FFAG as a phase rotatorfor the PRISM project

A. Sato, M. Aoki, Y. Arimoto, Y. Kuno, M. Yoshida, Osaka University

S. Machida, Y. Mori, C. Ohmori, T. Yokoi, K. Yoshimura, KEK

Y. Iwashita, Kyoto ICRS. Ninomiya, RCNP

Physics motivation

10- 1 4

10- 1 2

10- 1 0

10- 8

10- 6

10- 4

10- 2

1940 1950 1960 1970 1980 1990 2000

Upper limits of Branching Ratio

Y e a r

KL0 → µe

K+ →πµe

µA→eA

µ→ eee

µ→ eγ

History of LFV Search limits

Search for the Lepton Flavor Violating Process

Future experiment will cover most of parameter space with PRISM

One of the important particle physics topics achievable with PRISM is a search for lepton-flavor violating muon rare processes. Lepton flavor violation attracts much attention, theoretically and experimentally, since it would have a large discovery potential to new physics beyond the Standard Model, for instance supersymmetric extension to the Standard Model. An example of proposed experiments of such at PRISM is a search for μ−−e− conversion process in a muonic atom at a sensitivity of 10^-18.

Sensitivities are superb in muon systems

muon decay in orbit

nucleus µ−

µ− → e−νν µ− + (A, Z)→νµ + (A,Z −1)nuclear muon capture

µ− + (A, Z)→ e− + (A,Z )

neutrinoless muon nuclear capture (= m-e conversion)

physics beyond the Standard Model

A negative muon stopped in some material :

Requirement to a μ beam for next-gene. experiment High Intensity

The potential sensitivity achievable in searches for rare processes is ultimately limited by the number of muons available. The muon beam intensity of 1011−1012 μ−/sec should be required, yielding about more than 1020μ− per year.

High PurityBeam contaminations are necessary to be removed, to reduce any background associated

with them. It is already shown that the past experiments like SINDRUM-II have already seen a background event just above the signal region, and they suspect that it comes from pion contamination in a beam through radiative pion capture. Therefore, it is the most important to reduce pion contamination in a beam.

Narrow Energy WidthNarrow energy spread of the beam will allow a thin muon stopping target to improve the

momentum resolution of e− detection, which is limited by energy loss in the muon stopping target.

High Resolution SpectrometerTo improve the intrinsic momentum resolution in an e− spectrometer, it is critical to construct

a thin tracking chamber system.

super muon source = PRISM

PRISMPhase Rotated Intense Slow Muon source

PRISM is a project to provide a dedicated source of a high intensity muon beam with narrow energy-spread and small beam contamination. PRISM stands for “Phase Rotated Intense Slow Muon source”. The aimed beam intensity is 10^11−10^12μ±/sec, four orders of magnitude higher than that available at present. It is achieved by a large solid-angle pion capture with a high solenoid magnetic field. Narrow energy spread can be achieved by phase rotation, which accelerates slow muons and decelerates fast muons by a radio frequency (RF) field. The pion contamination in a muon beam can be removed by a long flight path in PRISM so that most of pions decay out.

muon intensity 10^11-10^12μ/sec

kinetic energy 20MeV

energy spread +-(0.5-1.0)MeV

beam repetition 100-1000Hz

pion contamination < 10^-18

Anticipated PRISM beam design characteristics

PRISM LayoutPion capture sectionThe highest beam intensity in the world could be achieved by large-solid angle capture of pions at their production. Decay sectionπ − μ decay section consisting of a 10-m long superconducting solenoid magnet.Phase rotatorto make the beam energy spread narrower. To achieve phase rotation, a fixed-field alternating gradient synchrotron (FFAG) is considered to be used.

