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

Orbit Studies on Pre-extraction for the RIKEN Superconductin g Ring Cyclotron
Jong-Won Kim, Toshinori MITSUMOTO, Akira GOTO, Hiroki OKUNO, Toshiharu TOMINAKA,Toshiyuki KUBO, Takeo KAWAGUCHI, Shiro FUJISHIMA Kumio IKEGAMI, Naruhiko SAKAMOTO,Shigeru YOKOUCHI, Kazuo SUGII, Tetsuya MORIKAWA, Yasushi TANAKA, and Yasushige YANOThe Institute of Physical and Chemical Research (RIKEN)
2-1, Hirosawa, Wako-shi, Saitama 351-01, JapanAbstract
A six-sector superconducting ring cyclotron has been
designed as a primary accelerator in the RIKEN RI
beam factory project. As for the design of sector magnet
and main cyclotron components, significant progress has
been made and reported previously. With those results
obtained we now undertake detailed study of beam optics to further optimize our design. In the orbit study
a main issue is to reduce beam losses throughout injection, acceleration, and extraction processes. A method
called off-centered injection would be used to enhance
the turn separation in front of the extraction channel,
which will allow a single turn extraction. A care has
been taken in the injection region to avoid losses dueto this off-centering. Since the SRC is designed not tocross any dangerous resonances, this method works well.
The magnetic field map used in calculations includes thestray fields from injection and extraction magnets for amore realistic evaluation. Some preliminary results aregiven in this report.
1 Introduction
The six-sector superconducting ring cyclotron (SRC)
which is under design at RIKEN as a booster of theexisting ring cyclotron (RRC), will accelerate heavy ionsto produce radioactive ion beams by the technique of theprojectile fragmentation [I]. Since the primary beam isaccelerated up to 400 MeV ju and the current is in therange of hundred particle micro amps for light ions, one
major design issue is to avoid beam loss which leads toheating and activation of cyclotron components. A seriesof orbit computations is under way to simulate the beam
dynamics in order to achieve zero beam loss.
The beam loss occurs predominantly during the injection and extraction processes. In addition, to reduce
the extraction loss the beam .quality should not be deteriorated during acceleration. The sector magnet of theSRC is designed not to cross serious resonances that cancause beam emittance growth [2].
The turn separation by acceleration is not large
enough for single turn extraction especially for lightions, so that a mechanism to enhance turn separationis needed. As demonstrated in the RRC and other ring
cyclotrons, the off-centered injection appears to be very
effective [3][4]. We resort to this method to achieve sufficient turn separation even for light ions. On the otherhand, injection loss can occur due to the off-centering of
the beam in the first turns. Orbit tracking was carriedout to ensure the clearing the injection elements by afinite emittance beam.
When a single-frequency rf system is employed, thephase acceptance is very narrow [5]. For instance, in
our case the increase of beam size at extraction is unacceptable when the initial phase width is larger than 5 rf
degrees. A use of flat-topping cavity is being considered
to ease this requirement.
2 Single Turn Extraction
Since the SRC is a high-energy and high-current cyclotron, a single turn extraction should be achieved with
100 % efficiency in order to avoid beam loss on the extraction elements. The last turn needs to be well separated in front of the extraction septum. If the beam
does not precess, the turn separation is determined byacceleration, which mainly depends on the energy gain
per turn and the radial focusing frequency (vr) as thefinal beam energy and the extraction radius are fixed.
For the SRC having six sectors, three cavities will beused with double gaps or a single gap. The properties ofboth kinds of cavities are currently under investigation.
We assumed in the present calculation the voltage gain
per turn to be 1.62 MV, considering the performance of
the RRC cavities. The design particle is 16 07+, accelerating from 126.6 MeV ju to 400 MeV /u, which imposes
the most stringent condition on turn separation. The Vr
is 1.62 at 400 MeV /u, and the resulting turn separationby acceleration is only 2 mm.
The radial beam width at extraction is roughly determined by the transverse and the longitudinal emittances. The transverse emittance from the RRC isapproximately known to be 10 mm·mrad. This value
is used because the injection energies to the SRC for
light ions are similar to the current extraction energies
from the RRC. The beam energy spread used is ±0.05%(ilE/E). The radial beam width calculated with these
conditions is about 5 mm at the entrance of the electrostatic deflection channel (EDC). A stronger restriction
lies on the phase width of the beam bunch. In the caseof using a single frequency rf, a small phase width is arequisite for the single turn extraction. The use of thethird harmonic flat-topping is under consideration. Fig.
1 shows the radial beam spread at 400 MeV /u as a function of the initial rf phase for the single frequency andthe flat-topping cases. As can be seen in the figure, aphase width less than 5 rf degrees is required to keep
the additional radial beam spread within 2 mm for thesingle frequency case. With addition of a flat-topping
cavity, the phase acceptance becomes larger than 30 rf
degrees. In the present calculations the flat-topping isassumed.
Orbit calculations have been carried out to evaluate
the beam behavior throughout the acceleration process.
The code SPRGAP was used, which integrates orbits in-288-

