Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005....

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Lattice Design for PRISM-FFAG Akira Sato Osaka University 4th Aug. 2004 : NP04 at Tokai

Transcript of Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005....

Page 1: Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005. 8. 29. · Anticipated PRISM beam design characteristics high intensity muon beam

Lattice Design for PRISM-FFAG

Akira SatoOsaka University

4th Aug. 2004 : NP04 at Tokai

Page 2: Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005. 8. 29. · Anticipated PRISM beam design characteristics high intensity muon beam

contents

• PRISM overview

• PRISM-FFAG dynamics study

• method

• acceptance

• current parameters

• summary

Page 3: Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005. 8. 29. · Anticipated PRISM beam design characteristics high intensity muon beam

PRISMPhase Rotated Intense Slow Muon source

muon intensity 1011-1012μ/sec

kinetic energy 20MeV

energy spread +-(0.5-1.0)MeV

beam repetition 100-1000Hz

pion contamination < 10^-18

Anticipated PRISM beam design characteristics

high intensity muon beamnarrow energy-spread high purity

dedicated for the stopped muon experiments

LFV : mu-e conversion sensitivity of 10-18

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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

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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

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Optics Design for PRISM-FFAG

Large Transverse Acceptance horizontal > 20000 pi mm mrad

vertical > 3000 pi mm mrad

Long Straight section

to install RF cavities

Requirements

magnets : large aperture and small opening angle.non-linear effect and magnetic fringing fields are important to study the beam dynamics of FFAGs.

toward the high intensity and narrow energy spread muon beam

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conventional method

Dr. thesis of M.YoshimotoPoP-FFAG(KEK)

TOSCA is the best. but takes much time.

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New method to study dynamics

to study :acceptance (H,V)tunetune shiftbeam size etc

parameters :number of cellFD,DFD,FDFk valueF/D ratiogap size

quasi-realistic magnetic field

3D tracking by geant3.21

can model realistic fringing field

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How to make quasi-realistic 3D magnetic fieldsstep 1 : calculate magnetic field (Bx(~Bθ),Bz) of each z-θcross sections (r1-r5). x-axis is considered as θ-axis (approximation).

step 2 : convert the field (Bθ,Bz) to (Bz,Bθ,Br) by using Maxwell eq.

Bz(zi) = By (zi)Bθ (zi) = Bx (zi)

Br(zi) =dBz

dr

(Z i )

(Zi − Zi−1) + Br(Zi−1)

step 3 : to make a fine mesh field map, apply a 2D spline interpolation to the above field map.

r1

r2

r3

r4

r5

r

x(θ) z

F magnetD magnet D magnetfieldclump

fieldclump

MAGNET CYCLE = 3420

FD D

z

x(θ) r

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Comparison (field map)TOSCA quasi-realistic

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bz(gauss)

-4000

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bt(gauss)

0

200

400

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Br(gauss)

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bz(gauss)

-4000

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bt(gauss)

0

200

400

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Br(gauss)

TOSCA quasi-realistic

TOSCA quasi-realistic

TOSCA quasi-realistic

> 8 hours several min.!

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Comparison (tracking results)

N=8k=5

F/D = 7.1r0=5m

TOSCA quasi-realistic

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Acceptance StudyDFD, N=10, half gap=17cm, w/o field clamps, r0=6.5m for 68MeV/c

Horizontal phase spaces are plotted in a tune diagram.

Vertical phase spaces are plotted in a tune diagram.

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Acceptance dependence on gap size of magnets

DFD, N=10, w/o field clamps, r0=6.5m for 68MeV/c

5cm 10cm 15cm 20cm

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Tracking resultsDFD, N=10, F/D=6, k=4.6,

half gap=17cm, r0=6.5m

horizontal vertical

35000πmm mrad

An effective horizontal acceptance is 35000 pi mm mrad in consideration of correlation between horizontal and vertical acceptance

150000πmm mrad 4000πmm mrad

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Parameters of PRISM-FFAG

5mRF PS

RF AMP

RF Cavity

FFAG-Magnet

Kicker Magnet for Extraction

Kicker Magnet for Injection

Figure 4: Beam trajectories in horizontal (left) and vertical (right) phase space are plotted on tune diagrams. The area

of each plot indicates the acceptance. In this study the other emittance was set to zero. Therefore correlation between

horizontal and vertical dynamic cannot be seen. Figures beside each plots means F/D ratio in current setting (in BL

integration).

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bz(gauss)

-4000

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bt(gauss)

0

200

400

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Br(gauss)

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bz(gauss)

-4000

-2000

0

2000

4000

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Bt(gauss)

0

200

400

10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35

z=0(cm)

z=3(cm)

z=6(cm)

z=9(cm)

z=12(cm)

theta(deg)

Br(gauss)

TOSCA quasi-realistic

TOSCA quasi-realistic

TOSCA quasi-realistic

Figure 3: Comparison between a TOSCA field and a quasi-

realistic field. Bz , Bθ and Br are plotted as a function of

θ.

BEAM DYNAMICS STUDY

In order to search the best optics parameter set for

PRISM-FFAG, the beam dynamics was studied by per-

forming beam tracking using the quasi-realistic field maps.

A tracking program based on GEANT3.21 [5] was used for

particle tracking. Parameters to be studied are:

• Number of sectors,• Combination of magnets: DFD, FDF, FD• Field index (k value)• Ratio of the magnitude of focusing field to that of de-focusing field: (F/D ratio)

Table 1: Present parameters of PRISM-FFAG

Number of sectors 10

Magnet type Radial sector

DFD triplet

Field index (k-value) 4.6

F/D ratio 6.2

Opening angle of magnets F/2 : 2.2deg.

D : 2.2deg.

Half gap of magnets 17cm

Maximum field Focus. : 0.4 Tesla

Defocus. : 0.065 Tesla

Average radius 6.5m for 68MeV/cTune horizontal : 2.73

vertical : 1.58

• Gap size of magnets

Figure 4-(left) and 4-(right) show an example of the

acceptance study of horizontal and vertical respectively.

Beam trajectories in a phase space are plotted on tune dia-

grams. The area of each plot indicates the acceptance.

Taking resonance lines and the transition energy into ac-

count, parameters were selected to be the beam acceptance

as large as possible. Present parameters of PRISM-FFAG

are shown in Table 1.

Figure 5 shows the phase space and the dependence

of tune on the amplitude for horizontal (left) and vertical

(right) respectively using the parameters shown in Table 1.

The initial emittance in the other plane is set to zero. It

is found that the PRISM-FFAG of the present design has a

dynamic aperture of more than about 140,000 πmm·mradin the horizontal plane and about 3,000 πmm·mrad in thevertical in 5 turns. The correlation between horizontal and

Page 16: Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005. 8. 29. · Anticipated PRISM beam design characteristics high intensity muon beam

Summary

• Beam dynamics were studied and optics design were performed for PRISM-FFAG by new method using quasi-realistic fields.

• This method enables quick iterations in search of the optics parameters such as tune compared with that of using TOSCA fields. That can be used widely to study and design FFAGs with a complex magnetic field. PRISM-II, NuFact-FFAG ...

• The current design has a very large acceptance of 35000 pi mm mrad in horizontal plane. But we still have some items to be studied to finalize the design.

Page 17: Lattice Design for PRISM-FFAGprism.phys.sci.osaka-u.ac.jp/papers/slides/20040802-np04... · 2005. 8. 29. · Anticipated PRISM beam design characteristics high intensity muon beam

Study items• 6D acceptance with phase rotation.

• zero chromaticity

• gap size optimization

• injection & extraction

• ...