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

2. Page 2 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 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.

3. Page 3 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup PRISM The PRISM cavities are 150-200 kV/m 5MHz. A simplified waveform is used in these simulations.

4. Page 4 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup Dynamic Aperture Generated a beam evenly spaced in x, px, y and py for different momenta. –x=x 0 (-0.5m+0.8m) in 0.1m steps, y=y 0 ± 0.15m in 0.03m steps –px=px 0 ±0.02GeV/c in 0.005GeV/c steps –py=py 0 ±0.005GeV/c in 0.001GeV/c steps –P= P 0 ±0.04GeV/c in 0.01GeV/c steps –x 0, y 0, px 0, py 0 and P 0 =68MeV/c are the coords of the closed orbit particle. For 10 turns of the ring  x  60000  mm mrad  y  5500  mm mrad

5. Page 5 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 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 0 2 3 4 5 6 7 1

6. Page 6 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 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.

7. Page 7 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup Dynamic Aperture Generated a beam evenly spaced in x, px, y and py for different momenta. –x=x 0 (-0.5m+0.8m) in 0.1m steps, y=y 0 ± 0.15m in 0.03m steps –px=px 0 ±0.05GeV/c in 0.01GeV/c steps –py=py 0 ±0.012GeV/c in 0.002GeV/c steps –P= P 0 (-0.15 + 0.2)GeV/c in 0.05GeV/c steps –x 0, y 0, px 0, py 0 and P 0 =0.2GeV/c are the coords of the closed orbit particle. For 10 turns of the ring  x  90000  mm mrad  y  4800  mm mrad

8. Page 8 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 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. For 7 turns of the ring 02 3 4 5 6 7 1

9. Page 9 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup Phase Rotation (3) 10GeV protons on a mercury target MARS14 simulation. –Produced by H. Kirk and includes capture solenoid. –No muons survived 7 turns. Selection Criteria No. of positive muons in input file none978 0.16<p<0.24 GeV/c 177 |px|<0.02 GeV/c 154 |py|<0.01 GeV/c 86 all1 This muon only survives 4.5 turns.

10. Page 10 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 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.

11. Page 11 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 150MeV Proton FFAG Example Start by looking at the 150MeV proton FFAG example. Scale down the B d and B f fields by the ratio of the momenta. –i.e. 551/400 = 0.726 400MeV/c 280MeV/c 200MeV/c 140MeV/c 100MeV/c Closed orbits DFD radial sector k = 7.6 R 0 = 540cm B d = 8.83kG B f = 12.26kG

12. Page 12 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup Dynamic Aperture For 10 turns of the ring  x  30000  mm mrad  y  12000  mm mrad Quick look at the dynamic aperture –Populate phase space about the closed orbits for 100,140,200,280 and 400 MeV/c

13. Page 13 Tracking Studies of Phase Rotation Using a Scaling FFAG FFAG07 12th – 17th April 2007 Ajit Kurup 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.