MI Beam Loss upon Acceleration Slow loss 9

MI Beam Loss upon Acceleration Slow loss 9. 8 Ge. V/c 5 E 11/div Fast loss ~10 ms 9. 28 Ge. V/c Start of Ramp 11 BLMA=LM 634

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 MI 30 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 Ge. V.

Dynamic Dispersion Bump II (Dispersion Un-suppressor) • 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.

Some numbers Energy spread during slip stacking Df = +/- 1400 hz -> Dp = +/- 26 Me. V bucket separation Bucket height +/- 7 Mev Total energy spread Dp = +/- 33 Me. V Dp/p (max) = +/- 0. 37% s. T = 4. 47 mm for b = 60 m and e=20 p s. L = 0. 65 mm with sp/p = 0. 33 E-3 How fast does un-captured beam move radially inward? At 6 Ge. V/sec ->. 06 Me. V/turn 20 G/s ->. 2 Mev/turn -> Dp/p ~ 0. 0006% 0. 0022% -> Dx ~ 13 mm/turn ( D of 2 m) 45 mm/turn So, un-captured beam is scraped in ~10 ms once it contacts the aperture (i. e. 66 Me. V/. 06 Me. V/turn = 1100 turns)

How to create Dispersion bump • Utilize trim coils in IQC/IQD dispersion suppressor on either side of MI 30 to create a symmetric matched non-zero dispersion wave in MI 30 – MI dispersion suppressors not matched – For ~ meter dispersions in MI 30 phase advance across straight section increases by. 25 to. 4 • Use Main Quad bus to compensate • Install trim quads inside MI 30 to create phase trombone to compensate (keep it local) • Install phase trombone in MI 60 – For smaller dispersion bump • MI main quad bus is sufficient

Current Layout MI 30 ECOOL Q 314 Q 309 Q 308 Q 305 K 304 QXR Q 301 Q 302 Q 229 (Between 305 & 307)

Potential MI 30 Layout Fixed collimator (not motorized) MI trim quad TC 3 Q 314 Q 308 ECOOL Q 309 H TC 5 QXR Q 305 TC 4 K 304 Q 301 Q 302 Q 229 V H TC 2 TC 1

Trim Coils and Trim Quads • Main Injector Trim quads – Integrated strength 0. 0269 T-m/m/A – Assume max current 10 A -> Gdl ~. 27 T (K 1 L ~0. 01) • Trim Coils – – – 16 turns #14 sq. IQC: R = 2. 4 ohms L = 20 m. H IQD: R = 2. 8 ohms L = 23. 4 m. H Integrated strength 0. 0585 T-m/m/A Assume max strength 10 A -> Gdl ~. 59 T (K 1 L ~0. 02) Voltage required to ramp to max in 50 ms V ~ 24 v + IR drop from cable + induced voltage from main coil

Nominal MI 30 Lattice functions

Nominal Ring Lattice Functions

Matched -1. 2 m solution

Circuit Currents for -1. 2 m Solution

Matched -. 6 m solution

Delta Beta/Beta for 3 Solutions

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

Conclusions / Recommendations • Solutions for local Dynamic Dispersion insert in MI 30 for collimating uncaptured beam during acceleration – Small dispersion (< ½ m) done with only IQC/IQD trim coils – Larger dispersion (> ½ m) require trim quads in MI 30 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.