1. 2002/7/02 NuFact02@Imperial College, London Muon Phase Rotation at PRISM FFAG Akira SATO Osaka University

2. 2002/7/02 NuFact02@Imperial College, London Contents PRISM Overview Tracking Simulation by Geant3.21 Phase rotation Acceptance of FFAG Muon decay - survival rate Large Gap FFAG Betatron tune dependence Summary

3. 2002/7/02 NuFact02@Imperial College, London PRISM Beam Characteristics intensity : 10 11 -10 12  ± /sec muon kinetic energy : 20 MeV (=68 MeV/c) range = about 3 g kinetic energy spread : ±0.5-1.0 MeV ±a few 100 mg range width beam repetition : about 100Hz Search μN→eN with sensitivity of 10 -18 Cf. MECO @BNL-AGS 10 -16 Phase Rotated Intense Slow Muon source

4. 2002/7/02 NuFact02@Imperial College, London PRISM layout Pion capture section Decay section Phase rotation section FFAG Based a ring instead of linear systems reduction of # of rf cavities reduction of rf power consumption compact not in scale

5. 2002/7/02 NuFact02@Imperial College, London FFAG for Phase Rotation synchrotron oscillation for phase rotation not cyclotron (isochronous) large momentum acceptance larger than synchrotron ± several 10 % is aimed large transverse acceptance strong focusing large horizontal emittance reasonable vertical emittance at low energy Fixed Field Alternating Gradient Synchrotron

6. 2002/7/02 NuFact02@Imperial College, London Phase Rotation Phase Rotation = decelerate particles with high energy and accelerate particle with low energy by high-field RF A narrow pulse structure (<1 nsec) of proton beam is needed to ensure that high-energy particles come early and low- energy one come late. energy time

7. 2002/7/02 NuFact02@Imperial College, London Simulation of the PRISM Phase Rotator By GEANT3.21 Full simulation Muon decay -> intensity Interaction -> background Acceptance study Phase rotation study Muon survival rate

8. 2002/7/02 NuFact02@Imperial College, London Muon phase rotation was studied by the GEANT3.21 3D simulation. except kicker parts. GEANT3 has single precision. Cf. Double precision DPGeant Geant4 Simulation Setup

9. 2002/7/02 NuFact02@Imperial College, London Magnet Model and Field 3D magnetic field of FFAG magnet was calculated by TOSCA. Field gradient was made by gap size. Magnitude of the field D : Bz = -0.0717(r(m)/r0) 5 (T) F : Bz = +0.435(r(m)/r0) 5 (T) r0 = 5 m for 68MeV/c 1 Cell = 45.0 deg. Straight sect. = 16.49 D = 2.46 FD 間 = 0.10 F/2 = 3.00 r r in =460 r out =550cm Half gap = 10 x (500/r) 5 cm FFAG Lattice Triplet : DFD

10. 2002/7/02 NuFact02@Imperial College, London RF modeling Total # of RF cavity : 12 4gaps/cavity RF wave field type: Sinusoidal Saw tooth ２m２m

11. 2002/7/02 NuFact02@Imperial College, London Information @θ ＝０ (r,θ,z) momentum ToF Particle ID θ θ ＝０

12. 2002/7/02 NuFact02@Imperial College, London Muon injection Muon was injected from θ=0 momentum: 68MeV/c+-20% 54.4, 61.2, 68.0, 74.8, 81.6MeV/c Phase space: r : r(p)+-8 cm ur : 0+-0.2 rad. z : 0+-16 cm uz : 0+-0.08 rad. Timing ： Arrival time to solenoid exit is taken into account. 10ns 81.6 71.2 68.0 61.2 54.4MeV/c t=0,+-5ns

13. 2002/7/02 NuFact02@Imperial College, London Typical Muon Track 54.4MeV/c μ Because FFAG has momentum dispersion, radius of the muon orbit becomes lager gradually.

14. 2002/7/02 NuFact02@Imperial College, London Phase Rotation Study Sinusoidal Saw tooth

15. 2002/7/02 NuFact02@Imperial College, London Sinusoidal RF RF : 5MHz, 128kV/m Energy spread after 5turns Δp/p = 68MeV/c+8%-6% ΔE/E = 20MeV+12%-10%

16. 2002/7/02 NuFact02@Imperial College, London Saw tooth RF RF : 5MHz, 250kV/m Energy spread after 5turns Δp/p = 68MeV/c+2%-2% ΔE/E = 20MeV+4%-5%

17. 2002/7/02 NuFact02@Imperial College, London How to realize saw tooth It is difficult to realize saw tooth with a field gradient of 250kV/m. Fit the saw tooth wave to the function: Each RF have just sinusoidal wave.

18. 2002/7/02 NuFact02@Imperial College, London Simulation Result ① ① ① ② ② ③ ① ① ① ① ① ① ② ② ② ② ③ ③

19. 2002/7/02 NuFact02@Imperial College, London Acceptance Study Horizontal acceptance Vertical acceptance Survival rate Large gap FFAG

20. 2002/7/02 NuFact02@Imperial College, London Horizontal Phase Space Initial Phase After 1 turn After 2turns After 3turns After 4 turns After 5turns 54.461.268.074.881.6MeV/c Horizontal Acceptance 10000pi mm mrad

21. 2002/7/02 NuFact02@Imperial College, London 54.461.268.074.881.6MeV/c Initial Phase After 1 turn After 2 turns After 3 turns After 4 turns After 5 turns Vertical Phase Space Vertical Acceptance 2000pi mm mrad

22. 2002/7/02 NuFact02@Imperial College, London Muon surviving Surviving rate after 5turns : 60% e - contamination : < 1/1600 Decay OFF Decay ON # of surviving muon after 5 turns

23. 2002/7/02 NuFact02@Imperial College, London Survival Rate vs. Momentum Why do large momentum particles have low survival rate? Gap ∝ (r0/r) 5 Physical aperture limits the dynamical acceptance. Lager Gap Magnet → Lager Acceptance We Need Lager Gap Magnet ! r r in r out

24. 2002/7/02 NuFact02@Imperial College, London FFAG Magnet with Large Gap(1)

25. 2002/7/02 NuFact02@Imperial College, London Dose an acceptance depend on betatron tune? Selection of Betatron Tune

26. 2002/7/02 NuFact02@Imperial College, London Long Term Acceptance (Region1)

27. 2002/7/02 NuFact02@Imperial College, London Long Term Acceptance (Region2)

28. 2002/7/02 NuFact02@Imperial College, London 5 turns Acceptance - Number of lost particle Region1Region2 FFAG acceptance depends on betatron tune.

29. 2002/7/02 NuFact02@Imperial College, London Surviving Rate (Region2)

30. 2002/7/02 NuFact02@Imperial College, London

31. 2002/7/02 NuFact02@Imperial College, London

32. 2002/7/02 NuFact02@Imperial College, London Summary PRISM phase rotation was studied by GEANT3.21. We can achieve energy spread of ΔE/E=+-5% after phase rotation. Even present design PRISM FFAG has large acceptance : H=10000, V=2000  mm mrad. These acceptance was limited by physical aperture. We have some idea to get lager acceptance. These will be studied soon.