FFAG advantages:synchrotron oscillation

need to do phase rotationlarge momentum acceptance

necessary to accept large momentum distribution at the beginning to do phase rotation

large transverse acceptance muon beam is broad in space

Phase rotationPhase rotation is a method to achieve a beam of narrow energy spread. The principle of phase rotation is to accelerate slow muons and decelerate fast muons by a strong radio-frequency (RF) electric field, in order to yield narrow longitudinal momentum spread. By phase rotation, the initial time spread is converted into the final energy spread. It corresponds to 90 degree rotation of the distribution of the muons in the beam in the energy-time phase space.

Phase rotation simulation01

2345

012

3

4

5

RF : 5MHz, 128kV/m

ΔE/E = 20MeV+12%-10%

RF : 5MHz, 250kV/m

ΔE/E = 20MeV+4%-5%

Phase rotation simulationphase space6.4. PRISM-FFAG SIMULATIONS 31

Initial Phase

After 1 turn

After 2turns

After 3turns

After 4 turns

After 5turns

54.4 61.2 68.0 74.8 81.6MeV/c

Figure 6.9: Horizontal acceptance of the PRISM-FFAG by Monte Carlo simulat ion.

54.4 61.2 68.0 74.8 81.6MeV/c

Initial Phase

After 1 turn

After 2 turns

After 3 turns

After 4 turns

After 5 turns

Figure 6.10: Vert ical acceptance of the PRISM-FFAG by Monte Carlo simulat ion.

6.4. PRISM-FFAG SIMULATIONS 31

Initial Phase

After 1 turn

After 2turns

After 3turns

After 4 turns

After 5turns

54.4 61.2 68.0 74.8 81.6MeV/c

Figure 6.9: Horizontal acceptance of the PRISM-FFAG by Monte Carlo simulation.

54.4 61.2 68.0 74.8 81.6MeV/c

Initial Phase

After 1 turn

After 2 turns

After 3 turns

After 4 turns

After 5 turns

Figure 6.10: Vertical acceptance of the PRISM-FFAG by Monte Carlo simulation.

6.4. PRISM-FFAG SIMULATIONS 31

Initial Phase

After 1 turn

After 2turns

After 3turns

After 4 turns

After 5turns

54.4 61.2 68.0 74.8 81.6MeV/c

Figure 6.9: Horizontal acceptance of the PRISM-FFAG by Monte Carlo simulat ion.

54.4 61.2 68.0 74.8 81.6MeV/c

Initial Phase

After 1 turn

After 2 turns

After 3 turns

After 4 turns

After 5 turns

Figure 6.10: Vert ical acceptance of the PRISM-FFAG by Monte Carlo simulat ion.

Lattice Design In order to achieve a high intensity muon beam, it is necessary for the PRISM-FFAG to have both of large transverse acceptance and large momentum acceptance. Furthermore, long straight sections to install RF cavities are required to obtain a high surviving ratio of the muon. Therefore, the PRISM-FFAG requires its magnets to have large aperture and small opening angle. In such magnets, not only nonlinear effects but also fringing magnetic field are important to study the beam dynamics of FFAGs. Three-dimensional tracking is adopted to study the dynamics of FFAG from the beginning of the lattice design procedure. In this process, quasi-realistic 3D magnetic field maps, which are calculated applying spline interpolation to POISSON 2D field, were used instead of TOSCA field in order to estimate the optical property quickly

quasi-realistic 3D magnetic field

r1

r2

r3

r4

r5

r

x(θ)

Comparison by tracking result

N=8k=5

F/D = 7.1r0=5m

Tracking resultsN=10F/D=8k=5

r0=6.5m140000πmm mrad 3000πmm mrad

35000πmm mrad

Layout of PRISM-FFAG

ing simulations, The present design of PRISM-FFAG has

more than about 35,000 πmm·mrad in the horizontal ac-ceptance and about 3000 πmm·mrad in the vertical accep-tance.

