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Resonance crossing and error tolerances

Resonance crossing and error tolerances. Shinji Machida KEK FFAG05 at Fermilab, April 3-7, 2005. Purpose. To simulate non-scaling muon FFAG, electron FFAG from 10 to 20 MeV is proposed. There are mainly two issues to be studied. Acceleration without an RF bucket.

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Resonance crossing and error tolerances

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  1. Resonance crossing and error tolerances Shinji Machida KEK FFAG05 at Fermilab, April 3-7, 2005

  2. Purpose • To simulate non-scaling muon FFAG, electron FFAG from 10 to 20 MeV is proposed. • There are mainly two issues to be studied. • Acceleration without an RF bucket. • Fast crossing of integer and half-integer resonances. • 6D full tracking is performed to study resonance crossing and error tolerances in an electron FFAG. • Alignment • Gradient • Kinematic errors are included

  3. Lattice model • Trbojevic and Courant lattice at TRIUMF workshop. • C=15 m, N=45. • Each magnet is split into 10 thin lens elements. • Tune • Lattice functions • Momentum dependent path length are reasonably reproduced. Trbojevic at TRIUMF FFAG2004

  4. Error source • Alignment errors • Specified +-100%. (0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1 mm) • Distribution is uniform. • Excite integer resonances. • Gradient errors • Specified +-100%. (0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1 %) • Distribution is uniform. • Excite half-integer resonances.

  5. Resonance crossing and its speed • During acceleration • Integer resonance crossing 6 times (H), 7 times (V) • Half-integer crossing 12 times (H), 14 times (V) • Crossing speed can be varied with different RF frequency and voltage. Tune variation in a cycle Horizontal tune: 13.6 - 7.9 Vertical tune: 9.2 - 2.2

  6. Crossing speed in a cycle Longitudinal phase space dp/p vs. time Tune variation in a cycle dp/dt is almost constant. -> crossing speed becomes small at higher momentum.

  7. Animations Resonance crossing in phase space (vertical only). Tune spread due to chromaticity. eFFAG_seed2/kb_rmax005_ellipse eFFAG_seed2/kq_rmax0005_ellipse

  8. Alignment errors (seed#1) Initial emittance = 100p mm-mrad (norm.)

  9. Gradient errors (seed#1) Initial emittance = 100p mm-mrad (norm.)

  10. Alignment errors, 5 turns

  11. Alignment errors, 50 turns

  12. Alignment errors, 400 turns

  13. Alignment errors

  14. Gradient errors, 5 turns

  15. Gradient errors, 50 turns

  16. Gradient errors, 400 turns

  17. Gradient errors

  18. Summary • Resonance crossing is demonstrated in phase space. • Additional distortion due to finite chromaticity (tune spread) is inevitable. • Error tolerances depend on crossing speed (and criterion). (+-100%, uniform distribution.) (growth is less than twice.)

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