1. Study of Resonance Crossing in FFAG Masamitsu Aiba (KEK) Contents 1.Introduction 2.Crossing experiment at PoP FFAG 3.Crossing experiment at HIMAC synchrotron 4.Summary

2. Introduction FFAG accelerator: –For proton driver –For muon acceleration, phase rotation Resonance crossing –In scaling FFAG: tune variation due to imperfection of scaling –In non-scaling FFAG: tune variation in wide range Dynamics of resonance crossing is important. Experimental study at PoP FFAG and HIMAC

3. Crossing experiment at PoP FFAG Parameter list PoP FFAG: radial sector type scaling FFAG Experiment of resonance crossing with various driving term and crossing speed

4. Remodeling magnets Crossing third order resonance during acceleration 4mm iron plates

5. Driving term Feed Down: Driving term with COD Controlling COD Driving term can be varied and controlled.

6. Beam measurement Beam scraping & intensity measurement turn intensity Particle distribution in beam emittance was measured before and after crossing.

7. Fast crossing BeforeCrossingAfter Fast crossing: no clear signal of a damage due to crossing 110 130 150 (keV) Energy gain 1.6kV/turn =  x 1.4×10 -3 Current error –2% Scraping data Particle distribution in beam emittance

8. Slow crossing Slow crossing: a part of beam is transported to large amplitude Crossing After 130 150 170 190 (keV) Energy gain 0.13kV/turn =  x 1.2×10 -4 Current error –2% Scraping data Particle distribution in beam emittance

9. “Particle trapping” model Reference: A.W.Chao and M.Month, NIM 121, P.129 (1974) “PARTICLE TRAPPING DURING PASSAGE THROUGH A HIGH-ORDER NONLINEAR RESONANCE” Phase space topology during crossing third order resonance Distance from resonance This model explains the experimental result. Assuming: nonlinear detuning (octupole) driving term (sextupole)

10. Trapping efficiency Nonlinear detuning: Driving term: Linear tune shift: Nonlinear tune shift: Excitation width:  s ： the beam emittance of island center the total area of islands the adiabatic parameter The adiabatic parameter means a speed of islands moving during crossing. Crossing speed: : Trapping efficiency for third order resonance *Assuming  >>1 to derive the trapping efficiency

11. Comparison of trapping efficiencies The experiment results are consistent to simulations. Efficiency in experiment Trapping efficiencies   are about 3.

12. Criterion to avoid trapping Adiabatic parameter more than 7 will be harmless.

13. Crossing experiment at HIMAC Crossing: Varying quadrupole strength Driving term: SXFr*2 sextupole Nonlinear detuning: Second order effect of SXH sextupole Crossing 3vx=11 in both direction Observing beam profile with Gas Sheet Monitor directly SXFr SXH for all SP Gas Sheet Monitor

14. Crossing in a direction of tune decreasing x =3.668 x =3.662 x =3.661 x =3.660 x =3.658 x =3.652 x =3.647 Crossing speed: 4.6*10 -6 Nonlinear detuning: 2.52m -1 Driving term: 0.019m -1/2 Beam profiles during crossing

15. Crossing in a direction of tune increasing x =3.654 x =3.657 x =3.676 x =3.711 Crossing speed: 4.6*10 -6 Nonlinear detuning: 2.52m -1 Driving term: 0.019m -1/2 Beam profiles during crossing

16. Simulation – tune decreasing

17. Simulation – tune increasing

18. Difference due to crossing direction x =3.668 x =3.647 x =3.654 x =3.711 Tune decreasing Tune increasing The effect due to crossing depends upon crossing direction. In one direction: “particle trapping” In other direction: “emittance growth”

19. Crossing without sextupoles (1) Crossing speed: 8.5*10 -6 Nonlinear detuning: 0 m -1 Driving term: 0 m -1/2 Beam profiles during crossing (tune decreasing) “Particle trapping” occurred even when all magnets are linear elements. Possible source for nonlinear components: allowed poles, fringing field …

20. Crossing without sextupoles (2) In tune decreasingIn tune increasing Beam intensity during crossing Beam loss due to crossing 3Nx=11 Crossing speed: 5.5*10 -6 Nonlinear detuning: 0 m -1 Driving term: 0 m -1/2 *Data acquired by Machida and Uesugi

21. Summary Experiment at PoP FFAG (crossing 3 x=7) –“Particle trapping” due to resonance crossing was observed. –Trapping efficiency are understood qualitatively. –Adiabatic parameter more than 7 was harmless. Experiment at HIMAC (crossing 3 x=11) –Difference due to crossing direction was clearly observed. –Even sextupoles are not excited, the effect of crossing was “particle trapping”.