The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

FFAG(Fixed-field Alternating Gradient) Proton Synchrotron
Y.Mori, T.Adachi, K.Koba, S.Machida, R.Murarnatsu, C.Ohmori,I. Sakai, Y.Sato,M.Yoshii, KEK-Tanashi
R.Murarnatsu, Univ. of Tokyo
R.Ueno, M.Matoba,Kyusyu Univ., Fukuoka

K.Noda, M.Kanazawa, S.Yamada,
Abstract
Fixed field alternating gradient(FFAG) focusing is attractive for acceleration of high intensity hadron beams bec11use
acceleration cycle could be increased. The magnetic fieldof FFAG is static, therefore, the repetition rate of acceleration could be increased more than 10 times larger than thatof ordinary rapid cycling synchrotron(RCS) if an efficienthigh voltage RF accelerating system becomes available.
Recently, a new type of high gradient RF cavity (HGC) using high permeability magnetic alloy (MA) has been developed and FFAG synchrotron becomes very promising. Inorder to clarify the feasibility of rapid cycling FFAG synchrotron experimentally, proof-of-principle (POP) machine,which accelerates protons up to 1MeV with 1kHz repetition, is under development. We have also made several
designs on high intensity proton accelerators with FFAG
synchrotron for various applications such as spallation neutron source, proton driver for muon collider and accelerator
driven system(ADS) for energy breeder.

1 Introduction
High intensity medium energy ( 1Ge V- lOGe V ) proton
beams are required for many applications such as spallation neutron source, proton-driver for muon collider, accelerator-driven system (ADS) for nuclear energy production,etc. In these applications, large beam power of more than
1MW is requested. In order to realize such large beam
power with ordinary proton synchrotron, rapid cycling of
beam acceleration is inevitably. For example, an high intensity cyclotron with superconducting magnets has been
discussed for ADS as a possible candidate for the cyclic
accelerators. This is believed mostly because of the experience at the PSI cyclotron, which has obtained about morethan 1MW beams so far. As for a synchrotron, it has beenthought that it would be almost useless for ADS because
the operation is a pulsed mode and the average beam current is small. The magnetic field is time varying according
to beam acceleration in the synchrotron, the eddy-current
power loss in the magnets becomes serious when the repetition rate of the accelerating cycle is increased and themagnetic field ramping exceeds more than 200T/sec. On
the other hand, the accelerated particle number per pulse islimited by the space-charge effect. Practically, the maximum repetition of the rapid cycling synchrotron is limited
to be less than 50Hz or so. Therefore, the maximum available beam power would be at most about 1MW[l]. How-NIRS, Chiba

ever, the beam in the synchrotron is stable, because it isstrongly focused in the transverse and longitudinal directions, and the instantaneous beam current in the ring becomes very large. Fixed-field alternating gradient (FFAG)
synchrotron, thus, becomes attractive for this purpose.
Another issue is an electric power efficiency in operationof high intensity accelerator. For such large beam power
accelerator, the electric power required for operation increases to an acceptable level if the electric power efficiency
is small. The operational electric power efficiency of theaccelerator is defined by the ratio of the total beam power
to the total electric power requested for operation of thewhole accelerator system. The accelerator comprises
mainly the magnet and the rf accelerating systems. During operation, the 80-90% of the total electricity of the accelerator is dissipated for these two systems. The electric
power consumed by the magnet system can be dramaticallyreduced by using a superconducting technique, and can become negligibly small. On the other hand, the electric
power dissipated by the rf accelerating system would still
be an issue even if a superconducting rf system is applied.
A superconducting rf cavity system is inevitably essential
in a linear accelerator system to reduce the total rf power
requested for operation by increasing the effective shunt
impedance. On the other hand, for a cyclic accelerator,
such as cyclotron or synchrotron, the situation is more reluctant, because the cyclic accelerator is regarded as beinga very long accelerator. More than 50% electric power
efficiency seems to be possible in a cyclic accelerator, even
if the normal conducting rf cavity is used. In case of theordinary synchrotron, the eddy current loss becomes huge
if the repetition rate increases more than 10Hz, therefore,
the power efficiency can be very bad for the ordinary synchrotron. Since a superconducting maget could be used
for the FFAG synchrotron because the magnetic field isstatic, the power efficiency becomes pretty good .