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

126.05

499.5

"0.
0>

lu
499.0
0wQ)

~~3

126.00

UJ(L125.95+-'

0.-----.._

498.5

1+--.--.--.--.--.~+E

u..._____.,

327.0

327.2

327.4

327.6

r (em)

327.8

328.0

328.2

125.90 +---~-------------17.
3-1-51115¢(degree)

498.0
497.5
4 9 7. 0 +---,----'-----T----.------,-----.-----,----l---l15 201050-15 -10 -5¢.(degree)
IFig. 1 Radial beam spread at the entrance of the EDC
as a function of starting rf phase for single frequency and flat topping cases.
the magnetic fields [6). The magnetic field used allows
the phase excursion of 20°. On the other hand, using a
combination of superconducting and normal trim coils,
the excursion can be reduced to about 10° [7). This difference, however, does not yield different optics behaviorsince flat-topping is assumed.
The turn separation can be enhanced by accelerating ions with off-centered injection. As demonstrated
at the RRC, one method to induce off-centering is bycontrolling the voltage of electrostatic inflector channel(EIC). Orbit calculations have been made to simulate
this mechanism, first in a perfect six-fold symmetricfield. A four-dimensional phase space is used as an initial phase space, which has a coupling between radial
and longitudinal phase spaces. A coupling with axial
phase space was not included because that coupling isnot strong. The initial phase space at the center of EIC
is shown in the upper part of Fig. 2. One thousand
particles are randomly generated to fill the eigen-ellipse.
In the lower part, the radial phase spaces are shown forthe last two turns. A sufficient turn separation appears
to be obtained.
The magnetic field of the real SRC does not have aperfect six-fold symmetry because of disturbance by theinjection and extraction elements. Near the injection region harmonic trim coils are located to compensate forthese stray fields. In fact, off-centering can be controlledwith the harmonic coils, but this effect is not fully investigated yet.
To generate the field map of the sector magnet, theprogram TOSCA [8) has been used. Using this program,
however, it is rather difficult to obtain sufficiently accurate results when all perturbing elements· are included
with no symmetry condition applied. On the other hand,
there is an advantage in the field calculation of highFig. 2 Upper: the initial radial and longitudinal
phase spaces which are coupled. Lower: thefinal radial phase spaces of the last two turns
in front of the EDC.
field superconducting magnets with saturated iron poles:
a perturbing field may be independently calculated assuming an air-core case, and added to the main field
map. The actual current distribution of the injection
and the extraction elements is rather complicated [9].
Instead of including all conductors, a single coil configuration is employed for each magnet. This approximationis thought to be reasonable since weuse only the strayfield of the magnets. Fig. 3 shows the Fourier components of the stray field as a function of radius, and theazimuthal distribution at two radii. The field amplitude
by the injection element is 50 gauss at the radius of 370
em, while the amplitude by the extraction element is 30
gauss near the last turn. As can be seen in the figure theamplitudes of the stray fields are assumed to be the sameat given radii for each injection and extraction element,respectively. More realistic calculations will follow.
Orbit calculations are performed to ensure the turnseparation at extraction when all perturbing fields areincluded. In Fig. 4, the radial phase spaces are plotted
for the last turns. Again the last turn is clearly separated. This is also a case when the voltage of the EIC isadjusted to optimize the last turn separation.

