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Study of Resonance Crossing in FFAG

Study of Resonance Crossing in FFAG. Contents Introduction Crossing experiment at PoP FFAG Crossing experiment at HIMAC synchrotron Summary. Masamitsu Aiba (KEK). Introduction. FFAG accelerator: For proton driver For muon acceleration, phase rotation Resonance crossing

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Study of Resonance Crossing in FFAG

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

  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 PoP FFAG: radial sector type scaling FFAG Parameter list 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 Driving term with COD Feed Down: Controlling COD Driving term can be varied and controlled.

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

  7. Fast crossing Energy gain 1.6kV/turn = Dnx 1.4×10-3 Current error –2% Scraping data 110 130150 (keV) Particle distribution in beam emittance BeforeCrossingAfter Fast crossing: no clear signal of a damage due to crossing

  8. Slow crossing Energy gain 0.13kV/turn = Dnx 1.2×10-4 Current error –2% Scraping data Particle distribution in beam emittance 130 150 170190 (keV) Crossing After Slow crossing: a part of beam is transported to large amplitude

  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 Assuming: nonlinear detuning (octupole) driving term (sextupole) Distance from resonance This model explains the experimental result.

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

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

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

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

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

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

  16. Simulation – tune decreasing

  17. Simulation – tune increasing

  18. Difference due to crossing direction nx=3.668 nx=3.647 Tune decreasing nx=3.654 nx=3.711 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) Beam profiles during crossing (tune decreasing) Crossing speed: 8.5*10-6 Nonlinear detuning: 0 m-1 Driving term: 0 m-1/2 “Particle trapping” occurred even when all magnets are linear elements. Possible source for nonlinear components: allowed poles, fringing field …

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

  21. Summary • Experiment at PoP FFAG (crossing 3nx=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 3nx=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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