1. 2002/7/04 NuFact02@Imperial College, London Beam Dynamics Studies of FFAG Akira SATO Osaka University

2. 2002/7/04 NuFact02@Imperial College, London Contents PRISM FFAG studies Large gap FFAG Experimental studies of PoP FFAG Summary

3. 2002/7/04 NuFact02@Imperial College, London PRISM FFAG Studies PRISM Overview Phase Rotation Acceptance

4. 2002/7/04 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

5. 2002/7/04 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

6. 2002/7/04 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

7. 2002/7/04 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

8. 2002/7/04 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 PRISM FFAG Simulation

9. 2002/7/04 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. 2002/7/04 NuFact02@Imperial College, London Typical Muon Track 54.4MeV/c μ Because FFAG has momentum dispersion, radius of the muon orbit becomes lager gradually.

11. 2002/7/04 NuFact02@Imperial College, London Phase Rotation RF : 5MHz, 128kV/m ΔE/E = 20MeV+12%-10% RF : 5MHz, 250kV/m ΔE/E = 20MeV+4%-5%

12. 2002/7/04 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.

13. 2002/7/04 NuFact02@Imperial College, London Simulation Result ① ① ① ② ② ③ ① ① ① ① ① ① ② ② ② ② ③ ③

14. 2002/7/04 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

15. 2002/7/04 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

16. 2002/7/04 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

17. 2002/7/04 NuFact02@Imperial College, London FFAG Magnet with Large Gap(1)

18. 2002/7/04 NuFact02@Imperial College, London Dose an acceptance depend on betatron tune? Selection of Betatron Tune

19. 2002/7/04 NuFact02@Imperial College, London Long Term Acceptance (Region1)

20. 2002/7/04 NuFact02@Imperial College, London Long Term Acceptance (Region2)

21. 2002/7/04 NuFact02@Imperial College, London

22. 2002/7/04 NuFact02@Imperial College, London

23. 2002/7/04 NuFact02@Imperial College, London Studies of the beam dynamics in the PoP-FFAG Beam Acceleration Horizontal acceptance Dynamic aperture PoP FFAG

24. 2002/7/04 NuFact02@Imperial College, London

25. 2002/7/04 NuFact02@Imperial College, London Beam position monitor

26. 2002/7/04 NuFact02@Imperial College, London Beam Acceleration

27. 2002/7/04 NuFact02@Imperial College, London Horizontal acceptance

28. 2002/7/04 NuFact02@Imperial College, London Beam motion at the resonance conditions

29. 2002/7/04 NuFact02@Imperial College, London 150-MeV proton FFAG With “ return yoke free ” magnet Now under construction

30. 2002/7/04 NuFact02@Imperial College, London

31. 2002/7/04 NuFact02@Imperial College, London Summary The PoP FFAG worked as designed. Proton can be accelarated in 1msec. PRISM phase rotation was studied by GEANT3.21. Energy spread of ΔE/E=+-5% was achieved. The 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 FFAG. These will be studied soon.