaped hole [1] which is often used is rather complicated. Oleksiuk et al. [2] adopted a circular hole with septa o f 3 . 8 - 5 m m thickness. We m a d e a m o d e l magnet having a circular hole o f a = 12 m m and septa o f c = I, 3 and 8 m m , where a and c are illustrated in fig. 1. Fig. 1 shows a schematic cross section o f the hole and the septum. Each pole tip is 60 m m wide and 41 m m high. The gap field Bg up to l 1 k G was produced in a gap o l d = 4, 8 and 14 m m b e t w e e n two pole tips. Distributions o f the hole
POLE TIP
~,,
GAP POLE
,
Bg "~
d
l/l/s/l-----
TIP ~
......
a a
L -a
I
I
0
a
Fig. 1. Schematic cross section of a circular hole and septum. Bg means the gap field for the gap distance d, and B o the hole field at the center of the hole with radius a and septum thickness c. 0 0 2 9 - 5 5 4 X / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland
field Bo and o f the gap field Bg were measured with a Hall detector. The b e a m can be split by the strong gap field Bg and by the w e a k field Bo. The magnetic potential V(r, O) in a circular hole is expressed as
v(r, o) : - ~ n n
cos nO,
(1)
where r is the distance from the center o f the hole, and 0 is the angle f r o m the Y axis. Parameters An can be determined by using the field B0 = (Box, Boy). The parameter A1 = a B 0 is deduced from the field B0 y(0, 0) = Bo at the center o f the hole. For the case o f c N a and d, the field Bo is described as the constant distribution, because of An = 0 for n ~> 2. Fig. 2 shows the measured gap field Bg at 2 m m f r o m the surface o f the lower pole tip for X = 0, and Bo at the center o f the hole. Curves ( a ) - ( d ) indicate results for a circular hole o f a = 12 m m radius. Curves (a), (b) and (c) show the results for d = 14, 8 and 4 r a m at c = 1 m m , respectively. For the case o f d = 14 ram, curves for c = 3 and 8 m m were not different from curve (a) for c = 1 m m within several percent. But for the case o f d = 4 m m , the curve for c = 8 m m is similar to curve (d) for c = 3 nun which is different from that for c = 1 ram. Curve (e) shows the result o f a = 2.5 m m , c = 19,5 m m and d = 3 m m , that is, the case c >> a and d, where the Bo distribution is constant in the hole. The curve also indicates that Bo is roughly p r o p o r t i o n a l to an exponential f u n c t i o n o f Bg for c >> a, d and Bg < 10 kG. The field distribution Bo = (Box, Bor) o f a hole o f a = 12 m m was measured up to Bg = 9 kG for c = 1 , 3
H. Noma et al. / Circular hole iron septum magnet
588
d=14 mrn c=lmm
Bo(O)
~ .... ~ 3000
Bg(0) 1 - 5 kG
-(a)
1000
(b)
/
./
////./ij,
---
,"(e)
""'"
'
-20 m
.I -10 -a
'
I 0
'
-
I. 10
"7
'
Ix 20mm
a=12 mm d=4mm c : l m m
500
10C re
~ ~ ' - ~ , ( ~
9C
I- 3
kG
Fig. 4. Gap field d i s t r i b u t i o n s a l o n g the X axis for c = 1 m m and d = 14 and 4 mm.
5O #., •
(c)
lO 5
i
2
4
6
i
(d)
4 4
(e)
c >~ a , d
i
1 3
i
8 Bg(kG)
i
value o f a b o u t - 0 . 2 for t h e field Og h i g h e r t h a n 5 k G , and is o f t h e same o r d e r as t h e ratios A3/A1 and A4/A 1. Results for e = 8 m m were shnilar to t h o s e for c = 3 ram. F o r t h e case o f c = 1 m m and d = 4 m m , Az/A1 ratios are as small as a b o u t - 0 . 2 for a field higher t h a n B g = 3.5 k G and t u r n positive for a field higher t h a n B g = 5 kG. B u t t h e ratio A J A ~ is negative for e='3mm a n d d = 4 m m at 9 k G ~ > B g ~ > 3 . 5 k G . Results for c = 8 m m were similar to t h e case o f c = 3 m m . F o r b o t h cases c = 1 m m a n d d = 14 m m at B g ) 5 k G , and c = 1 m m and d = 4 m m a t B g ~ 3.5 k G , t h e p a r a m e t e r A 1 is larger t h a n A 2 , A 3 a n d A 4 .
i
10
12
Fig. 2. Observed hole field B o and gap field Bg. Curves (a) (d) were m e a s u r e d for a hole radius o f a = 12 ram. Curve (e) was for e >> a and d at a = 2.5 ram, c = 19.5 m m and d = 3 ram.
or 8 m m a n d d = 4 or 14 m m . The d i s t r i b u t i o n s were fitted b y t h e p a r a m e t e r s A n for n ~< 4. Fig. 3 shows ratios o f A2, A 3 a n d A 4 t o A 1 . F o r d = 1 4 m m and c = 1 or 3 m m , t h e ratioA2/A1 is r e d u c e d to a smaller
Ar ,
-0.5
B (kG) g 10
5
0.5
I
. . . .
