The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

A New Dipole Bending Magnet with Improved Magnetic Field Distribution
Masumi UMEZAWA, Kazuo HIRAMOTO, Masatsugu NISHI, Masahiro TADOKORO*, Jun'ichi HIROTA*,
Yoshihisa !WASHITA** and Akira NODA**
Hitachi Research Laboratory, Hitachi Ltd., Hitachi shi, Ibaraki, 319-12 JAPAN*Hitachi Works, Hitachi Ltd., Hitachi shi, lbaraki, 317 JAPAN**Institute for Chemical Research, Kyoto University, Uji shi, Kyoto, 611 JAPANAbstract

We propose a new design for dipole bending magnets
which has improved magnetic field distribution. The
present bending magnet controls the flow of the magnetic flux by introducing some vacant portions in themagnet pole. This dipole magnet realizes better magnetic field distribution in a wide range of magnetic fieldstrengths. We have investigated these dipole magnets
using two-dimensional numerical analysis. In this paper,
the principle of the design and examples of calculated results will be presented.
1 Introduction
It is necessary that bending magnets for synchrotrons provide good magnetic field distributions forvarious magnetic field strengths, which change from low
tohigh values, for beam acceleration. In order to obtain
good distributions at various magnetic field strength values, i.e. in wide dynamic range, magnet pole shape has
been studied.
Generally, the saturation effect of the magnet pole
deforms the magnetic field distribution at high magnetic
fields. The magnet pole shape has, therefore, been designed to achieve good magnetic field distribution in therequired good field region, especially at high magnetic
fields. Unfortunately, the pole shape designed for highmagnetic fields with iron saturation tends to bring about
deterioration in the quality of the magnetic Held distribution at low magnetic fields without saturation. These
characteristics have limited the dynamic range of bending magnets in synchrotrons.
Based on these conditions, we propose a new typeof dipole bending magnet which has improved magnetic
field distribution. A new design concept is based on
the control of the flow of the magnetic flux in the magnet pole with use of vacant portions, hereafter called airslots, introduced in the magnet's iron core. This newconcept was originally proposed for the development of
combined function bending magnets[1], and we have investigated the possibility of applying it to a dipole bending magnet by numerical analysis.
The concept for the improvement of magnetic field
distribution is described in section 2, and a comparison of the designs and calculation results of the conventional shim-type and the new air-slot-type magnet aredescribed in sections 3 and 4.

2 Improvement of magnetic field distribution

In the conventional dipole bending magnet, application of shims to the magnet pole face has been consideredan effective way of improving the uniformity of magnetic
field distribution at high magnetic field. However, theshape of shims for very high magnetic fields often exerts
a bad influence on the field distribution at low magnetic
fields, and the shape for low magnetic field is not suitable for high field. In order to obtain good uniformity
in a wide range of magnetic field strengths, it is necessary to cure this problem. Therefore, we propose a new
design for dipole bending magnets to improve magnetic
field distribution at various magnetic field strengths.
The scheme for improving magnetic field distribution by introducing air slots in the magnet pole is shownin ·Fig. 1. The magnetic susceptibility of the air slots
in the magnet poles is much lower than that in the ironcore. Without the air slots, the perimeter of the iron

Required Good Field Region

Fig. 1 The scheme of improvement of magnetic field
distribution by introducing air slots into themagnet pole
pole saturates earlier than the central area as excitation
goes up, and thus the magnetic flux density on the median plane around the perimeter does not keep up withthat of the central area. Because of this effect, the magnetic flux density immediately decreases off center andthe magnetic field distribution gets worse. On the otherhand, introducing air slots in the iron core leads to anincrease of the magnetic flux density in the iron region
around the air slots. At high magnetic fields, therefore,
if the position and shape of the air slots are adjusted
to equalize the magnetic flux densities in the whole poleiron, the magnetic field distribution can be flattened asshown in Fig. 1. At low magnetic field where the iron
doesn't saturate, the effect of air slots is very small andthe magnetic field distribution is controlled only by the-380-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

shape of the pole surface.
This new concept may be useful for improving thedynamic range of the magnetic field and extending the. good field region size.

1040
R1400[~R1890

3 Designs of Bending Magnet
0

As an example of the magnet design, we assume themagnets for a compact proton synchrotron that accelerates proton beams from 7MeV up to 270MeV[2]. The
mean radius and the circumference of the synchrotron
are about 3.5m and 22m, respectively. So the curvatureradius of the bending magnet is 1.4m. The minimum
magnetic field strength is 0.273T for beam injection andthe maximum is 1.808T for extraction. The good fieldregion is determined based on our analysis of the beam
size in the synchrotron. The required magnetic field uniformity in the good field region is ±0.04%. The specifications of the magnets are listed in the Table 1.

340

00

I~~56l

4 Calculation results

0.273
1.808
1.460
56±50±0.04Figures 4 and 5 show two-dimensional magnetic field
distribution of the air-slot-type magnet and the shimtype, respectively. They are calculated with use of thecomputer code PANDIRA. The horizontal axis shows
the radial distance from the design orbit and the verticalaxis shows the deviation of the magnetic field strengthfrom the value on the design orbit(R=O). The packing
factor was assumed to be 0.90 in both cases.