5mRF PS

RF AMP

RF Cavity

FFAG-Magnet

Kicker Magnet

for Extraction

Kicker Magnet

for Injection

Figure 2: Schematic layout of the PRISM-FFAG

Table 2: Present parameters of PRISM-FFAG

No. of sectors 10

Magnet type Radial sector

DFD triplet

C-shaped

Field index (k-value) 4.6

F/D ratio 8.0

Opening angle F/2 : 2.2deg.

D : 2.2deg.

Half gap 17cm

Maximum field Focus. : 0.24 Tesla

Defocus. : 0.026 Tesla

Average radius 6.5m for 68MeV/c

Tune horizontal : 2.69

vertical : 1.30

MAGNET

We adopted a scaled radial sector type FFAG with a

triplet focusing magnet (DFD). Figure 3 shows schematic

views of the PRISM-FFAG magnet. The field gradient (kvalue=4.6) is generated by the pole shapes basically. The

gap distance g is a function of radii r. Identically, the equa-tion is g = h0(r0/r)k. Such a gap variation will break a

scaling condition because of the fringing field effect. In

order to avoid this situation, a intermediate pole made of

anisotropic magnet material is used [3]. Owing to the in-

termediate pole, the magnet can have not only constant

gap but also smaller fringing field compared with a con-

ventional one. The magnet have a set of trim coils on the

intermediate pole to make the k value tuneable. It is alsoworth to mention that the intermediate pole filters out local

irregularity of the magnetic field distribution. Thus the ac-

curacy of the pole shape is not necessary and the number

of trim coils can be reduced.

The three-dimensional magnetic field was calculated by

using a 3D field calculation code, TOSCA. Figure 4 shows

results of the calculation of Bz as a function of θ (top),the local k value (middle) and the F/D ration (bottom) asa function of radius. The local k and F/D ratio were cal-culated by the BL integration and they are almost constant

over the beam region. Therefore, the scaling condition is

fulfilled.

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

0 2 4 6 8 10 12 14 16 18

! (Deg.)

Bz

(Gau

ss)

r=580 cm

r=600 cm

r=620 cm

r=640 cm

r=660 cm

r=680 cm

r=700 cm

r=720 cm

z = 0 cm

0

1

2

3

4

5

6

7

8

9

10

580 600 620 640 660 680 700 720

F ComponetD Componet

r (cm)

k v

alu

e +

1

0

1

2

3

4

5

6

7

8

9

10

580 600 620 640 660 680 700 720

r (cm)

F/D

rati

o

Figure 4: Calculation results of the magnetic field using

TOSCA.

RF SYSTEM

Since the muon is an unstable particle (life time∼2.2µs),it is crucial to complete phase rotation as quickly as possi-

5mRF PS

RF AMP

RF Cavity

FFAG-Magnet

Kicker Magnet for Extraction

Kicker Magnet for Injection

Features of PRISM-FFAG Magnetscaling radial sector Conventional type. Have larger circumference ratio.triplet (DFD) F/D ratio can be tuneable. the field crump effects. large packing factor. the lattice functions has mirror symmetry at the center of a straight section.large aperture important for achieve a high intensity muon beam.thin Magnets have small opening angle. so FFAG has long straight section install RF cavities as mach as possibleC-shaped

intermediate pole made of anisotropic magnet material. the magnet can have not only constant gap but also smaller fringing field. A scaling condition can be easy to fulfill. the intermediate pole filters out local irregularity of the magnetic field distribution. Thus the accuracy of the pole shape is not necessary and the number of trim coils can be reduced.trim coils k value is tuneable. Therefore, not only vertical tune and also horizontal tune are tuneable.

Magnet Design

Field Calculation

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

0 2 4 6 8 10 12 14 16 18

! (Deg.)

