Muon Phase Rotation at PRISM FFAG

1. Muon Phase Rotation at PRISM FFAG Akira SATO Osaka University

2. 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. PRISM Beam Characteristics Phase Rotated Intense Slow Muon source • intensity : 1011-1012m±/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

4. 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 PRISM layout not in scale

5. 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 FFAG for Phase Rotation Fixed Field Alternating Gradient Synchrotron

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

7. 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. 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. 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 Half gap = 10 x (500/r)5 cm rout=550cm r rin=460 Magnet Model and Field FFAG Lattice Triplet : DFD

10. Total # of RF cavity : 12 4gaps/cavity RF wave field type: Sinusoidal Saw tooth ２m RF modeling

11. Information @θ＝０ (r,θ,z) momentum ToF Particle ID θ＝０ θ

12. 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 10ns Muon injection 81.6 71.2 68.0 61.2 54.4MeV/c t=0,+-5ns

13. 54.4MeV/c μ Because FFAG has momentum dispersion, radius of the muon orbit becomes lager gradually. Typical Muon Track

14. Phase Rotation Study Sinusoidal Saw tooth

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

16. RF : 5MHz, 250kV/m Energy spread after 5turns Δp/p = 68MeV/c+2%-2% ΔE/E = 20MeV+4%-5% Saw tooth RF

17. 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. How to realize saw tooth

18. ① ② ① ① ③ ② ② ① ① ① ② ② ① ③ ① ① ② ③ Simulation Result

19. Acceptance Study Horizontal acceptance Vertical acceptance Survival rate Large gap FFAG

20. Initial Phase After 3turns 54.4 61.2 68.0 74.8 81.6MeV/c After 1 turn After 4 turns After 2turns After 5turns Horizontal Phase Space Horizontal Acceptance 10000pi mm mrad

21. 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 Vertical Phase Space Vertical Acceptance 2000pi mm mrad

22. Surviving rate after 5turns : 60% e- contamination : < 1/1600 Decay OFF Decay ON Muon surviving # of surviving muon after 5 turns

23. 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 ! rout r rin Survival Rate vs. Momentum

24. FFAG Magnet with Large Gap(1)

25. Dose an acceptance depend on betatron tune? Selection of Betatron Tune

26. Long Term Acceptance (Region1)

27. Long Term Acceptance (Region2)

28. 5 turns Acceptance- Number of lost particle Region1 Region2 FFAG acceptance depends on betatron tune.

29. Surviving Rate (Region2)

32. 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=2000pmm mrad. These acceptance was limited by physical aperture. • We have some idea to get lager acceptance. These will be studied soon.