1. 1 FFAG Role as Muon Accelerators Shinji Machida ASTeC/STFC/RAL 15 November, 2007 http://www.astec.ac.uk/intbeams/users /machida/doc/othertalks/machida_20071115.pdf/machida/doc/othertalks/machida_20071115.pdf & ppt

2. 2 Contents Neutrino factory and FFAG (5 slides) Tracking studies (6 slides) –“Longitudinal emittance blowup in FFAG muon accelerators”, by S. Machida, Phys. Rev. ST AB 9, 104002 (2006). –“Orbit and optics distortion in FFAG muon accelerators” by S. Machida and D. J. Kelliher, accepted to Phys. Rev. ST AB. EMMA overview (3 slides) Summary

3. 3 Neutrino factory and FFAG

4. 4 Neutrino factory and FFAG (1) Schematic view Neutrino Factory requires 20 to 50 GeV muon beam. –Muon accelerators are the most costly part of the machine complex. –FFAG is considered as the most cost effective option. neutrino factory complex International Scoping Study has been completed last year. International Design Study has started.

5. 5 Neutrino factory and FFAG (2) FFAG in one word FFAG is a Fixed Field Alternating Gradient accelerator. –It separates the guiding field from the acceleration process. No synchronization. –Quick acceleration is possible. The rate only depends on voltage. Nonscaling FFAG looks like a “storage ring”. –Lattice with ordinary dipoles and quadrupoles. –Dispersion function is small enough to give large momentum acceptance. –Orbit shift from injection to extraction is small. lattice functions of 10 to 20 MeV electron model

6. 6 Neutrino factory and FFAG (3) nonscaling and scaling Constant gradient magnets give a focusing force inversely proportional to particle momentum. With acceleration, the machine ‘tune’ decreases. –> Nonscaling FFAG Field nonlinearities can make the tune constant. –> Scaling FFAG Nonlinear field profile cancel chromaticity. Scaling FFAG

7. 7 Neutrino factory and FFAG (4) why nonscaling for muons? Magnets of a nonscaling FFAG are expected to be –smaller because of smaller orbit shift, –simpler because no nonlinearities. However, the machine tune changes a lot during acceleration. –Revolution frequency depends on the transverse amplitude. –Crossing of ‘resonance’ becomes a concern. Tune excursion from 10 to 20 GeV/c muon ring.

8. 8 Neutrino factory and FFAG (5) ongoing projects Understand beam dynamics with particle tracking simulation. –A new code development. –Identify accelerator physics issues. Demonstrate a nonscaling FFAG –EMMA project at Daresbury laboratory.

9. 9 Tracking studies

10. 10 Tracking studies (1) new acceleration scheme and issues There is a path outside of a bucket. A beam is accelerated in the path. Phase (1/2 pi) dp/p (normalized) Phase space with high frequency rf Large amplitude particles take more time to finish one revolution. –Those particles do not come back to the same phase. –They may be decelerated. 36  mm 25 0 Amplitude effects

11. 11 Tracking studies (2) longitudinal emittance growth and its cure Deterioration is observed. Chromaticity correction mitigates the emittance growth in longitudinal phase space. Linear lattice Lattice with sextupole

12. 12 Tracking studies (3) amplitude depending revolution time Orbit shift becomes twice as much. –Need a bigger aperture magnet. Exchange of transverse emittance. –Can be cured by tune choice? Time of flight range increases 50%. –Need a higher voltage.

13. 13 Tracking studies (4) single particle behavior Orbit distortion is not necessarily excited when a particle crosses integer tune with large harmonic strength.

14. 14 Tracking studies (5) rms orbit distortion rms orbit distortion due to alignment errors agrees with random walk model. Distortion for different acceleration rates. –Circles are simulation results. –Lines are random walk model. ? model tracking 17 turns

15. 15 Tracking studies (6) a limitation of the model When the acceleration becomes slower, ‘resonance’ behavior starts appearing.

