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

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. Iron plate Relatively, a gap outside is more widen than inside. Therefore, k value decrease as increasing radius. r Schematic view of magnet cross section Mainly, horizontal tune varies.

5. Variation of Tunes Third order (normal) Fourth order (normal) Integer or Half integer open circle: experiment colored plot: calculation 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) Straight SectionDefocusFocus Magnetic field error with RF coreCOD due to RF core RF cores disturb magnetic field of straight section. COD and octupole becomes sextupole driving term (feed down). Core Feed Down: (calculated with TOSCA) (calculated with TOSCA field & RK-tracking)

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

10. Driving Term (3) : Fourier amplitude of 3Nx=7 : horizontal beta-function : coefficient of sextupole : horizontal tune : phase advance :phase factor 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=948mm Scraper pos. r=928mm Scraper pos. r=948mm Scraper pos. r=968mm Scraper pos. r=928mm Scraper pos. r=948mm Scraper pos. r=968mm

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

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

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

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.