The II th Symposium on Accelerator Science and Technology, Harima Science Garden City, I997

Analysis of the Injection and Extraction Trajectories
in the RIKEN Superconducting Ring Cyclotron
Shiro FUJISHIMA, Hiroki OKUNO, Toshiharu TOMINAKA, Toshinori MITSUMOTO, Toshiyuki KUBO,Takeo KAWAGUCHI, Jong-Won KIM, Kumio IKEGAMI, Naruhiko SAKAMOTO, Kazuo SUGII,Tetsuya MORIKAWA, Yasushi TANAKA, Takesi WADA, Akira GOTO andY asushige YANOThe Institute Physical and Chemical Research (RIKEN),Wako, Saitama, 351-01 JAPANAbstract
Current status of the analysis of the injection andextraction trajectories in the RIKEN superconducting ring
cyclotron is described. The purpose of this analysis is tooptimize the layouts and specifications of the injection andextraction elements. For the optimization, differences oftrajectories in the elements and required fields of theelements are minimized. Beam envelopes are also studied toadjust the beam width.

trajectories between the beams also becomes maximum.
To minimize the bore of the elements, the difference oftrajectories must be suppressed as small as possible.
Table 1
Energies and magnetic rigidities of typical beams.

16 0 7+, (1)16 0 7+, (2)238 u 58+

1 Introduction
For the RIKEN RI Beam Factory project, a six-sector
superconducting ring cyclotron (SRC) is designed[1)[2]. The
SRC has strong stray fields from the sector magnets, andthese fields strongly depend on the condition of acceleration.
Thus, the trajectories of various beams differ very muchfrom each other. Besides, the injection and extraction
elements must be placed in small space limited with thesector magnets, the RF-cavities and the beam chambers.
These difficulties make the design of the injection andextraction systems challenging. The injection system
consists of four bending magnets (BM1, BM2, BM3 andBM4), three magnetic inflection channels (MICl, MIC2 andMIC3), and an electrostatic inflection channel (EIC). The
extraction system consists of a bending magnet (EBM),
three magnetic deflection channels (MDC 1, MDC2 andMDC3), and an electrostatic deflection channel (EDC)[3].

Energy [MeV/u]
Ext.
Inj.

B p [Tm]
Ext.
Inj.

74.2
126.7
58.0

2.89
3.83
4.57

200
400
150

4.90
7.25
7.52

4 Injection
Figure 1 shows schematic layout of the injection
elements and the injection trajectories of typical beams.
Table 2 shows specifications of the injection elements.
The MIC3, BM1, BM2, BM3 and BM4 aresuperconducting. Length of each element was determinedin consideration of balance between the difference oftrajectories in the element and required field of the element
Table 3 shows the differences of trajectories in theinjection elements.

2 Method of the Analysis
To analyzethe injection and extraction trajectories of theSRC, we modified a computer program originally developed
to analyze injection and extraction beam trajectories of theexisting four-sector normal-conducting RIKEN Ring
Cyclotron (RRC). In this computer program, a Lorentz
equation concerning the time is solved with Runge-KuttaGill method. Magnetic fields of the sector magnets used inthese analyses were calculated with a 3D-code "TOSCA".
Magnetic field of each element was added on the field of thesector magnets. Voltage of one RF-cavity was assumed tobe 460 kV at injection and 550 kV at extraction.

3 Property of the Beams
Table 1 shows energies and magnetic rigidities of typicalbeams. In the case of the oxygen beam of200MeV/nucleon(Ext.) and the uranium beam of150MeV/nucleon(Ext.), the difference of B p between thetwo beams becomes maximum, so that the difference ofFig.l Schematic layout of the injection elements
and the injection trajectories of typical beams.

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

Table 2Specifications of the injection elements.

EIC
MIC1
MIC2
MIC3
BM1
BM2
BM3
BM4

Radius[em]

Angle[deg.]

Length[em]BorEmaximumvariable
111
110
87
132
130.5
128492.5

variable
46.5
52.5
73.9
52.0
52.0
52.07.010090101112
120118116
6095 kV/cm
0.18 T
0.27T
1.5 T
4.02 T
3.92 T
3.96T-0.8,+0.7 T

40e200c

238 u 58+
1501607+:~8.

0120200...

<40-340-325-320

Radial position [ em ]Table 3Differences of trajectories in the injection elements.

Fig.2 Difference of trajectories in the EIC.

Difference [em]8495~

EIC(movable)
MIC1
MIC2
MIC3
BM1BM2
BM3
BM4

10
1.0
1.2
1.3
0.9
0.6
0.7
2.5~

t:Q

494

..!!
....0~'a1607+, 200493

i..!!

