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

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Presentation on theme: "Study of Resonance Crossing in FFAG Masamitsu Aiba (KEK) Contents 1.Introduction 2.Crossing experiment at PoP FFAG 3.Crossing experiment at HIMAC synchrotron."— Presentation transcript:

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 (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 (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”.


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