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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 4.Summary

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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

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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

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

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

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

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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

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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

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“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)

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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

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

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

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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

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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

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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

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Simulation – tune decreasing

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Simulation – tune increasing

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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”

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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 …

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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

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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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