492.:::.,0491e

4.I Injection Elements
Figure 2 shows the difference of trajectories in the EIC.
The maximum change in the radius of the orbit is about 10em Accordingly, the EIC must be movable in the radial
direction by 10 em, and the radius of curvature of the EIC
should be adjustable in the range from about 10m to almost
infinity. The turn separation between the first equilibrium
orbits and the injection trajectories at the MIC1 is required
about 5 an to place the MICl. To give this turn separation,
the EIC is required to generate the maximum electrostatic
field of 95 kV/cm and to have the length of 1m.
The MIC1 gives the turn separation about 10 an for theMIC2. The MIC2 is required to give appropriate turnseparation about 25 an for the M1C3. The position of theMIC3 was determined in consideration of effective use of
background magnetic field by the sector magnet.
The edge size and width of the BMl are required as small
as possible, because the space to place the BMl is extremely
restricted by a yoke-link and a cryostat of the sector magnet.
Because of high field and small space, design of the BM 1 ismost challenging. The BM2 and BM3 have almost the same
specification as that of the BMl. The BM4 must accept
various beams corning from a pre-accelerator. The beams
come through a long valley with stray fields from the sector
magnets, so that the increment of the difference oftrajectories in the BM4 is inevitable. To minimize thedifference of trajectories, the BM4 generates not only
positive magnetic field but also negative one. Therefore, thedifference of trajectories in the BM4 can be less than 2.5 em
Figure 3 shows the difference of trajectories in the BM4.

238 u 58+, 150~.~

0490

228

Azimuth around the center of arc of the BM4 [degree]

Fig.3 Difference of trajectories in the BM4.

4.2 Injected Beam Envelopes
1.50

1.25

Ii]

1.00

0.75

0.50

0.25

0.00

05

101520length of the trajectory [m]Fig.4 Envelopes of the injected beam of uranium,
without gradient-field-coils.
Figure 4 shows the envelopes of the injected beam ofuranium. Emittance at the injection point was assumed tobe 10 p m·rad. The beam widens around the BM2, BM3
and BM4. To suppress the beam spread, we added gradientfield-coils generating 200 gauss/em at the maximum in-306-The II th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Table 4
Specifications of the extraction elem,ents.

the BM2 and in the BM3. Figure 5 shows the adjustedenvelopes of the injected beam.
1.50

1.25

8EDC
MDCI
MDC2
MDC3EBM

1.00~-50.75""....c0.50'0-~Radius[em]

Angle[deg.]

Length[em]BorEmaximumvariable
185
190
230
175

variable
32.0
32.0
30.0
52.0

199
103
106120159

100 kV/cm0.2 T0.3 T
1.12 T
3.9 T

Table 5Differences of trajectories in the extraction elements.

0.25

Difference [em]0.000510152025

10
0.6
0.6

EDC(movable)
MDCl
MDC2
MDC3EBM

length of the trajectory [m]Fig.5 Envelopes of the injected beam of uranium,
adjusted with gradient-field-coils.

1.2
1.1

5 Extraction
0.8

The extraction system is similar to the injection system,so that the extraction trajectories were analyzed in almost thesame way as for the injection trajectories. Figure 6 shows
schematic layout of the extraction elements and theextraction trajectories of typical beams. Table 4 shows
specifications of the extraction elements. The MDC3 andEBM are superconducting. Table 5 shows the differences oftrajectories in the extraction elements.
Figure 7 shows the envelopes of the extracted beam ofuranium. In consideration of adiabatic damping, emittance atthe extraction point was assumed to be 6.6 p m•rad. Widthof the extracted beam is small enough. Thus, additional
gradient-field-coil is not necessary.

0.6

8~

-5'00.4-~....c""
0.2

EDC

0.0

0510152025

length of the trajectory [m]Fig.7 Envelopes of the extracted beam of uranium.

6 Conclusion
Layout and specifications of the injection and extraction
elements of the SRC have almost been optimized. Furtheroptimization is in progress.

References[1] A.GOTO et al., "Superconducting Ring Cyclotron for
the RIKEN RI Beam Factory", in this proceedings.
[2] T.MITSUMOTO et al., "Orbit Analysis for theRIKEN Superconducting Ring Cyclotron", in thisproceedings.
[3] H.OKUNO et al., "Design Study of the Injection andExtraction systems for the RIKEN Superconducting
Ring Cyclotron", in this proceedings.

Fig.6 Schematic layout of the extraction elements
and the extraction trajectories of typical beams.

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