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

Orbit Analysis for the RIKEN Superconducting Ring Cyclotron
Toshinori MITSUMOTO, Akira GOTO, Takeo KAWAGUCHI, Jong-Won KIM, Yasushi TANAKA,Toshiyuki KUBO, Hiroki OKUNO, Toshiharu TOMINAKA, Shiro FUJISHIMA, Kumio IKEGAMI,Naruhiko SAKAMOTO, Tetsuya MORIKAWA, Shigeru YOKOUCHI, Kazuo SUGII and Yasushige YANOThe Institute of Physical and Chemical Research (RIKEN)
2-1, Hirosawa, Wako-shi, Saitama 351-01, Japan
Abstract
An "RI beam factory" has started to be constructedas the next project of the RIKEN Accelerator Research
Facility (RARF)[1]. The "RI beam factory" aims atproduction and acceleration of radioactive isotope beams
covering the whole mass region. It requires the energy ofion beam to be higher than 100 MeV/nucleon. To
accomplish this requirement, the following two ring
cyclotrons have been adopted as post-accelerators of theexisting RIKEN Ring Cyclotron (RRC): a 4-sector ring
cyclotron for the first stage (IRC) and a 6-sector
superconducting ring cyclotron for the second stage(SRC)[2], The sector magnet of the SRC has to be flexible
enough to generate isochronous fields in a wide range ofenergies and for various q/A values. In this report wedescribe the isochronous field generation and orbitanalysisof the SRC,

SRC. Six sector magnets, three main resonators, one
flattop resonator and injection and extraction devices.
together with injection and extraction orbits are displayed.
Table 1Main parameters of the SRC
Number of sectors
Harmonics
injection
Mean radius
extraction
Orbit frequency

66
3.56m
5.36m
3.00- 6.35 MHzSector

Magnet1 Introduction
The maximum acceleration energy of the SRC wasdetermined by experimental requirements. The SRC isexpected to boost the energy of ion beam up to 400
MeV/nucleon for light heavy ions like carbon and 150
MeV/nucleon for very heavy ions like uranium. Beamcurrent is expected to be more than 100 pjlA for light heavy
ions and about 0.2 pjlA for 150 MeV/nucleon uranium
ions. Figure 1 shows the region of expected ions from theSRC (grey area) and typical ions (white circle).
Main parameters of the SRC are listed in Table 1.
Velocity gain factor is 1.51. Figure 2 shows a layout of theFig. 2 Layout of the SRC.
400

2 Isochronous field generation'20" 300'0-E=>

e">- 200e.'l"c:: 100

Ul000.1

0.2

0.3

0.4

q/AFig. 1 Performance expected for the SRC.

0.5

The maximum magnetic field is required for theacceleration of 150 MeV/nucleon 238 U58 +. The magnetic
field of the sector magnet is 4.0 T at the injection and 4.3 Tat the extraction. In the case of 400 MeV/nucleon 160 7+, themagnetic field is 3.3 T at the injection, and 4.1 T atextraction side.
In order to realize the high magnetic field andvarious magnetic inclinations, the sector magnet of the SRC
has a set of superconducting main coils for base field
generation, five sets of superconducting trim coils forcoarse fitting to the isochronous field and about 20 sets of-487-

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

normal conducting trim coils for fine adjustment to theisochronous field. Magnetic field distribution is calculatedby three dimensional code TOSCA[3].

1.60
1.58
1.56>.

g

2.1 Pole and superconducting main coil
Size of the superconducting main coil is 284 mm(width) x 310 mm (height). The maximum excitation
current is 6 MA for one sector magnet (two coils). Thesuperconducting main coil is installed inside a He vessel
made of stainless steel which is tightly fixed to the cold
pole. Pole gap is 380 mm[ 4].
Sector angle of the pol~ is 25 degree at injection
side. From the middle of the radial direction, the pole shape
has a curvature in order to increase the. axial betatronfrequency Vz at the extraction side.
Construction of a 1/lscale model of the pole and themain coil is started[5].
2.2 Yoke
Stray field in the valley region is used in order toincrease axial focusing force. Distribution of the stray field
is affected by the shape of the yoke. Thus by modificationof the shape of the yoke, axial betatron frequencies can becontrolled. Figure 3 shows original yoke shape (upper) andmodified one (lower). The axial betatron frequency has themaximum value in the case of acceleration for 150 MeV/nucleon 238U58+, which is around the resonance line ofvz =Fig. 3 Two yoke shapes of a quarter part is displayed:original (upper) and modified (lower).

