Study of Resonance Crossing in FFAG

Transcription

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

2 FFAG accelerator: For proton driver For muon acceleration Resonance crossing Introduction 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 Experiment at PoP FFAG PoP FFAG: radial sector type scaling FFAG Parameter list sector number 8 (DFD triplet) k value 2.5 kinetic energy 5-5keV fmagnetic field t(f).4-.13t(d) average radius m betatron tune (Hor.) (Ver.) revolution freq mhz RF voltage 5kVpp Resonance crossing with various driving term and crossing speed

4 Remodeling magnets horizontal tune ν x =7 (ν x =2.333) Beam Energy (kev) After remodeling Before remodeling 4mm iron plates Crossing third order resonance during acceleration

5 Driving term Driving term with COD Feed Down: Controlling COD O ( x + D) = O( x + 3x D + 3xD D 3 ) COD (mm) current error current error septum azimuthal angle (deg.) Driving term is 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 = ν x Current error 2% Scraping data (kev) BeforeCrossingAfter Particle distribution in beam emittance Nor. intensity current error -2%, speed r from 5keV (mm) π π Fast crossing: no clear signal of a damage due to crossing

8 Slow crossing Energy gain.13kv/turn = ν x Current error 2% Scraping data (kev) Particle distribution in beam emittance Crossing After Normalized intensity (-) r from 5keV (mm) π 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 1 ξ p ν 3 This model supports the experimental result.

10 Trapping efficiency Trapping efficiency for third order resonance P T = A πα s exp( α 1) α s = α 1, 1, if if α > 1, 1 α < 1 1 α s the beam emittance of island center 2 1 π A κ 2α s : 2 3 the total area of islands ε 1 4 α = : the adiabatic parameter π NL e The adiabatic parameter means a speed of islands moving during crossing. Crossing speed: Nonlinear detuning: Driving term: 2π < β > Ap = dθ e 8πν 1 Linear tune shift: L = p ν 3 Nonlinear tune shift: = 12B a Excitation width: κ 3 NL 4 e, ε B NL e < β > 2π = d θ O( θ ) 16πν 1 2 = 3 a A p 1 2 ipθ ξ 3 L 2 e *Assuming k>>1 to derive the trapping efficiency S( θ )

11 Nor. integral (-) Comparison of trapping efficiencies Efficiency in experiment error 2%, speed.13kv/turn, scraper 948mm trapping efficiency (%) Trapping efficiencies num. of turn energy gain (kv/turn) The experiment results are consistent to simulations. current error theory: -2% theory: % theory: -3% exp.: -2% exp.: % exp.: -3% sim.: -2% sim.: % sim.: -3%

12 Criterion to avoid trapping trapping efficiency (%) adiabatic parameter Adiabatic parameter more than 7 will be harmless.

13 Crossing experiment at HIMAC Gas Sheet Monitor SXFr SXH for all SP Flat bottom operation parameter circumference 129.6m super period / cell particle carbon 6+ inj. energy 6MeV/u operation point (3.69, 2.13) SXFr 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

14 Crossing in a direction of tune decreasing Beam profiles during crossing ν x =3.668 ν x =3.662 ν x =3.661 ν x =3.66 ν x =3.658 ν x =3.652 ν x =3.647 Crossing speed: Nonlinear detuning: 2.52m -1 Driving term:.19m -1/2

15 Crossing in a direction of tune increasing Beam profiles during crossing ν x =3.654 ν x =3.657 ν x =3.676 ν x =3.711 Crossing speed: Nonlinear detuning: 2.52m -1 Driving term:.19m -1/2

16 Simulation tune decreasing x' (mrad.) 8 ν x = x (mm) x' (mrad.) ν x = x (mm) x' (mrad.) 2 ν x = x (mm) Number of particle 5 ν x = Number of particle ν x =3.66 Number of particle ν x = x (mm) x (mm) x (mm)

17 Simulation tune increasing x' (mrad.) ν x = x (mm) x' (mrad.) 2 ν x = x (mm) 4 ν x = ν x =3.75 Number of particle Number of particle x(mm) x (mm)

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

19 Crossing without sextupoles 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 Crossing speed: Nonlinear detuning: m -1 Driving term: m -1/2

20 Summary Experiment at PoP FFAG Particle trapping due to resonance crossing was observed. Trapping efficiency are understood qualitatively. Adiabatic parameter more than 7 was harmless. Experiment at HIMAC Difference due to crossing direction was shown. Even sextupoles are not excited, the effect of crossing was particle trapping.

21 Crossing without sextupoles Normalized beam profiles during crossing Crossing speed: Nonlinear detuning: m -1 Driving term: m -1/2