Orbit and optics distortion in a muon FFAG accelerator

1. Orbit and optics distortion in a muon FFAG accelerator Shinji Machida ASTeC/STFC/RAL 3 October, 2007 http://www.astec.ac.uk/intbeams/users /machida/doc/othertalks/machida_20071003.pdf & ppt

2. Contents • Neutrino Factory and a nonscaling FFAG as an introduction. • Tracking results of integer (and half-integer) tune crossing. • Random walk model and its limitations. • “Orbit and optics distortion in FFAG muon accelerators” by S. Machida and D. J. Kelliher, submitted to Phys. Rev. ST AB. http://prst-ab.aps.org/

3. Neutrino factory and FFAG

4. Neutrino factory and FFAG (1)Schematic view neutrino factory complex • Neutrino Factory: 20 to 50 GeV muon beam. • c.f. Muon Collider: a few TeV muon beam. • Accelerators are the most costly part of the machine complex. • FFAG as the most cost effective option.

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

7. Neutrino factory and FFAG (4) why nonscaling for muon? • Magnets of a nonscaling FFAG are expected to be • smaller because of smaller orbit shift, • simpler because of no nonlinearities. • However, the machine tune changes a lot during acceleration. • Crossing of ‘resonance’ becomes a big concern. • Only plausible argument is that a muon does not stay long. Tune excursion from 10 to 20 GeV/c muon ring.

8. Tracking results

9. Tracking results (1)source of ‘resonances’ • ‘resonance’ is excited by various kinds of machine errors. • Integer tune: by alignment and gradient errors. • Half-integer tune: by gradient errors. • Track a particle with reasonable amount of errors, and see how orbit and optics change when a particle crosses integer and half-integer tunes.

10. Tracking results (2)orbit distortion with alignment and gradient errors • Distribution of maximum horizontal orbit distortion out of 501 different alignment errors. • Distribution of maximum horizontal orbit distortion out of 501 different gradient errors.

11. Tracking results (3)optics distortion with gradient errors • Distribution of maximum optical distortion out of 501 different gradient errors. Initial emittance is 0.003 p. • Distribution of maximum optical distortion out of 501 different gradient errors. Initial emittance is 30 p.

12. Tracking results (4)scaling parameters • Amplification factor • Maximum orbit distortion [mm] / Rms alignment errors [mm] • 0.1 mm (rms) alignment errors make 10 to 15 mm orbit distortion. • Growth factor • Relative amplitude growth / Gradient errors • dG/G=1x10-3 (rms) gradient errors make 25% emittance growth.

13. Random walk model

14. Random walk model (1) integer resonance width • Orbit distortion is not necessarily excited when a particle cross integer tune with large harmonic strength.

15. Random walk model (2) half-integer resonance width • Optics distortion is not necessarily excited when a particle cross half-integer tune with large harmonic strength.

16. Random walk model (3)another explanation • Tracking results do not show any “resonance” behavior. • Since tune changes quickly (one unit per turn), dipole and quadrupole errors kick a beam in a random way, not excite ‘resonance’. Random walk model (conceptual) Individual trajectory rms deviation at each step

17. Random walk model (4)rms orbit distortion • rms orbit distortion due to alignment errors agrees with random walk model. • Distortion for different acceleration rate. • Circles are simulation results. • Lines are random walk model. ? tracking model 17 turns

18. Random walk model (5)a limitation of the model • When the acceleration becomes slower, ‘resonance’ behavior starts appearing.

19. Random walk model (6)rms optics distortion • rms optics distortion due to alignment errors agrees with random walk model. • Distortion for different acceleration rate. • Circles are simulation results. ? tracking model 17 turns

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

21. Conclusions

22. 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.