!
j]

1.54
1.52
1.50
1.48
1.46
1.44

Original shape"\~
Modified shape

1.42
1.40 !-:-":"+.:""":"+.:--:-!:::"""':~""':""!~~"""!""!~':""!-::~~-:-:!
1.14 1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.30 1.32 1.34

Radial betatron frequency

Fig. 4 Working paths of radial and axial betatronfrequencies for two different yoke shapes for 150
MeV/nucleon 238U 58+ ions.
1.5. By this modification, the maximum axial betatronfrequency decrease by 0.05 (Fig.4) without decrease of theminimum axial betatron frequency in the case for 400
MeV/nucleon 12C6+, which is near the resonance line of
Vz=l. Optimization of the yoke shape is under way, taking
mechanical design into consideration.
2.3 Superconducting trim coil
Five sets of superconducting trim coils are placed on
the inner surface of the cold pole. Two sets at the extraction
side have current returns at the extraction side, which are
not wound along beam orbits but just straight in the beam
region in order to avoid concave curvature of conductors.
The other three sets have current returns at the injection
side. Schematic view of the superconducting trim coils isshown in Fig. 5. The first coil on the injection orbit iswound along beam orbit, then it gradually becomes straight
towards the extraction side.
Using the five sets of superconducting trim coils, it
is possible to adjust various distributions of isochronous
fields within ±0.1 %.

Fig. 5 Configuration of the superconductin g trim coils.
Two of five sets have current returns at theextraction side and the others have current returns
at the injection side.

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

2.4 Normal conducting trim coil

Normal conducting trim coils are used for fineadjustment to the isochronous field. We plan to use about
20 coils at acceleration region and one or two more coils at
injection and extraction regions.
The maximum current of each coil is considered to
be 500 A. By using the normal conducting trim coils,
errors from isochronous condition becomes less than ±0.01%. Schematic layout of the normal trim coils with the poleis shown in Fig. 7. The conductor is shaped along the beamorbit. Cross-sectional view around the symmetry plane of
the magnet is shown Fig. 8. The wall of beam chamber isused in common as the wall of the cryostat. The normal
conducting trim coils are put in the wall.

Vr - Vz diagram. Figure 8 shows the working paths oftypical ions. All the working paths are between theresonance lines of Vz=l and Vz=l.5. But some of them areclose to the resonances. In the case that the extractionenergy higher than 300 MeV/nucleon, the working pathcrosses vr=1.5 line. Detail study is in progress.
1.7...--'""T""---..~--r----r--T"""---r----,

1.6>..

(,)

1:::
0

1.5'---'(1);::l0"
0<.1:::
1:::

1.4

(2)

e(;:j 1.3

(3)

0.0

Ol 1.2

(4)

':;(

< 1.1
l.Oi::---~-~.&:--"":"'::~'""""':..1.:---:-'::--'""""':~--:-'

1.0

l.l

1.2

1.3

1.4

1.5

1.6

1.7

Radial betatron frequency
Fig. 8 Working paths of the radial and axial betatronfrequencies of typical ions for the SRC:
(1) 150 MeV/nucleon 238 U58+,(2) 400 MeV /nucleon 160 7+,(3) 400 MeV/nucleon 12C6+ and(4) 200 MeV/nucleon 160 7+.

4 SummaryFig. 6 Schematic layout of normal conducting trim coils.
Current returns of the coils are not shown in thisfigure, but will be put at the extraction side.

Design study of the sector magnet and orbit analysis
for the SRC for the RIKEN RI beam factory has been
carried out. Combination of the superconducting main coil,superconducting trim coils and normal conducting trimcoils can generate isochronous field for various ions within±0.01 % errors to the isochronous condition. The axial
betatron frequency is set between 1.0 and 1.5 in order toavoid crossing the Vz=1 and Vz=l.5 resonance lines.
Estimation of the risk that working paths lie near theresonance lines and further optimization are under way.

References

Fig. 7 Cross-sectional view around the symmetry plane ofthe pole.
The vertical position of thesuperconducting trim coils is 160 mm from thecenter and that of normal trim coils is 55 mm.

3 Orbit analysis
Working paths of radial and axial betatronfrequencies for the SRC are spread in a wide region of the[1] Y. Yano et at., "Progress ofRIKENRIBeamFactory
Project", Proc. 1996 European Part. Accel. Conf., Sitges(Barcelona) (1996) 536.
[2] A. Goto et al., "Superconducting Ring Cyclotron for theRIKEN RI Beam Factory", this meeting.
[3] Vector Field Limited. Oxford, England.
[4] T. Kawaguchi et al.,"Design of the Sector Magnets for
the RIKEN Superconducting Ring Cyclotron", Proc.
1997 Part. Accel. Conf., Vancouver, to be published.
[5] T. Kubo et al.,"Design of a Model Sector Magnet for
the RIKEN Superconducting Ring Cyclotron", thismeeting.

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