Based on these specifications, magnet shape is determined with use of the computer code PANDIRA. The
air-slot-type pole magnet is shown in Fig. 2, and as areference, the conventional shim-type is shown in Fig. 3
0.06---o-o.27T--o-o.ssT""--t•t-- 1.65T--4et--- 1.81T

1.49T

0.04

1000

~:

Fig. 3 Cross-sectional view of the conventional shimtype magnet

Table 1
Specification of the dipole magnet
Minimum Magnetic Field T
Maximum Magnetic Field(T)Curvature Radius(m)Bending Angle( degree)
Gap Height(mm)Good Field Region(mm)Required Magnetic Field Uniformity(%)

J\0R1870

R1400t~........
,......_

0.02

0'-"~0--,......_~

300[00\0r'-"~"IJ~lI~ 56it~Air Slots

Main Coil<l0-0.02~:.

-0.04
-0.06
-100

Fig. 2 Cross-sectional view of the air-slot-type magnet
The pole width of the air-slot-type magnet is 300mm
and quarter circles are used to prevent the local edge
effect at both ends of the pole. Air slots have race-track
shape with 70mm height and 10mm wide. The width ofshim-type pole is 340mm and the height of the shims is0.8mm.

-500R[mm]50100

Fig. 4 Two-dimensional magnetic field distribution of
the Air-slot-type magnet
As shown in Fig. 4, the good field region width isover ±60mm, and the magnetic field distribution does
not change very much from 0.27T to 1.8T. The position,
width and height of the air slots are adjusted to flat--381-

The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997--o-o.27T--D-0.98T.t.
1.49T.·.·. ·.·. ·. ·..· ·.1 ----o---0.15
0.2-••-L67T--4e._- 1.81T•

Air-slot-type
Shim-type

I·············~·.'~---~-~~~.,.......
_§ 0.1.....

i= 0.05 :::::::;:;r;::::::::::r:::::::::::::::::r:::::::··:::::::Jgrll-g
j:Q: : : : :_: : : :i: : : : : : : : : r: : : : : : ·: :t:~'i: : ji -0.05~ -0.1<I -0.02

rll

.

-0.15

. . . . . . . . .L. . . . . . . . . L. . . . . . . . ..l. . . . . . . . ..J-0.2
00.5

1.5

2-0.06 L.....IIIL.LLLI..-L.I.L-IL....L....L...I--L.....L...L--L-J....I,;LJ_L11Jl..L-J-100-50050100

R[mm]Fig: 6 Dependence of calculated sextupole strength
on magnetic field strength, B 0 , at design orbit

Fig. 5 Two-dimensional magnetic field distribution of
the conventional shini-type magnet
ten the magnetic field distribution in all magnetic field
ranges.
Figure 5 shows that the required field uniformity ingood field region of ±50mm wide is barely obtained up
to a magnetic field of 1.8T. The distribution at 1.8T isdeformed because of the saturation of iron. On the other
hand, at a magnetic field strength of 0.27T, the distribution is deformed by the effect of the pole face shape,
especially of the shims. If the shim height and position
are optimized for the magnetic field distribution at 1.8T,
the required uniformity of the field distribution at 0.27T
cannot be achieved. So it is difficult to obtain the poleshape which can achieve the uniformity in required value
from 0.27T to 1.8T.
Comparing results of these calculations, the field
uniformity of the air-slot-type magnet is much better
than that of the shim-type at low magnetic fields. These
results indicate the dynamic range can be extended to
low magnetic field in the case of the air-slot-type magnet. The injection energy of synchrotrons can be lowered
than that of synchrotrons using conventional magnets.
To compare the qualities of the magnetic field distribution, we estimated the nonlinear components, mainly
the sextupole, for the shim-type and air-slot-type bending magnet. Figure 6 shows the behavior of the sextupole strength in the good field region of ±50mm. At
1.8T, the absolute value of the sextupole strength in theair-slot-type is one-half of that in the shim-type. From
this estimation, it is found that the air slot is effective
in controlling the magnetic field distribution, especiallyat high magnetic fields where the iron core saturates.
In both cases, we calculated three-dimensional magnetic field distribution using the computer code TOSCA.
The calculated results were consistent with the above results.

5 Conclusion

We presented a new dipole bending magnet which
improves the magnetic field distribution by introducing
some vacant portions in the magnet pole. These portions, called air slots, control the flow of the magnetic
flux especially at high magnetic fields, so that a goodfield distribution can be obtained in a wide range of magnetic fields because of air slots.
We calculated the magnetic field distribution in amagnetic field range from 0.27T to 1.8T for a compact dipole magnet( curvature radius 1.4m) by using twodimensional numerical analysis. The results showed thatthe qualities of the magnetic field distribution at all themagnetic field strengths are better than these in the conventional shimmed pole magnet.
References[1] M. Tadokoro et al., "A Combined Function Magnet
for a Compact Synchrotron", Proc. 1996 Part. Accel.
Con£., Vancouver., in press.
[2] K. Hiramoto et al., "A Compact Proton Synchrotron
for Cancer Treatments", Proc. 1996 Part. Accel.
Con£., Vancouver., in press.

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