The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

ULTRA-HIGH FIELD GRADIENT RF SYSTEMFOR PRISM-MUON BUNCH ROTATION
C. Ohmori, Y. Mori, KEK, Tsukuba, JapanY. Iwashita, Kyoto Univ. Kyoto, Japan
S. Ninomiya, RCNP, Osaka Univ, Osaka, Japan
M. Aoki, Y. Arimoto, Y. Kuno, A. Sato, M. Yoshida, Osaka Univ., Osaka, Japan
Abstract
PRISM is a project to produce a high quality, highpurity and high intensity muon beam by the bunchrotation technique in FFAG synchrotron using ultra-highfield gradient RF systems. The system to achieve the field
gradient of 200-300 kV/m at 5 MHz is designed andunder construction.

than an ordinary sinusoidal wave. Figure 3 shows apreliminary result for the bunch rotation in the phasespace. It shows that the particles which have ±20 %spread will be rotated and the final momentum after 4
turns is less than ±5 %. In case of the optimum energy
and RF voltage shape, the final momentum spread of ±3%
will be obtained for initial spread of ± 30 %.

INTRODUCTION

Fig. 1. Schematic layout of PRISM.
Wave Comp.
E(kV)

wave136.dat

300
200
1000-100

2000-200-300-100

E = 350.0 sin( π1 x / L + -0.1530)-50050phase(nsec)100

Wave Comp.
E(kV)

E(kV)

1500

300
200
1000-100-200

1000-300-100

E = -275.1 sin( 2π x / L + -0.6583)
-50

050

100phase(nsec)

E(kV)

Wave Comp.

300
200

500

1000-100-200-300-1000

E = 350.0 sin( π1 x / L + -0.1530)-50

050100phase(nsec)

E(kV)

Wave Comp.

300
200
1000-500-100-200-300-100

E = 350.0 sin( 1 π x / L + -0.1530)
E = -275.1 sin( 2 π x / L + -0.6583)

E(kV)

-1000

-50050100phase(nsec)

300
200

E = 350.0 sin( 1 π x / L + -0.1530)

1000-100

E = -275.1 sin( 2 π x / L + -0.6583)

-1500
-2000
-100

E = -275.1 sin( 2π x / L + -0.6583)

Wave Comp.

-200
-300

E = 350.0 sin( 1 π x / L + -0.1530)
E = 249.8 sin( 3 π x / L + -0.9613)-100

E = 350.0 sin( π1 x / L + -0.1530)
-50

050

100
phase(nsec)

Wave Comp.
E(kV)

PRISM [1] is an experimental proposal for constructionof a highly intense muon source based on a novel idea ofphase rotation in a FFAG synchrotron. PRISM stands for
Phase Rotated Intense Slow Muon source. It would
provide a muon beam having an intensity of about 10111012 µ/sec, a narrow momentum width of a few % and nopion contamination. The energy of the PRISM beam isrelatively low (20 MeV in kinetic energy), since it isaimed to be used for stopped muon experiments ingeneral.
PRISM will use a pulsed proton beam from the J-PARC
50 GeV proton synchrotron [2] by fast extraction.
Experimental apparatus and PRISM will be placed at a
proposed pulsed proton beam facility which is notincluded in the Phase I plan of J-PARC.
PRISM consists of• a pulsed proton beam to produce a short pion
pulsed beam,• a pion capture system with large-solid angle by ahigh selenoidal magnetic field,• a pion decay and muon transport system in a longsolenoid magnet of about 10 m long,• and a phase rotation system which accelerates
slow muons and decelerate fast muons by an RFfield.
Schematic layout of PRISM is shown in Fig. 1. One offeatures of PRISM is to do phase rotation at a Fixed-Field
Alternating Gradient synchrotron (FFAG), which has
several advantages, such as a large momentum acceptance.
Because of a short life time of muons, the bunch rotation
should end in 5 turns (1 µs) and RF voltage of 2-3 MV isrequired.
To obtain the beam which has a small momentum
spread after the rotation, the shape of RF voltage isimportant. Figure 2 shows the proposed saw tooth like RF
voltage [3]. In case of the saw tooth RF voltage, theparticle motion in the longitudinal phase space is linear
and angular speed of rotation is constant. The otheradvantage of saw tooth RF is that it has larger acceptance

300200100-50050100phase(nsec)

0-100-200-300-100

E = 249.8 sin( π3 x / L + -0.9613)-50

050100phase(nsec)

Fig. 2. Saw-tooth-like RF voltage. The bold line is thesum of three harmonics(thin lines), H=1, H=2 and H=3 .

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 20031 0234Fig. 3. Bunch rotation in case of saw-tooth-like RFvoltage. Test particles which have different initialmomentum and phase are tracked. The initial beamincludes the bunch width of initial proton beam (± 5 ns).

RF SYSTEM

is possible to design it as a wide band system [6]. By
choosing the optimum air gap of cut core and minimising
the gap capacitance, it is possible to change the quality
factor of the cavity at the fixed frequency. We are also
considering the dual harmonic operation of RF system byminimising the air gap.
The cavity will be driven by push-pull amplifiers using
tetrode tubes, 4CW150,000E. The tube can be used at thehigh DC voltage of 40kV and RF current of 60 A ispossible to generate. In case of 1 kΩ cavity impedance, 60
kV will be available as a gap voltage.
To achieve the required field gradient, we also adopt
the ultra-thin cavity design. The 1 m cavity consists of 4gaps and each gap has 4 MA cores. Two sets of cavity are
installed in a straight section as shown in Fig. 4. The sideand front views of two cavities are shown in Fig. 5. Eachgap generates the RF voltage of ± 25-37.5 kV and isdriven by two bus bars which are connected to a RFamplifier. To drive 4 gaps in a cavity, 4 push-pull
amplifiers are used. Two amplifiers are located above thecavities and others are set below it.