Bz

(Gau

ss)

r=580 cm

r=600 cm

r=620 cm

r=640 cm

r=660 cm

r=680 cm

r=700 cm

r=720 cm

z = 0 cm

0

1

2

3

4

5

6

7

8

9

10

580 600 620 640 660 680 700 720

r (cm)

F/D

rati

o

0

1

2

3

4

5

6

7

8

9

10

580 600 620 640 660 680 700 720

F ComponetD Componet

r (cm)

k v

alu

e +

1

The 3D magnetic field was calculated by using a 3D field calculation code, TOSCA. These figure shows results of the calculation of Bz as a function of θ (top), the local k value (middle) and the F/D ration (bottom) as a function of radius. The local k and F/D ratio were calculated by the BL integration and they are almost constant over the beam region. Therefore, the scaling condition is fulfilled.

Stray Field

50 Gauss100 Gauss

RF Systemultra-high field gradient

Proton Synchrotron RF System

0

50

100

150

200

250

0 2 4 6 8 10 12

Frequency (MHz)

Fie

ld G

radie

nt

(kV

/m)

SATUNE

MIMAS

CERN PSB

CERN PS

AGS

ISIS

KEK BSTR

KEK PS

J-PARC 50GeV MR

J-PARC 3GeV RCS

50GeV MR Upgrade

KEK-HGC

PRISM

Ferrite Cavities

J-PARC MA Cavities

(High Duty)

PRISM Cavity

Since the muon is an unstable particle (life time~2.2us), it is crucial to complete phase rotation as quickly as possible in order to increase a number of surviving muons. In present design, PRISM requires very high field gradient of 200kV/m at the low frequency (4-5 MHz). As compared with usual cavities, PRISM has to operate its cavities at a remarkably outstanding condition.

Figure 3: Schematic views of a PRISM-FFAGmagnet. A bird’s-eye view (left), a top view (center) and a side view (right).

ble in order to increase a number of surviving muons. In

present design, PRISM requires very high field gradient of

200kV/m at the low frequency (4∼5 MHz). As comparedwith usual cavities, PRISM has to operate its cavities at a

remarkably outstanding condition. Such an operation can

be achieved by a low duty factor and ultra-thin magnetic al-

loy (MA) cavities [4]. MA core [5] has stable impedance at

a required magnetic field for PRISM(320-490 Gauss). The

thickness of MA cores is 35 mm. The racetrack-shaped

core is adopted. Cores are all air-cooled since the RF power

loss into the core is very small owing to small duty factor

(about 0.1%).

To optimize phase rotation, not only a high field gradient

but also the shape of RF voltage are important. Accord-

ing to our simulations, a saw-tooth RF voltage makes a fi-

nal energy spread narrower than that by a sinusoidal one.

Therefore, adding higher frequency harmonics to form a

saw-tooth pulse shape is being considered. By using the

cut core configuration [6], a wide band RF system with µQf@ 5MHz = 5.5 × 109 can be designed. The first and sec-

ond harmonics could be applied on RF simultaneously with

sufficient efficiency. A cavity, which consists of 5 gaps, is

installed in one straight section. In the current design, each

gap has 6 MA cores and has a length of 35 cm along the

beam direction. One gap generates the RF voltage of± 25-

38 kV and is driven by two bus bars which are connected to

an RF amplifier. Each gap will be driven by push-pull am-

plifiers using tetrode tubes, 4CW150,000E. The plate volt-

age of 30-40 kV will be applied and RF current of 60 A per

gap maximum is possible to generate. Tetrode amplifiers

are installed either on-the-top-of or underneath the cavity.

A low duty factor enables the tubes to generate the maxi-

mum RF power of 1.8 MW. Parameters of the RF system

are summarized in Table 3.

