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

Octupole Magnet for Expansion of Irradiation Area
Akio MORlTA, Makoto INOUE, Akira NODA, Yoshihisa !WASHITA,ToshiyukiSHIRAI, Eriko URAKABE, Kazuo HIRAMOTO*, and Kouji NODA**
Accelerator Laboratory, Nuclear Science Research Facility,Institute for Chemical Research, Kyoto University, Gokanosho, Uji, Kyoto 611, Japan*Power & Industrial Systems R&D Division, Hitachi Ltd., 711, Omika, Hitachi, Ibaragi 319-12, Japan**National Institute of Radiological Sciences, 9-1, Anagawa-4, Inage, Chiba, Chiba 263, JapanAbstract
An octupole magnet for experiments is designed toprove a scheme for expanding beam irradiation area withgood flatness. The length and maximum strength of theare 0.6m and 4000T/m3 , respecoctupole field
tively.

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1 Introduction
In charged particle radiotherapy for cancer, a wideand uniform irradiation area is required. To make wide
irradiation areas, the beam should be expanded. Buta beam expansion by quadrupole magnetic field is linear, which means that the structure of the expanded
beam is similar to that of the original one. Because thebeam structures have neither sharp edges nor uniform
distributions, an expansion field must have nonlinearity
to modify the beam structures. A leading component of
the magnetic field nonlinearity that is required to deforma gaussian beam structure is an octupole field[1].
A proof of principle experiment of this method in theHIMAC beam line is scheduled. Figure 1 shows the experimental beam line configuration. Specifications of an
octupole magnet designed for the experiment are listedin Table 1.
Table 1
Specifications of an octupole magnet
magnet length
bore radius
octupole strength -},B 111

Fig. 1 Experimental beam line configuration mHIMAC
This Bn notation is given from a general form of B(x, y)in bore:B:~:(x,y)- iB11 (x,y) = L)An + iBn)(x + iy)n.
nConsidering the symmetries of an octupole, we can selectx-axis to eliminate B:~:(x, 0) , and write down B 11 (x, 0)-En Bnxn. Further thein simple form: B 11 (x,O)
rotational symmetry for an octupole gives Bn = 0 at
n =F 3 mod 8. Thus main components of an octupole isB3 = t,B"', and distortion components are Bu, B1g, ....
The necessary excitation current N I is given by=0.6m
52mm
4000T/m3

2 Basic Consideration

1Constraints of the octupole magnet which were determined from experimental requirements and resource
availabilities were as follows:• Bore Radius: 52mm
• BaL = 2.4 x 103 Tfm2

• Power Source Limitation: 42V 390A
• Maximum Pole Thickness: 40mm
• Available Hollow Conductors: 6mm x 6mm (with3mm ¢for cooling channel), 7 x 7(4x 4), 8 x 8(4x 4)

Jl.o1roo1

B3 r 3dr=
4 - Bar6,Jl.owhere Jl.o and ro are vacuum permeability and bore radius, respectively. Then, the lower limit N I Lmin calculated from B 3 L becomes 3.5 X 103Am. NILmin• andpower source limitation determines the selection of conductors.
At first, in order to make full use of thepower source we shall use coil impedance Rcoil ofVma:~:/(8Ima:~:)[Ofcoi~ , where Vma:~: and Ima:~: are maximum rating of the available power supply. The coillength becomes greater than 2N L where N are the number of coil turns per pole. Thus the upper limit of NIL
IS

where pole thickness is indicated in Fig. 2, L is magnet
length, and Bn is weight of rn component in B(x, y).

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

where u and S are the conductivity of the coil and conductor cross section, respectively. Table 2 shows thisupper limit of hollow conductors with series connection.
These values do not include return connection at bothends, coil leadout, and design margin. For example theupper limit of NIL is reduced 10 percents by a condition: return connection length at both ends 40mm,
L = 400mm. To make enough margin, we should use
hollow conductors of 8 x 8(4 x 4).
Table 2The upper limit of NIL
Conductorlmmj
6 X 6(3</J)
7 X 7(4 X 4)
8 X 8(4 X 4)

SfulOfmj
7.3 X 10 .-.
6.4 X 10-4
4.4 X 10- 4

NILmao:lAmj
3.6 X 10.,
4.1 X 103
6.0 X 103

F'irstly we assume that the coil sapce can be filled byconductors without dead-space to consentrate the current around the pole tip. The magnet length L, strength
B3, and excitation current NI are 0.6m, 4000T/m3,and 5833A, respectively. To make 10 percent margin
for power line drop, and same margin for magnetic resistance of poles, we needed 18 turns per pole, namely
seoil min = 18 X 8 2 "" 1728mm2 • From this conditionw, h, and /2 are determined as 20mm, 117mm, 117mm,respectively.
Figure 3 shows a dependence of Bu/ Bs on parameters Rand w. Figure 4 shows a relation between Bmao:
and Bu/ Bs in above conditions. There is a trade-off
0.12 . . . . . - - - - , - - - - . - - - - , - - - - . - - - - . - - - - , . - - - - - ,~r.:: ~I