2 FFAG focuding synchrotron
A fixed-field alternating gradinet(FFAG) synchrotron seems
to be very attractive for this purpose, because the repetition
rate of the accelerating cycle could be raised ten times ormore compared to that of the ordinary synchrotron. Theidea of a FFAG synchrotron was proposed independently
by Ohkawa[2], Symon[3] and Kolomensky[4] in the early
1950's, and electron-beam machines demonstrating thisprinciple have been successfully built in the MURA

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project.[3]In FFAG synchrotron, where the magnetic
field is constant in time, the shape of the magnetic fieldshould be such that the betatron tunes for both the horizontal and vertical planes should be constant for all closed orbit, and departing from all of the dangerous resonance lines.
The condition above is called " zero-chromaticity".

~(_!_)I
dp Ko=0iJ=const.

'~I=0.
iJ=const.

A magnetic field satisfying the scaling conditions describedabove must generally have the form ,where q is a spiral angle. If q is zero, the magnetic field
does not depend on 0, and the corresponding orbit points
are distributed on a radial vector. The type of having thismagnetic shape is called " radial sector". One the otherhand, if 0 behaves in a logarithmic manner, such asr0-qln-;,=const.,
lthe orbits remain geometrically similar, but move aroundthe beam center towards larger radii. This type is called "spiral sector".
The FFAG synchrotron is very attractive for acceleration
intense proton beams as described above and several proposals have been submited.[5][6] However, no practical
proton-beam machine has been built so far. One of themost difficult technical issues to realize a high-repetition
Table. I Fundamental parameters of l.SGeV FFAG synchrotron.
0.25 GeV
Injection Energy
1.5 GeV
Extraction Energy
5.5xl0 13ppp
Beam Intensity
750Hz
Repetition Rate6.6mA
Average Beam Current
No. of Sectors
16
Circumference Factor
2.68
Average Beam Radiusinjection
12.2m
extraction
13.4m
Magnetic Field
injection
0.536T
extractionl.ST
Field Index
10.5
Effective Field Index
3.9
Spiral Angle
64.6 deg
8.34 deg
Fractional Angle
Betatron oscillation tune
horizontal
3.73
vertical
3.23
3.442
Transition Gamma
0.56MV
Max. RF Voltage
RF Frequency
2.39MHz-3.3 MHz

FFAG synchrotron is rf acceleration. The requested accelerating rf voltage per one turn is~V=21t'(l+n{~)P.
Here, dr/ dt is the orbit excursion rate. In the case of al GeV
FFAG synchrotron with the repetition rate of 1kHz, the requested rf voltage becomes almost lMV. This is a rather
difficult number if an ordinary ferrite-loaded rf cavity isapplied, which has been conventionally used for the proton
synchrotron so far. In the ordinary ferrite-loaded rf cavity, the maximum accelerating field gradient is at most 10kV/m or so. Therefore, more than lOOm long straight sections are necessary for the rf cavities in the ring, although
the total circumference of the 1Ge V FFAG synchrotron
would be less than 150m.
Recently, a new type of highgradient rf cavity using a high-permeability magnetic alloy
has been developed at KEK for the JHF project, and a field
gradient of lOOkV/m has been successfully achieved. [7]Using this high-gradient cavity, the most difficult technicalissue in realizing a high-repetition FFAG synchrotron canbe solved.
A preliminary design of the l.SGeV and lOMW beam power
FFAG synchrotron has been carried out.[8] The fundamental parameters are listed in Table 1.
Design of magnet
8sectors - Triplet

Weight 0.9t(lcell)
7.2t(Total)~-----...J-"~~ ~!
...

