Tracking Studies of Phase Rotation Using a Scaling FFAG

1. Tracking Studies of Phase Rotation Using a Scaling FFAG Ajit Kurup FFAG07 12th – 17th April 2007

2. Introduction • A. Sato was kind enough to give me the TOSCA field map of the PRISM magnet. • Averaged the field map to use with ICOOL. • First simulations in ICOOL with the coarse grid and without cavities. • Obtain closed orbit and look at dynamic aperture. • Include cavities and look at phase rotation. • Use simple saw-tooth waveform for the rf with a gap size of 0.33m. • Scale up B-field map for neutrino factory scenario. Ajit Kurup

3. PRISM The PRISM cavities are 150-200 kV/m 5MHz. A simplified waveform is used in these simulations. Ajit Kurup

4. Dynamic Aperture • Generated a beam evenly spaced in x, px, y and py for different momenta. • x=x0(-0.5m+0.8m) in 0.1m steps, y=y0± 0.15m in 0.03m steps • px=px0±0.02GeV/c in 0.005GeV/c steps • py=py0±0.005GeV/c in 0.001GeV/c steps • P= P0±0.04GeV/c in 0.01GeV/c steps • x0, y0, px0, py0 and P0=68MeV/c are the coords of the closed orbit particle. x 60000 mm mrad For 10 turns of the ring y  5500 mm mrad Ajit Kurup

5. 1 0 2 3 4 5 6 7 Phase Rotation • Generated a Gaussian beam (with no correlations) of 1000 muons using: x=0.05, y=0.025, z=0.0001, px=0.001, py=0.001 and pz=0.034 For 7 turns of the ring Ajit Kurup

6. Neutrino Factory Scenario • Required momentum range is now 200 MeV/c ± 100 MeV/c • Scale field map by 200/68 = 2.94 • Keep everything else the same to start off with. • First use a Gaussian generated beam then use beam from a mercury target simulation. Ajit Kurup

7. Dynamic Aperture • Generated a beam evenly spaced in x, px, y and py for different momenta. • x=x0(-0.5m+0.8m) in 0.1m steps, y=y0± 0.15m in 0.03m steps • px=px0±0.05GeV/c in 0.01GeV/c steps • py=py0±0.012GeV/c in 0.002GeV/c steps • P= P0(-0.15 + 0.2)GeV/c in 0.05GeV/c steps • x0, y0, px0, py0 and P0=0.2GeV/c are the coords of the closed orbit particle. x 90000 mm mrad y  4800 mm mrad For 10 turns of the ring Ajit Kurup

8. Phase Rotation(2) • Generated a Gaussian beam (with no correlations) of 1000 muons using: x=0.05, y=0.025, z=0.0001, px=0.01 and py=0.005 and pz=0.1 • RF same as for the PRISM case but effective field is 10 times. 2 0 1 3 4 5 6 7 For 7 turns of the ring Ajit Kurup

9. Phase Rotation (3) • 10GeV protons on a mercury target MARS14 simulation. • Produced by H. Kirk and includes capture solenoid. • No muons survived 7 turns. This muon only survives 4.5 turns. Ajit Kurup

10. Other Magnets • Need to use different magnet to achieve 200 MeV/c ± 100 MeV/c and to increase dynamic aperture. • Look at other scaling FFAG magnets with k  4.6 • Have to use analytic models. • i.e. ZGOUBI. • ZGOUBI uses Enge function for the fringe field. Ajit Kurup

11. 400MeV/c 280MeV/c 200MeV/c 140MeV/c 100MeV/c 150MeV Proton FFAG Example • Start by looking at the 150MeV proton FFAG example. • Scale down the Bd and Bf fields by the ratio of the momenta. • i.e. 551/400 = 0.726 DFD radial sector k = 7.6 R0 = 540cm Bd = 8.83kG Bf = 12.26kG Closed orbits Ajit Kurup

12. Dynamic Aperture • Quick look at the dynamic aperture • Populate phase space about the closed orbits for 100,140,200,280 and 400 MeV/c x 30000 mm mrad y  12000 mm mrad For 10 turns of the ring Ajit Kurup

13. Conclusions and Plan • PRISM FFAG magnet scaled for a neutrino factory doesn’t have a large enough dynamic aperture • can only do p±20% • The 150MeV FFAG dynamic aperture is smaller in x’-x but bigger in y’-y than the PRISM aperture • can do p±100%. • Needs further investigation. • Need to implement rf harmonics in ZGOUBI so can look at ~sawtooth rf waveforms. Ajit Kurup