Lattice Design for PRISM-FFAG. A. Sato Osaka University for the PRISM working group

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1 Lattice Design for PRISM-FFAG A. Sato Osaka University for the PRISM working group

2 contents PRISM overview PRISM-FFAG dynamics study & its method

3 PRISM Phase Rotated Intense Slow Muon source Anticipated PRISM beam design characteristics high intensity muon beam narrow energy-spread high purity dedicated for the stopped muon experiments muon intensity kinetic energy energy spread beam repetition μ/sec 2MeV +-(.5-1.)MeV 1-1Hz LFV : mu-e conversion sensitivity of 1-18 pion contamination < 1^-18

4 PRISM Layout Pion capture section The highest beam intensity in the world could be achieved by large-solid angle capture of pions at their production. Decay section π μ decay section consisting of a 1-m long superconducting solenoid magnet. Phase rotator to 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 rotation large momentum acceptance necessary to accept large momentum distribution at the beginning to do phase rotation large transverse acceptance muon beam is broad in space

5 Phase rotation simulation RF : 5MHz, 128kV/m E/E = 2MeV+12%-1% RF : 5MHz, 25kV/m E/E = 2MeV+4%-5%

6 Construction of the PRISM-FFAG Among the all PRISM components, the phase rotator section can be constructed from japanese fiscal year (JFY) of 23 for five years. RF PS RF AMP RF Cavity FFAG-Magnet Kicker Magnet for Injection FY23 Lattice design, Magnet design RF R&D FY24 RFx1gap construction & test Magnetx1 construction & field meas. FY25 RF tuning Magnetx9 construction FFAG-ring construction FY26 Commissioning Phase rotation FY27 Muon acceleration (Ionization cooling) 5m

7 Optics Design for PRISM-FFAG Large Transverse Acceptance horizontal > 2 pi mm mrad vertical > 3 pi mm mrad Long Straight section to install RF cavities magnets : large aperture and small opening angle. non-linear effect and magnetic fringing fields are important to study the beam dynamics of FFAGs.

8 conventional method Dr. thesis of M.Yoshimoto

9 new method to study dynamics parameters : number of cell FD,DFD,FDF k value F/D ratio gap size to study : acceptance (H,V) tune tune shift beam size etc

10 How to make quasi-realistic 3D magnetic fields step 1 : calculate magnetic field θ) of each z-θcross sections (r1-r5). x-axis is considered as θ-axis (approximation). field clump D magnet F magnet D magnet field clump r5 r4 r3 step 2 : convert the field (Bθ,Bz) to (Bz,Bθ,Br) by using Maxwell eq. B z (z i ) = B y (z i ) B θ (z i ) = B x (z i ) B r (z i ) = db z dr (Z i ) (Z i Z i 1 ) + B r (Z i 1 ) r2 D F D x(θ) z r r1 MAGNET CYCLE = 342 x(θ) r z step 3 : to make a fine mesh field map, apply a 2D spline interpolation to the above field map.

11 Comparison (field map) TOSCA Bz(gauss) 4 2 z=(cm) z=3(cm) TOSCA Bz(gauss) 4 2 z=(cm) z=3(cm) quasi-realistic Bt(gauss) z=(cm) 2 z=3(cm) TOSCA Bt(gauss) 4 z=(cm) 2 z=3(cm) quasi-realistic Br(gauss) 4 z=(cm) z=3(cm) TOSCA Br(gauss) 4 z=(cm) z=3(cm) quasi-realistic 2 2 > 8 hours several min.!

12 Comparison (tracking results) TOSCA N=8 k=5 F/D = 7.1 r=5m

13 Acceptance Study DFD, N=1, half gap=17cm, w/o field clamps, r=6.5m for 68MeV/c Horizontal phase spaces are plotted in a tune diagram. Vertical phase spaces are plotted in a tune diagram.

14 Tracking results DFD, N=1, F/D=6, k=4.6, half gap=17cm, r=6.5m horizontal vertical An effective horizontal acceptance is 35 pi mm mrad in consideration of correlation between horizontal and vertical acceptance

15 Parameters of the PRISM-FFAG 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). Bz(gauss) 4 z=(cm) z=3(cm) 2 FFAG-Magnet Bt(gauss) Br(gauss) -2 4 z=(cm) 2 z=3(cm) -2 RF AMP RF Cavity TOSCA -4 4 z=(cm) z=3(cm) 2 TOSCA TOSCA Bz(gauss) Bt(gauss) Br(gauss) 4 z=(cm) z=3(cm) z=(cm) 2 z=3(cm) -2 Kicker Magnet for Extraction Kicker Magnet for Injection -4 4 z=(cm) z=3(cm) 2 quasi-realistic quasi-realistic quasi-realistic Table 1: Present parameters of PRISM-FFAG Number of sectors 1 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. :.4 Tesla Defocus. :.65 Tesla Average radius 6.5m for 68MeV/c Tune horizontal : 2.73 vertical : 1.58 RF PS Figure 3: Comparison between a TOSCA field and a quasirealistic field. B z, B θ and B r are plotted as a function of θ. 5m 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-

16 Summary PRISM : super muon beam with high intensity, high purity and narrow energy spread. A construction program has started in 23 as 5-year program. Beam dynamics were studied and optics design were performed with new method using quasi-realistic field. Current design has very large acceptance of 35 pi mm mrad in horizontal plane.