++
+
The gap field d i s t r i b u t i o n s B g ( X ) w e r e m e a s u r e d along t h e X axis at 2 m m f r o m t h e surface o f t h e
I
d=1
mrn
c=
mm
Bg(kG) 10
5
0.5
. . . .
0
__t.,
I
. . . .
I
++
=3ram
- 10
-0.5/ 0
,
,
I
o--
AJA
mm
,
5
I -0.5
I0 I
x --
A3//'AI
,
0
]
d=4mm c=3mm
I if c-
,
,
I
i
i
i
5 • - - A4//A 1
Fig. 3. R a t i o s o F A 2 , A 3 a n d A 4 t o A 1 for the hole field d i s t r i b u t i o n s .
,
I
10
H. Noma et al. / Circular hole iron septum magnet
lower pole tip. Fig. 4 shows the field Bg(X) for c = 1 mm and d = 14 or 4 mm. The field Bg(X) for d = 1 4 mm is uniform up to 5 k G , and the ratio [Bg(20)-Bg(0)]/Bg(20) is about 2% at Bg(0) = 7 kG, where Bg(0) and Bg(20) mean the fields at X = 0 and 20 ram, respectively. For d = 4 ram, the field is uniform up to 3 kG, and the ratio becomes about 11% at Bg(0) = 7 kG. From our experimental results one could adopt a circular hole with a small septum thickness of c = 1 ram, in the condition of a hole field B0 = 6 0 250 G for a hole radius of about 12 mm and a gap
589
field Bg = 5 - 6 kG for a gap distance of about 8 mm. These results were almost independent of the properties of the soft iron.
References [11 L. Evans, A. Hilaire, A. Ijspeert, B. de Raad, N. Siegel and E. Weisse, IEEE Trans. Nucl. Sci. NS-24 (1977) 1571. [2] L.W. Oleksiuk, R.A. Andrews, E.J. Bleser and C.tt. Rode, IEEE Trans. Nucl. Sci. NS-20 (1973) 428.
CIRCULAR
HOLE
IRON
SEPTUM
587
MAGNET
Hiroshi N O M A , T e t u h i r o S H I O D A and Yasukazu Y O S H I Z A W A
Department of Physics, HiroshirnaUniversity,Hiroshima,Japan Received 10 March 1980 and in revised form 25 November 1980
An iron septum magnet was designed for the charged-particle beam splitting system. Magnetic field measurements of the septum model magnet with a circular hole were performed for several conditions. The hole field is B 0 = 60-250 G for a hole radius of 12 mm and the gap field is Bg = 5--6 kG for a gap distance of 8 mm with a septum thickness of 1 mm. The multipole field strength in the circular hole is obtained from the field distribution.
An iron s e p t u m magnet has been used for the splitring system o f the high energy p r o t o n beam. This magnet has a hole in the pole tip and some part of the beam passes through the hole where the magnetic field is weak. The magnetic field in the wedge shaped hole [1] which is often used is rather complicated. Oleksiuk et al. [2] adopted a circular hole with septa o f 3 . 8 - 5 m m thickness. We m a d e a m o d e l magnet having a circular hole o f a = 12 m m and septa o f c = I, 3 and 8 m m , where a and c are illustrated in fig. 1. Fig. 1 shows a schematic cross section o f the hole and the septum. Each pole tip is 60 m m wide and 41 m m high. The gap field Bg up to l 1 k G was produced in a gap o l d = 4, 8 and 14 m m b e t w e e n two pole tips. Distributions o f the hole
POLE TIP
~,,
GAP POLE
,
Bg "~
d
l/l/s/l-----
TIP ~
......
a a
L -a
I
I
0
a
Fig. 1. Schematic cross section of a circular hole and septum. Bg means the gap field for the gap distance d, and B o the hole field at the center of the hole with radius a and septum thickness c. 0 0 2 9 - 5 5 4 X / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland
field Bo and o f the gap field Bg were measured with a Hall detector. The b e a m can be split by the strong gap field Bg and by the w e a k field Bo. The magnetic potential V(r, O) in a circular hole is expressed as
v(r, o) : - ~ n n
cos nO,
(1)
where r is the distance from the center o f the hole, and 0 is the angle f r o m the Y axis. Parameters An can be determined by using the field B0 = (Box, Boy). The parameter A1 = a B 0 is deduced from the field B0 y(0, 0) = Bo at the center o f the hole. For the case o f c N a and d, the field Bo is described as the constant distribution, because of An = 0 for n ~> 2. Fig. 2 shows the measured gap field Bg at 2 m m f r o m the surface o f the lower pole tip for X = 0, and Bo at the center o f the hole. Curves ( a ) - ( d ) indicate results for a circular hole o f a = 12 m m radius. Curves (a), (b) and (c) show the results for d = 14, 8 and 4 r a m at c = 1 m m , respectively. For the case o f d = 14 ram, curves for c = 3 and 8 m m were not different from curve (a) for c = 1 m m within several percent. But for the case o f d = 4 m m , the curve for c = 8 m m is similar to curve (d) for c = 3 nun which is different from that for c = 1 ram. Curve (e) shows the result o f a = 2.5 m m , c = 19,5 m m and d = 3 m m , that is, the case c >> a and d, where the Bo distribution is constant in the hole. The curve also indicates that Bo is roughly p r o p o r t i o n a l to an exponential f u n c t i o n o f Bg for c >> a, d and Bg < 10 kG. The field distribution Bo = (Box, Bor) o f a hole o f a = 12 m m was measured up to Bg = 9 kG for c = 1 , 3
H. Noma et al. / Circular hole iron septum magnet
588
d=14 mrn c=lmm
Bo(O)
~ .... ~ 3000
Bg(0) 1 - 5 kG
-(a)
1000
(b)
/
./
////./ij,
---
,"(e)
""'"
'
-20 m
.I -10 -a
'
I 0
'
-
I. 10
"7
'
Ix 20mm
a=12 mm d=4mm c : l m m
500
10C re
~ ~ ' - ~ , ( ~
9C
I- 3
kG
Fig. 4. Gap field d i s t r i b u t i o n s a l o n g the X axis for c = 1 m m and d = 14 and 4 mm.