High Field Gradient
PRISM requires very high field gradient of 200-300
kV/m at the low frequency (5 MHz). To realize such agradient, we have solved following problems;• Magnetic core:Magnetic Alloy• Way to drive the cavity: Tetrode tube which standfor 40 kV operation• Length of cavity : 25 m/gap.
Magnetic alloy (MA) cavity [4] has been employed.
One of advantages of MA is that the characteristics isstable at the high rf field. Figure 4 shows thecharacteristics of magnetic cores [5]. Ferrites are thematerial which is used in some accelerators, however,they show the impedance change at the high RF field. Incase of MA, the characteristics are constant at therequired magnetic field for PRISM (320-490 Gauss).
Characteristics of Magnetic Material
ferrite A
ferrite B
ferrite CMA(small core)
MA(large core)

upQf

1.00E+11

1.00E+10

Table 1: Parameters of PRISM cavities
Number of cavities

12

Number of gap per cavity

4Length of cavity

1mCore material

Magnetic Alloy

Core size

1.4 m X 1.0 m X 3.5 cm

Core shape

Racetrack

Number of cores16/cavity

RF frequency

5 MHz

Required field gradient

200 kV/m

Flux density in core

320 Gauss

Duty<0.1% (15 µs X 100 /3.4sec)

Racetrack Core
Because of a large horizontal physical aperture ofFFAG, the racetrack shape for MA core is adopted. In caseof racetrack and rectangular shapes, the shunt impedanceof a core is given by the following equation,

R p = µ0 µ p Qf ln(L2 /L1)t
1.00E+09
1101001000

10000

where L2 and L1 mean the inner and outer circumferencesof the racetrack core.

Brf (Gauss)

Table 2: Parameters of Racetrack coreFig. 4. Characteristics of magnetic cores. Solid lines mean
MA cores with different size. Dashed lines are ferrite
cores.
To resonate at 5 MHz, the cut core configuration [6]will be used to reduce the large core inductance to theoptimum value. Another advantage of MA cavity is that it(1)Inner size

74 cm X 34 cm

Outer/Inner circumference

3942mm/1868 mmµQf @ 5MHz (design value)

5.5 X 109

Shunt Impedance> 180 Ω/coreThe 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

Power AMP system
Because of low duty factor, the push-pull operation of
the tubes, 4CW150.000E, will generate the maximum RF
power of 1.8 MW. Operation of the power amplifier wasanalysed using a typical constant current characteristics ofthe tube. During the high power period, the cathode peakand DC currents will be 120 A and 40 A, respectively. Togenerate the RF current of 60 A, the required voltage
swing on the control grid is about 700 V. To drive thepower amplifier, 1.5 kW solid state amplifier isconsidered. In case of the narrow band operation togenerate only 5 MHz at the gap, the control grid circuit
will have a narrow band impedance and 1:3 step up
transformer will be used. In case of the dual harmonic
operation, the driving circuit is under consideration.
The anode power supply is designed to be suitable forthe pulse power operation. The maximum current is 400 A
for 15 µs pulse duration to supply 4 sets of the amplifiers.
Although the peak power of 12.8 MW is necessary for 4
AMP systems, the average power is below 10 kW. The
required power is stored in 4 high voltage capacitors. To
protect the tubes from the destruction by sparking,crowbar circuit is used.
The filament, control grid and screen grid power
supplies for 4 amplifiers are installed in an auxiliary unit.
The control grid power supply has a function to add thevoltage of 150 V in short time. By this function, we canchoose the class AB operation although the idling tube
cathode current during off-operation is almost 0 A.
Table 3: Parameters of AMP system
Operation mode of tube

Push-pull, class AB

Number of tubes per AMP

2Size of AMP

1.35 m X 0.8 m X 0.7 m

Tetrode4CW150,000E

Max. RF current

60 A

Max. cathode current (DC)50 A

Max. plate voltage

40 kV

Max. RF power

1.8 MW

CONCLUSIONSThe RF system for the PRISM project has been designed.
The amplifier system is now under construction and will
be tested using a test cavity at the RCNP, Osakauniversity in this winter. The ultra-thin RF cavity will betested in the next year.

Fig. 5. Side(left) and front(right) views of RF system

REFERENCES[1] Letter of Intent to the J-PARC 50 GeV Proton
Synchrotron Experiments, (LOI-24, 26)[2] The Joint Projct Team of JAERI and KEK, KEKReport 99-4, JAERI Tech. 99-059.
[3] M. Yamamoto et al., “Multi-Harmonic Acceleration
with High Gradient MA Loaded Cavity”, PAC99[4] C. Ohmori et al., “A Wide Band RF Cavity for JHF
Synchrotrons”, PAC97.
[5] M. Fujieda et al., “Studies of Magnetic Cores for JHF
Synchrotrons”, PAC97.
[6] C. Ohmori et al., “High Field Gradient Cavity loadedwith MA for Synchrotrons”, PAC99 (Invited).