3 Injection Loss Investigation
When the beam is well centered, the amplitude ofcoherent radial oscillation is minimized. However, since
we use off-centered injection method, coherent oscillation is inevitably induced, and its amplitude depends on
the perturbation strength. The initial turns were carefully observed to look into beam hitting on the injection-289-

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

40+---L--L~-L--~--+-Injection
50 - - Extraction

35- - 1st harmonic30--

3rd harmonic.
62o-- -

5rd harmonic'(;)25

40

~ "30

~ 20 I
I~~m 15m

10 1

105l

o+-~~~~--~--~-4360

400

440

480

R (em)

520

560-10 +--.--.---.-~,----.--+
060 120 180 240 300 360
Azimuth (degree)

Fig. 3 Right: azimuthal distribution of the strayfields. The amplitude is 50 gauss at the radius of 370 em, and 30 gauss at 550 em. Left:
Fourier components of the stray field as a function of radius.
3+---~----~--~----~--~----L___--+_ L_ _-400-300-200-1000100200300400

Radius (em)~"010loX(]_-1-20Fig. 5 Trajectory of inner radius of a finite emittancebeam for the first five turns. The beam clears
the MIC 1 which is located nearest to thebeam.

-3+----.----.----,----,----,----,-----,-----+
498.0

498.5

499.0

499.5

500.0

500.5

501.0

501.5

502.0

R (em)

Fig. 4 Radial phase spaces for the last few turns. The
last turn is well separated from the previous
turn by controlling the voltage of the EIC.
elements, since the present magnet locations were determined assuming centered injection.
Fig. 5 shows the first five turns when the orbit isstarted at the middle of the EIC. The trajectory shownin the figure is the inner radius of the beam. Comparedto the centered injection case, the radial clearance tothe MIC 1 is actually increased by 5 mm for 16 07+.
Because the MIC 1 is not located at the azimuth where
the peak oscillation amplitude appears, there seems tobe no serious problem in avoiding the injection loss for
all ions.
Although it is possible to analytically interpret thisoff-centering effect, different harmonic components ofthe stray field make such an analysis rather complicated.
Numerical orbit computations have mainly been used.
At present we have considered the case that the strayfield is not corrected by the harmonic trim coils. Detailed analysis will be needed to optimize the harmonic
coil design and the strength of the stray field.
4 Conclusion

In order to obtain a sufficient turn separation at extraction, ions will be accelerated with off-centering atinjection. In the simulation, it is shown that the voltageof the EIC can be controlled to induce the proper separation of the last turn, even in the presence of uncorrected
stray fields from injection and extraction elements.. Inaddition, this off-centering seems not to cause interference with the injection elements by the first turn. The
effect of the harmonic trim coils has not been considered yet. Further refinements on the simulation will bepursued.
References[1) Y. Yano et al., "RIKEN RI Beam Factory Project",
Proc. of 1997 Partl. Accel. Conf., in press[2) T. Mitsumoto et al., "Orbit Analysis for the RIKENSuperconducting Ring Cyclotron", this meeting[3) Y. Yano, "Status Report on RIKEN Accelerator Research Facility", The 8th Sympo. on Accel. Sci. andTech., Saitama, Japan (1991) 10[4) W. Joho, S. Adam, "Setting up the SIN 590 MeVRing Cyclotron for Single Turn Extraction", IEEE
Trans. on Nucl. Sci., NS-26, No. 2, April (1979) 2358
[5) M. M. Gordon, "Single Turn Extraction", IEEE
Trans. on Nucl. Sci., NS-13 (1966) 48[6) M. M. Gordon, "Effects of Spiral Electric Gaps inSuperconducting Cyclotrons", NIM 169 (1980) 327[7) J. W. Kim et al., "Trim Coil System for the RIKENSuperconducting Ring Cyclotron", Proc. of 1997
Partl. Accel. Conf., in press[8) Vector Field Limited, Oxford, England[9) S. Fujishima et al., "Numerical Analyses of the Injection and Extraction Trajectories for the RIKEN Superconducting Ring Cyclotron", Proc. of 1997 Partl.
Accel. Conf., in press-290-