R-14mmlIIIIIIIII

1
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0.1

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The short distance between adjacent poles makes
large leakage flux. Considering the Ampere's low, thecurrent should be concentrated around the pole top as
high as possible. Large leakage flux pushs up the maximum magnetic field in the pole center plane, Bmao:· Incase iron poles are saturated with magnetic-flux, L shuld
be elongated for smaller B3.
To sum up, we should use hollow conductors of
8 X 8(4 X 4) to satisfy N I Lmin = 3.5 X 103 Am withenough margins. Pole design should be determined compromising iron saturation with magnet length.

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3 Practical Design

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R[mm]

We use circular poles to reduce machining costs.
Pole shapes are represented by 4 parameters-R, w, It, 12 which are shown in Fig. 2.

Fig. 3 R dependence of B 11 r 11 jB3 r 3 (r = 47mm) inseveral w. Condition: h = 12 = l17mm, B(r =50mm) =5kG-- -- ---

0.12

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1iIiIIIII-----i-------wl-22mm

I--------+--------i---------r-------~1--O.Ol!

1IIIIThe design optimization principles are as follows:IIIIIIII--------+--------4---------0.1)1Fig. 2 Tapered circular pole and its parameters:

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1 wlbclne~: Allah:',A·14mml

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BmiU<[kG]• make enough coil spaces

Fig. 4 Bmao:- B11r 11 /Bsr 3 (r = 47mm) relation inseveral (R, w). Condition: h = l2 = 117mm,B( r = 50mm) = 5kG• prevent iron saturation• suppress distortion components :Bu, B19, ...
Parameters 11 and 12 have strong dependence on coilspaces; then two parameters R and w are optimized preventing pole saturation and suppressing Bu/ B3.

between Bu/Ba and Bmao:·
Because real magnet coils with hollow conductors
have winding dead-space between conductors, the coilspace has to be expanded. Then the currenent spreads-400-The 11th Symposium on Accelerator Science and Technology, H arima Science Garden City, 1997

Table 3
Final specifications of an octupole magnet

out and the leakage flux increases, which makes BmtJII:
increase.
In order to reduce the winding dead-space of coils,
we selected a convenient parameter set:

Rmagnet length
bore radius
octupole strength Ba
hollow conductors
turn number N*
maximum current
weight= 27mm, w = 23mm, h = 138mm, l2 = 160mm.

Figure 5 shows a pole shape and a magnetic-flux cal-0.6m
52mm
4000T/m3
8mm x 8mm(4mm x 4nu:D.)
20turn/1coil
360A
650kg• N = 19turn/1coil u8ed in design calculatioori byPOISSON

Fig. 5 Final pole design and a magnetic-flux calculated by POISSON. Condition: R27mm, w
23mm, h138mm, 1;
162mm, N 19turn,B(r 50mm) 5kG*12 was modified from 160mm to avoid mesh problems

==

=

=

=

=

=

culated by POISSON, where the hollow conductors areapproximated by 10mm squares. POISSON calcula17.8kG, B 11 r 11 /B3 ,-3(r 47mm)
tion gives Bm 4~~:-7.0 x 10- 4 , and B 19 r 19 /B3 r3 (r47mm)-1.7 x10- 2 • Figure 6 shows errors between POISSON calculation and pure octupole in bore. Table 3 shows the final
magnet specifications which is shown Fig. 7.

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Mi'(mm]Fig. 6 Error of B between POISSON calculation andpure octupole.

is given by r 4 cos 40 = r~ which is used in early design.
The difference of pole tip shape should not be essential
for pole saturation ploblem.
At an excitation B3 of 400Cff/m3 , Bm4~~: for case
A was 17.8kG and that of case B was 21.8kG. This
result means that tapered pole is effective to prevent
pole saturation.

References

4 Discussion
Design of octupole magnets has serious saturationproblem by leakage flux. In order to verify an effect of
the tapered pole, we compared similar scale poles at thesame excitation. One is shown in Fig. 5{case A). The
other is a pole without both taper and dead-spaces ofcoil( case B). In case B, thickness and l2 are 40mm and170mm, respecti~ly. And the pole tip shape of case B[1] Kazuo HIRAMOTO, et al., "A Compact Proton
Synchrotron with a Combined Function Lattice Dedicated for Medical Use", Bulletin of the Institute for
Chemical Reserch, Kyoto University, Vol. 73, No. 1,
1995-401-