Resonance Crossing Experiment in PoP FFAG (preliminary report)

1. FFAG W.S. ’04 @ KEK Resonance Crossing Experimentin PoP FFAG (preliminary report) M. Aiba (Tokyo Univ.) for KEK FFAG Group

2. Motivation of Experiment • Beam dynamics of resonance crossing is studied for non-scaling FFAG. • There are few study on resonance crossing. Especially, experimental studies are only… (as far as I know) • Fifth integer (Particle Trapping) @ CERN ISR (1975) by A. W. Chao et al. • Half integer @ TRIUMF Cyclotron (‘80) by R. Baartman et al. • Third integer, coupling resonance etc.. @ HIMAC (under going) by S. Machida et al. • PoP FFAG is good machine for beam study.

3. Basic Parameter of PoP FFAG ・Crossing speed can be changed in wide range. ・It is necessary to introduce a variation of tune.

4. Remodel of Magnet 4mm iron plates are inserted to all 8 magnets. Schematic view of magnet cross section r Iron plate Relatively, a gap outside is more widen than inside. Therefore, k value decrease as increasing radius. Mainly, horizontal tune varies.

5. Variation of Tunes open circle: experiment colored plot: calculation Integer or Half integer Fourth order (normal) Third order (normal) 3Nx=7 is focused here.

6. Longitudinal Beam Handling(1) Crossing speed is one of important parameter! However, it is impossible to accelerate all particles with same energy gain because of synchrotron oscillation. For clear observation of speed dependence, careful attentions are paid to longitudinal beam handling. Beam chopper: 100nsec chopped beam (～±10deg. of RF phase) Mountain-plot: Bunch monitor signal is transferred to mountain plot to check an amplitude of dipole oscillation.

7. Longitudinal Beam Handling(2) Example of Mountain Plot (RF capture @ injection energy) Dipole oscillation is perfectly suppressed.

8. Driving Term (1) Magnetic field error with RF core COD due to RF core (calculated with TOSCA) (calculated with TOSCA field & RK-tracking) Core Straight Section Defocus Focus Feed Down: RF cores disturb magnetic field of straight section. COD and octupole becomes sextupole driving term (feed down).

9. Driving Term (2) COD with weak excited magnets Error Septum Error Error Septum Error Variable driving term can be introduced with changing coil current.

10. :Fourier amplitude of 3Nx=7 :phase factor :horizontal beta-function :coefficient of sextupole :horizontal tune :phase advance Driving Term (3) Due to the relation of phase between fixed and variable driving term, Fourier amplitude is not proportional to variable driving term.

11. Beam Size Measurement During acceleration, an orbit shifts to outer radius. Using a scraper and an intensity monitor, beam size, before and after crossing, can be measured. turn

12. Results (1) –data of driving term 0.18*10-8(m^3/2) Speed 0.13kV/turn Speed 0.49kV/turn Speed 1.6kV/turn Scraper pos. r=908mm Scraper pos. r=908mm Scraper pos. r=908mm Scraper pos. r=928mm Scraper pos. r=928mm Scraper pos. r=928mm Scraper pos. r=948mm Scraper pos. r=948mm Scraper pos. r=948mm Scraper pos. r=968mm Scraper pos. r=968mm

13. Results(2)-trapping efficiency Large driving term Large trapping efficiency Slow Crossing Large trapping efficiency The result can be understood qualitatively.

14. Particle Trapping Reference: “PARTICLE TRAPPING DURING PASSAGE THROUGH A HIGH-ORDER RESONANCE”, A.W. Chao and Melvin Month, NIM 121(1974) pp129-138 Particle Trapping: When a non-linear detuning is very larger than a driving term, some particles are trapped by islands during crossing resonance. Phase space topology for third integer resonance

15. ?Opposite Crossing? Particle trapping (tune decreases) Growth? (tune decreases) HIMAC experiment Num. of Cell =12 Crossing 3Nx=11

16. Summary Beam study in PoP FFAG was carried out to study a dynamics of resonance crossing. Tune crosses 3Nx=7, then… There seems no effect, when crossing speed is fast enough. Particle trapping is observed. The dependence of trapping efficiency on crossing speed and driving term can be understood qualitatively. Opposite crossing does not become trapping.