SUMMARY

The lattice and magnet design of PRISM-FFAG will be

finalized soon. The design of RF system had almost been

finished, and its construction will start. RF tests, magnets

construction and its field measurements will be carried out

in JFY 2004 to JFY 2005. The FFAG-ring will be com-

Number of gap per cavity 5

Length of cavity 1.75 m

Number of core per gap 6

Core material Magnetic Alloy

Core shape Racetrack

Core size 1.4m × 1.0m × 3.5cmShunt impedance ∼159Ω/core @ 5MHz

RF frequency 4∼5MHzField gradient 200kV/m

Flux density in core 320 Gauss

Tetrode 4CW150,000E

Duty <0.1%

Table 3: Parameters of PRISM-FFAG RF system.

pleted by the end of JFY 2005. After commissioning, phase

rotation, muon acceleration, and muon ionization will be

studied.

REFERENCES

[1] ”The PRISM Project – A Muon Source of the World-Highest

Brightness by Phase Rotation –”, LOI for Nuclear and Parti-

cle Physics Experiments at the J-PARC (2003)

[2] ”An Experimental Search for the µ− − e− Conversion Pro-cess at an Ultimate Sensitivity of the Order of 10−18 with

PRISM”, LOI for Nuclear and Particle Physics Experiments

at the J-PARC (2003)

[3] Y.Iwashita et al., to be published in the proceedings of EPAC

2004

[4] C.Ohmori et al., ”ULTRA-HIGH FIELD GRADIENT RF

SYSTEM FOR PRISM-MUON BUNCH ROTATION”, pro-

ceedings of SAST03

[5] C.Ohmori et al.,“ A Wide Band RF Cavity for JHF Syn-

chrotrons”, Proceedings of PAC97.[6] C. Ohmori et al.,“ High Field Gradient Cavity loadedwith

MA for Synchrotrons”, PAC99

Magnetic Alloy Cavity

1.00E+09

1.00E+10

1.00E+11

1 10 100 1000 10000

Brf[Gauss]

up'Qf

SY2

N5C

4M2-302

FT-small

FT-large

Magnetic Alloys

Ferrites

Characteristics of MAThin Tape , 18 mmHigh Field Gradient

Voltage limit: Brf <Bsat. (1T) and Voltage per layer < 5 V

High Curie TemperatureLarge core, Rectangular ShapeLarge permeability (about 2000 at 5MHz)Original Q value is small(0.6).High Q is possible by cut core configurationThickness -35mm (50mm in

future)

PRISM RF core Outer size : 1.4m x 1.0m x 0.35mInner size : 0.74m x 34 m

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 was

analysed using a typical constant current characteristics of

the tube. During the high power period, the cathode peak

and DC currents will be 120 A and 40 A, respectively. To

generate the RF current of 60 A, the required voltage swing on the control grid is about 700 V. To drive the

power amplifier, 1.5 kW solid state amplifier is

considered. In case of the narrow band operation to

generate 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 for

the 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 the

voltage of 150 V in short time. By this function, we can

choose 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 2

Size of AMP 1.35 m X 0.8 m X 0.7 m

Tetrode 4CW150,000E

Max. RF current 60 A

Max. cathode current (DC) 50 A

Max. plate voltage 40 kV

Max. RF power 1.8 MW

CONCLUSIONS

The 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, Osaka university in this winter. The ultra-thin RF cavity will be

tested 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, KEK-

Report 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 loaded

with MA for Synchrotrons”, PAC99 (Invited).

Anode PSClover

cavity cavity cavity cavity

HeaterSG

AMPcondenser

AMPcondenser

AMPcondenser

AMPcondenser

driveAMP

An RF amp system has been constructed. Its performance test is in the works.

Construction of the PRISM-FFAG

Among the all PRISM components, the phase rotator section can be constructed from japanese fiscal year (JFY) of 2003 for five years.

FY2003Lattice design, Magnet designRF R&D

FY2004RFx1gap construction & testMagnetx1 construction & field meas.

FY2005RF tuningMagnetx9 constructionFFAG-ring construction

FY2006Commissioning Phase rotation

FY2007Muon acceleration(Ionization cooling)

5m

RF PS

RF AMP RF Cavity

FFAG-Magnet

Kicker Magnet

for Injection