@tnj.(r-750)

Fig.llitat.(r=ll50)

lMeV MOS proof-of-principle machie.

3 POP(Proof-of-principle) machine of 1MeVand 1-kHz FFAG synchrotron
In order to clarify the availability of very rapid cycling in
FFAG synchrotron, we have been developing a small POP(proof-of-principle) machine. In this POP machine, themaximum energy is limited to lMeV but the repetition rateof acceleration is 1kHz. The magnet configuration is aradial sector type and eight fold symmetry is chosen as
shown in Fig.l. Each sector consists of three dipole magnets which form a triplet focusing configuration
DFD(defocus-focus-defocus) and field index of each dipole
magnet is 2.5, respectively. The maximum magnetic fieldsof the focusing and defocusing dipole magnets are O.ST and0.2 T, respectively. The magnetic field configurations inthree dimensional directions are calculated with OPERA--82-The 12th Symposium on Accelerator Science and Technology, Wako, Japan 1999

Fig.5 Particle tracking simulation in longitudinal direction.

Fig.2 Magnetic field configuration calculated withOPERA-3D.
~allrl•l~ ,._ - ;... - · ' • " '3D (Fig. 2) and their results are used for beam tracking simulation. The average beam radius changes from 0.81m to
1.13m according to the increase of beam energy from
1OOkeV to l.lMeV. The half gap heights of the magnet atthe radius of0.75m and 1.15m are 73mm and 25 mm, respectively.
The betatron tunes for horizontal and vertical directions
are varied with field index and the product of the magnetic
field and the effective magnet length (Bl-product). Thelines in Fig. 3 show the variations of the betatron tunes forboth directions calculated with the SAD code. The design
values of betatron tunes for horizontal and vertical direc-Fig. 3 Betarton tune
diagra of lMeV POPtions are 2.25 and 1.35, respectively. The open squares
and circles in Fig. 3 show the betatron tunes for two different field indices of 2.5 and 2.0, respectively, which are obtained with beam tracking simulation for 3D magnetic field
configurations presented in Fig. 2. The betatron tunes areslightly different from those estimated by SAD and change
gradually during acceleration. The beam behaviors in thetransverse direction obtained by beam tracking simulation
are shown in Fig. 4. The rf frequency changes from0.85MHz to 2.05MHz. At the condition of the constantradial displacement as a function of time (dr/dt=const.), therf voltage has to be increased from l.lkV to 3.1kV. This
rf voltage can be easily obtained by a magnetic alloy(MA)The longitudinal beam motions calloaded rf cavity.[7]simulation are shown in Fig.5.
trackingbeambyculated

4 Conclusion
A 1.5GeV and lOMW fixed field alternating gradient(FFAG) focusing synchrotron has been designed. Although
the repetition rate for accelerating cycle is rather high, 750Hz, the required rf voltage is relatively small, only 580,
because of its small ring size. A lMeV POP(proof-of-principle) proton machine with 1kHz repetition is under development.

REFERENCESmachine ..
[l]lliF Accelerator Design Study Report, KEK Report 97-16.
[2] T.Ohkawa; Proc. of annual meeting of JPS (1953).
[3] K.R.Symon et al.;Phys. Rev. 103 (1956) 1837.
[4] A.A.Kolomensky et al.;ZhETF 33,298(1957).
[5] R.L.Kustom et al.;IEEE,NS-32,2672 (1985).
[6] H.Sasaki;GEMINI Design Report, KEK-Report (1985).
[7] Y. Mori, Proc. ofEPAC98, Stockholm, 1998, page 299.
[8] Y.Mori, Proc. of Thorium Fuel Cycle, Genshikaku Kenkyu, 43(1999)27.

Injection

Extraction

Fig. 4 Particle tracking simulation in transeverse direction.

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