16. 16 EMMA overview

17. 17 EMMA overview (1) aims EMMA will be a Proof of Principle nonscaling FFAG. –Electron Model of Muon Acceleration or Electron Model of Many Applications Demonstrate that a nonscaling FFAG works as expected. –Examine quick acceleration and large acceptance. –Study acceleration outside bucket in detail. –Study “resonance” crossing in detail. PoP scaling FFAG (2000): The world’s first proton FFAG with MA rf cavity. EMMA is a nonscaling counterpart.

18. 18 EMMA overview (2) difficulties in demonstrating a nonscaling FFAG Nonscaling FFAG is for a high energy muon accelerator. –A beam is supposed to be already relativistic at injection. –Electron beam of 10 MeV (  =20) is needed. Beam dynamics rely on a high periodicity lattice. –Muon ring has 84 periods. –Electron model should have the same order of periodicity. Beams stay in the ring for only 10 to 20 turns. –Diagnostics for single path measurements. –Inject a beam with full momentum range to scan.

19. 19 EMMA overview (3) injector Energy Recovery Linac Prototype at Daresbury Laboratory provides: –Variable injection momentum from 10 to 20 MeV. –Small emittance to scan FFAG phase space. –Sufficient intensity in a bunch for single path diagnostics. 10 m ERLP EMMA

20. 20 Summary

21. 21 We have identified beam dynamics issues in a nonscaling FFAG for muon acceleration in a neutrino factory. Large transverse amplitude particles suffer phase slip. –This can be mitigated by chromaticity correction. Random walk is the correct way to understand orbit and optics distortion in a muon ring. –However, resonance behavior starts appearing when the acceleration rate is 5 times slower. EMMA will be the world first nonscaling FFAG.

22. 22 Backup slides

23. 23 Beam dynamics study

24. 24 Beam dynamics study (1) “resonance” crossing Integers and half-integers total tune are crossed. –If not much errors, they should not be any problem. Cell tune is between 0 and 0.5. Cell tune of 1/3 and 1/4 are crossed. –If nonlinearities are not significant, they should not be any problem. cell tune total tune = 84 x cell tune

25. 25 Beam dynamics study (2) “resonance” crossing Single particle trajectory does not show any “resonance” behavior. Rms orbit deviation over many different lattices shows almost square root growth. –Implies random kicks cause orbit distortion, not by resonances. H. orbit distortion

26. 26 Beam dynamics study (3) outside bucket acceleration Time of flight is a function of transverse amplitude as well as momentum. Large amplitude particles have too much phase slip to be accelerated to the maximum energy. phase (1/2 pi) dp/p (normalized) kinetic energy Time of flight momentum [GeV/c] phase (1/2 pi) (This is only for zero amplitude.) 0  emittance of 20  20  0 

27. 27 Beam dynamics study (4) outside bucket acceleration As a whole beam, longitudinal emittance blows up and momentum spread increases when the transverse amplitude is included. Chromaticity correction cures the problem (S. Berg, Nucl. Instrum. Methods, 2006 ), but it reduces aperture. zero transverse emittance 30  mm transverse emittance phase (1/2 pi) momentum [GeV/c]

28. 28 Hardware status

29. 29 Hardware status (1) ERLP (injector) ERLP has been built. It is currently being commissioned.

30. 30 Random walk model (7) a limitation of the model When the acceleration becomes slower, random walk model breaks down more quickly for optics distortion. model tracking

31. 31 Conclusions

32. 32 Amplification factor is 100~150. Growth factor is 250. –Practically important to determine magnet aperture. Orbit and optics distortion can be rather explained by random kick (walk) model, not by ‘resonance’ crossing. –One of EMMA goals: “See effects of resonance crossing” -> “See effects of machine errors” If we make the acceleration speed slower, 5 times or 85 turns for example, resonance behavior appears in addition to random kicks. That is the mixed regime of resonance and random kicks.