5O #., •
(c)
lO 5
i
2
4
6
i
(d)
4 4
(e)
c >~ a , d
i
1 3
i
8 Bg(kG)
i
value o f a b o u t - 0 . 2 for t h e field Og h i g h e r t h a n 5 k G , and is o f t h e same o r d e r as t h e ratios A3/A1 and A4/A 1. Results for e = 8 m m were shnilar to t h o s e for c = 3 ram. F o r t h e case o f c = 1 m m and d = 4 m m , Az/A1 ratios are as small as a b o u t - 0 . 2 for a field higher t h a n B g = 3.5 k G and t u r n positive for a field higher t h a n B g = 5 kG. B u t t h e ratio A J A ~ is negative for e='3mm a n d d = 4 m m at 9 k G ~ > B g ~ > 3 . 5 k G . Results for c = 8 m m were similar to t h e case o f c = 3 m m . F o r b o t h cases c = 1 m m a n d d = 14 m m at B g ) 5 k G , and c = 1 m m and d = 4 m m a t B g ~ 3.5 k G , t h e p a r a m e t e r A 1 is larger t h a n A 2 , A 3 a n d A 4 .
i
10
12
Fig. 2. Observed hole field B o and gap field Bg. Curves (a) (d) were m e a s u r e d for a hole radius o f a = 12 ram. Curve (e) was for e >> a and d at a = 2.5 ram, c = 19.5 m m and d = 3 ram.
or 8 m m a n d d = 4 or 14 m m . The d i s t r i b u t i o n s were fitted b y t h e p a r a m e t e r s A n for n ~< 4. Fig. 3 shows ratios o f A2, A 3 a n d A 4 t o A 1 . F o r d = 1 4 m m and c = 1 or 3 m m , t h e ratioA2/A1 is r e d u c e d to a smaller
Ar ,
-0.5
B (kG) g 10
5
0.5
I
. . . .
++
+
The gap field d i s t r i b u t i o n s B g ( X ) w e r e m e a s u r e d along t h e X axis at 2 m m f r o m t h e surface o f t h e
I
d=1
mrn
c=
mm
Bg(kG) 10
5
0.5
. . . .
0
__t.,
I
. . . .
I
++
=3ram
- 10
-0.5/ 0
,
,
I
o--
AJA
mm
,
5
I -0.5
I0 I
x --
A3//'AI
,
0
]
d=4mm c=3mm
I if c-
,
,
I
i
i
i
5 • - - A4//A 1
Fig. 3. R a t i o s o F A 2 , A 3 a n d A 4 t o A 1 for the hole field d i s t r i b u t i o n s .
,
I
10
H. Noma et al. / Circular hole iron septum magnet
lower pole tip. Fig. 4 shows the field Bg(X) for c = 1 mm and d = 14 or 4 mm. The field Bg(X) for d = 1 4 mm is uniform up to 5 k G , and the ratio [Bg(20)-Bg(0)]/Bg(20) is about 2% at Bg(0) = 7 kG, where Bg(0) and Bg(20) mean the fields at X = 0 and 20 ram, respectively. For d = 4 ram, the field is uniform up to 3 kG, and the ratio becomes about 11% at Bg(0) = 7 kG. From our experimental results one could adopt a circular hole with a small septum thickness of c = 1 ram, in the condition of a hole field B0 = 6 0 250 G for a hole radius of about 12 mm and a gap
589
field Bg = 5 - 6 kG for a gap distance of about 8 mm. These results were almost independent of the properties of the soft iron.
References [11 L. Evans, A. Hilaire, A. Ijspeert, B. de Raad, N. Siegel and E. Weisse, IEEE Trans. Nucl. Sci. NS-24 (1977) 1571. [2] L.W. Oleksiuk, R.A. Andrews, E.J. Bleser and C.tt. Rode, IEEE Trans. Nucl. Sci. NS-20 (1973) 428.