1. MI Beam Loss upon Acceleration 5E11/div 11BLMA=LM634 9.28 GeV/c 9.8GeV/c Start of Ramp Fast loss ~10 ms Slow loss

2. Dynamic Dispersion Bump (Dispersion Un-suppressor) Provide a well contained limiting momentum aperture to “catch” all un-captured beam at the beginning of the ramp. –Apply a dispersion time bump to MI30 zero dispersion straight section only on selected cycles (slip-stacking) to generate dispersion at 302 (and 308). –Use fixed collimator at 302 (radial inside) as the limiting momentum aperture to “catch” the un-captured beam at the start of acceleration –Utilize local dipole time bump to assure limiting aperture –Straight section optics are not effected during pbar transfers (i.e. zero dispersion/ nominal betas) –Bump is turned on after injection (for catching un captured beam) –Collapse bump to return to nominal optics after ~ 10 GeV.

3. Concept could be expanded to potentially clean up un– captured beam during the slip stacking process itself –Turn dispersion un-suppressor (and dipole time bumps) at injection if a beta wave allows (need to keep matched to MI-8) –Install collimator at 308 (radial outside) and use dipole bump to move higher momentum beam onto collimator Could be expanded even further to collimate vertically (at 301) –Vertical beta function increases from 60 to 80 meters at 301 during dynamic dispersion bump. Dynamic Dispersion Bump II (Dispersion Un-suppressor)

4. Some numbers Energy spread during slip stacking  f = +/- 1400 hz ->  p = +/- 26 MeV bucket separation  Bucket height +/- 7 Mev  Total energy spread  p = +/- 33 MeV  p/p (max) = +/- 0.37%  T = 4.47 mm for  = 60m and  =20    L = 0.65 mm with  p /p = 0.33E-3  How fast does un-captured beam move radially inward? At 6 GeV/sec ->.06 MeV/turn 20G/s ->.2Mev/turn  ->  p/p ~ 0.0006% 0.0022%  ->  x ~ 13  m/turn ( D of 2 m) 45  m/turn  So, un-captured beam is scraped in ~10 ms once it contacts the aperture (i.e. 66 MeV/.06MeV/turn = 1100 turns)

5. How to create Dispersion bump Utilize trim coils in IQC/IQD dispersion suppressor on either side of MI30 to create a symmetric matched non-zero dispersion wave in MI30 –MI dispersion suppressors not matched –For ~ meter dispersions in MI30 phase advance across straight section increases by.25 to.4 Use Main Quad bus to compensate Install trim quads inside MI30 to create phase trombone to compensate (keep it local) Install phase trombone in MI60 –For smaller dispersion bump MI main quad bus is sufficient

6. Current Layout MI30 Q301 Q305 Q309 Q229 Q314 Q302 Q308 K304 QXR ECOOL (Between 305 & 307)

7. Potential MI30 Layout Q301 Q305 Q309 Q229 Q314 Q302 Q308 K304 QXR ECOOL H VH MI trim quad Fixed collimator (not motorized) TC1 TC2 TC3 TC4 TC5

8. Trim Coils and Trim Quads Main Injector Trim quads –Integrated strength 0.0269 T-m/m/A –Assume max current 10A -> Gdl ~.27 T (K1L ~0.01) Trim Coils –16 turns #14 sq. –IQC: R = 2.4 ohms L = 20 mH –IQD: R = 2.8 ohms L = 23.4 mH –Integrated strength 0.0585 T-m/m/A –Assume max strength 10A -> Gdl ~.59 T (K1L ~0.02) –Voltage required to ramp to max in 50 ms V ~ 24 v + IR drop from cable + induced voltage from main coil

9. Nominal MI30 Lattice functions

10. Nominal Ring Lattice Functions

11. Matched -1.2m solution

12. Circuit Currents for -1.2 m Solution

13. Matched -.6 m solution

14. Delta Beta/Beta for 3 Solutions

15. Revised Delta Beta/Beta for 2 Solutions Plot Hor d  /  at Hor locations and visa versa. Dashed lines indicate dispersion suppressor and straight

16. Conclusions / Recommendations Solutions for local Dynamic Dispersion insert in MI30 for collimating un- captured beam during acceleration –Small dispersion (< ½ m) done with only IQC/IQD trim coils –Larger dispersion (> ½ m) require trim quads in MI30 straight section Concept expanded to provide transverse and momentum collimation in same straight section Preliminary investigation has included the impact on RR counterwaves, QXR, and Recycler injection/extraction kicker. This needs further investigation Need to determine collimator design (single/double stage) Need to investigate impact on losses in ECOOL section Need to model proposed layout using collimation model (Sasha) Need to model geometry of collimators (Nikolai) Trim coils look to be sufficient (need to look at rms power) Need to determine max current for MQTM trim quads for linear excitation (and rms current) Need to investigate cost/time for required power supplies Since tunnel time is at a premium, I would recommend pulling cables ASAP to IQC/IQD on either side of straight section. These may be used for testing dynamic dispersion concept and lattice function measurements.