Update on slow extraction for PS2: alternative sextupole locations and configurations

1. Update on slow extraction for PS2:alternative sextupole locations and configurations B.Goddard, W.Bartmann, M.Gyr March 26th 2009

2. Considerations • ES to MS phase advance is 78 degrees • Need separatrix angle at ES of about 40 degrees • Opening at MS and clearance for other separatrix branches • <40° means branch 1 approaches ES • >40° means branch 2 approaches MS • Phase advance of sextupoles to ES of 110, 230, 350 degrees ~40°

3. Zero Dx sextupole locations • Ideally have resonant 6poles in dispersion-free regions, so that there is no effect on chromaticity • In PS2 lattice looking for new locations with: • |Dx/bx | < 0.1 (compared to peak value of 1.5 and RMS of 0.4) • Free drift space at least 70 cm …assume 30-40 cm magnet and something for coil ends • Look for 50, 110, 170, 230, 290 and 350 degree locations (alternately –ve and +ve polarities respectively). • Phase error within 5-10 degrees acceptable. • Large horizontal beta functions preferred (6pole strength) • Used most recent lattice including • Chromaticity sextupoles • Correctors • BPMs

4. Possible locations (mod 60°) Arc Arc RF-LSS IE-LSS DS DS

5. Smaller Dx/bx at 6-poles • 6 Locations in arcs • 70 cm free drift (MB-MB or MB-corr) • Is this enough space??? • 4 locations in DS (one each) • 80 cm free drift between…. • 11 locations in LSS • 8 in RF straight. • 3 in IE straight.

6. Locations in lattice LSS (RF) Arc location (0.7 m available) DS location (0.8 m available)

7. Combinations evaluated • V1: arc locations – Dx of ~0.4m, betx ~20m, 0.7 m space • V2: DS locations – Dx of ~0.2m, betx ~24m,0.8 m space • V3: RF LSS – Dx of 0m, betx ~20-28m, space OK • V4: mixed locations (2 in DS, 1 per LSS) – Dx of 0 – 0.2m, betx of 9 - 25m

8. Separatrices (natural chromaticity (dq/Q)/(dp/p) of -1.654) V1 V2 V3 V4 • V1: arc locations – looks OK • V2: DS locations – 6poles need to be stronger • V3: RF LSS – looks OK – can optimise positions and phases • V4: mixed – very nice straight separatrices and angles

9. Other sextupole locations for orthogonal “steering” of separatrix angle • Locate pairs of sextupoles at phases of 15° around the ideal phase locations of 50, 110, …, 350 deg • Then possible to adjust by 15 degrees the phase advance at the ES by varying the powering of the two families Note 1: need twice as many magnets and power supplies… Note 2: required strength needs to be a factor of 2 higher to get the full tuning range… Note 3: larger range possible if supplies are bipolar…

10. Separatrix angle steering • Tried with 4 magnets arranged in 2 families at (120 –15) deg and (230 +15) deg • In reality would use 8 separately powered magnets

12. Conclusions • Suitable “0 Dx” locations for resonant extraction sextupoles • 4 positions in DS, 6 in arcs, 8 in RF-LSS, 3 in IE-LSS • Several configurations of sextupoles possible • Critical issue is magnet (+coil end) length needed • If feasible in 0.7 m drift, many possibilities in arcs, DS and LSS • If in 0.8 m drift, only 4 DS locations and LSS • If >0.8 m needed, only LSS • Separatrix angle adjustment at ES is possible • Divide 4 sextupoles into 8 magnets at 6015° • Increases required strength by factor of about 2 • Other issues should be considered • Lattice tuning accomplished where? Need to go from ~13.32 to 13.333 : would like to keep phase advances to ES fixed. • Servo-quadrupole for modulating spill – strength to be defined • Situation with chromaticity sextupoles ON to be evaluated